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## Summary of Content for Texas Instruments TI-83 Plus Calculator Guidebook PDF

Page 1

07/23/03 2001-2003 Texas Instruments

TI

TI-83 Plus /

TI-83 Plus Silver Edition

Graphing Calculator **Guidebook **

On/Off Graphing a function Menus Modes Using parentheses Lists

Tables Data and lists Matrices Split screen

Inferential statistics Archiving/Unarchiving Programming Menu maps

Sending and receiving Troubleshooting Formulas Support and service

**More Information **

**First Steps **

**Creating **

**Beyond the Basics **

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TI-83 Plus

Important

Texas Instruments makes no warranty, either express or implied, including but not limited to any implied warranties of merchantability and fitness for a particular purpose, regarding any programs or book materials and makes such materials available solely on an as-is basis.

In no event shall Texas Instruments be liable to anyone for special, collateral, incidental, or consequential damages in connection with or arising out of the purchase or use of these materials, and the sole and exclusive liability of Texas Instruments, regardless of the form of action, shall not exceed the purchase price of this equipment. Moreover, Texas Instruments shall not be liable for any claim of any kind whatsoever against the use of these materials by any other party.

Windows is a registered trademark of Microsoft Corporation. Macintosh is a registered trademark of Apple Computer, Inc.

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TI-83 Plus

US FCC Information Concerning Radio Frequency Interference

This equipment has been tested and found to comply with the limits for a Class B digital device, pursuant to Part 15 of the FCC rules. These limits are designed to provide reasonable protection against harmful interference in a residential installation. This equipment generates, uses, and can radiate radio frequency energy and, if not installed and used in accordance with the instructions, may cause harmful interference with radio communications. However, there is no guarantee that interference will not occur in a particular installation.

If this equipment does cause harmful interference to radio or television reception, which can be determined by turning the equipment off and on, you can try to correct the interference by one or more of the following measures: Reorient or relocate the receiving antenna. Increase the separation between the equipment and receiver. Connect the equipment into an outlet on a circuit different from that to

which the receiver is connected. Consult the dealer or an experienced radio/television technician for

help.

**Caution:** Any changes or modifications to this equipment not expressly approved by Texas Instruments may void your authority to operate the equipment.

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TI-83 Plus Operating the TI-83 Plus Silver Edition 1

Chapter 1: Operating the TI-83 Plus Silver Edition

Documentation Conventions

In the body of this guidebook, TI-83 Plus (in silver) refers to the TI-83 Plus Silver Edition. Sometimes, as in Chapter 19, the full name TI-83 Plus Silver Edition is used to distinguish it from the TI-83 Plus.

All the instructions and examples in this guidebook also work for the TI-83 Plus. All the functions of the TI-83 Plus Silver Edition and the TI-83 Plus are the same. The two calculators differ only in available RAM memory and Flash application ROM memory.

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TI-83 Plus Operating the TI-83 Plus Silver Edition 2

TI-83 Plus Keyboard

Generally, the keyboard is divided into these zones: graphing keys, editing keys, advanced function keys, and scientific calculator keys.

**Keyboard Zones**

**Graphing** Graphing keys access the interactive graphing features.

**Editing** Editing keys allow you to edit expressions and values.

**Advanced** Advanced function keys display menus that access the advanced functions.

**Scientific** Scientific calculator keys access the capabilities of a standard scientific calculator.

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TI-83 Plus Operating the TI-83 Plus Silver Edition 3

**TI-83 Plus**

Editing Keys

Advanced Function Keys

Scientific Calculator Keys

Graphing Keys

Colors may vary in actual product.

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TI-83 Plus Operating the TI-83 Plus Silver Edition 4

**Using the Color.Coded Keyboard**

The keys on the TI-83 Plus are color-coded to help you easily locate the key you need.

The light gray keys are the number keys. The blue keys along the right side of the keyboard are the common math functions. The blue keys across the top set up and display graphs. The blue key provides access to applications such as the Finance application.

The primary function of each key is printed on the keys. For example, when you press , the **MATH** menu is displayed.

**Using the **y** and **** Keys**

The secondary function of each key is printed in yellow above the key. When you press the yellow y key, the character, abbreviation, or word printed in yellow above the other keys becomes active for the next keystroke. For example, when you press y and then , the **TEST**

menu is displayed. This guidebook describes this keystroke combination as y :.

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TI-83 Plus Operating the TI-83 Plus Silver Edition 5

The alpha function of each key is printed in green above the key. When you press the green key, the alpha character printed in green above the other keys becomes active for the next keystroke. For example, when you press and then , the letter **A** is entered. This guidebook describes this keystroke combination as [A].

The y key accesses the second function printed in yellow above each key.

The key accesses the alpha function printed in green above each key.

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TI-83 Plus Operating the TI-83 Plus Silver Edition 6

Turning On and Turning Off the TI-83 Plus

**Turning On the Calculator**

To turn on the TI-83 Plus, press .

If you previously had turned off the calculator by pressing y M, the TI-83 Plus displays the home screen as it was when you last used it and clears any error.

If Automatic Power Down (APD) had previously turned off the calculator, the TI-83 Plus will return exactly as you left it, including the display, cursor, and any error.

If the TI-83 Plus is turned off and you connect it to another calculator or personal computer, the TI-83 Plus will wake up when you complete the connection.

If the TI-83 Plus is turned off and connected to another calculator or personal computer, any communication activity will wake up the TI-83 Plus.

To prolong the life of the batteries, APD turns off the TI-83 Plus automatically after about five minutes without any activity.

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TI-83 Plus Operating the TI-83 Plus Silver Edition 7

**Turning Off the Calculator**

To turn off the TI-83 Plus manually, press y M.

All settings and memory contents are retained by Constant MemoryTM.

Any error condition is cleared.

**Batteries**

The TI-83 Plus uses four AAA alkaline batteries and has a user- replaceable backup lithium battery (CR1616 or CR1620). To replace batteries without losing any information stored in memory, follow the steps in Appendix B.

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TI-83 Plus Operating the TI-83 Plus Silver Edition 8

Setting the Display Contrast

**Adjusting the Display Contrast**

You can adjust the display contrast to suit your viewing angle and lighting conditions. As you change the contrast setting, a number from **0** (lightest) to **9** (darkest) in the top-right corner indicates the current level. You may not be able to see the number if contrast is too light or too dark.

**Note:** The TI-83 Plus has 40 contrast settings, so each number **0** through **9** represents four settings.

The TI-83 Plus retains the contrast setting in memory when it is turned off.

To adjust the contrast, follow these steps.

1. Press and release the y key.

2. Press and hold or }, which are below and above the contrast symbol (yellow, half-shaded circle).

lightens the screen.

} darkens the screen.

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TI-83 Plus Operating the TI-83 Plus Silver Edition 9

**Note:** If you adjust the contrast setting to **0**, the display may become completely blank. To restore the screen, press and release y, and then press and hold } until the display reappears.

**When to Replace Batteries**

When the batteries are low, a low-battery message is displayed when you:

Turn on the calculator.

Download a new application.

Attempt to upgrade to new software.

To replace the batteries without losing any information in memory, follow the steps in Appendix B.

Generally, the calculator will continue to operate for one or two weeks after the low-battery message is first displayed. After this period, the TI-83 Plus will turn off automatically and the unit will not operate. Batteries must be replaced. All memory should be retained.

**Note:** The operating period following the first low-battery message could be longer than two weeks if you use the calculator infrequently.

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TI-83 Plus Operating the TI-83 Plus Silver Edition 10

The Display

**Types of Displays**

The TI-83 Plus displays both text and graphs. Chapter 3 describes graphs. Chapter 9 describes how the TI-83 Plus can display a horizontally or vertically split screen to show graphs and text simultaneously.

**Home Screen**

The home screen is the primary screen of the TI-83 Plus. On this screen, enter instructions to execute and expressions to evaluate. The answers are displayed on the same screen.

**Displaying Entries and Answers**

When text is displayed, the TI-83 Plus screen can display a maximum of 8 lines with a maximum of 16 characters per line. If all lines of the display are full, text scrolls off the top of the display. If an expression on the home screen, the **Y=** editor (Chapter 3), or the program editor (Chapter 16) is longer than one line, it wraps to the beginning of the next line. In numeric editors such as the window screen (Chapter 3), a long expression scrolls to the right and left.

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TI-83 Plus Operating the TI-83 Plus Silver Edition 11

When an entry is executed on the home screen, the answer is displayed on the right side of the next line.

Entry Answer

The mode settings control the way the TI-83 Plus interprets expressions and displays answers.

If an answer, such as a list or matrix, is too long to display entirely on one line, an ellipsis (**...**) is displayed to the right or left. Press ~ and | to display the answer.

Entry Answer

**Returning to the Home Screen**

To return to the home screen from any other screen, press y 5.

**Busy Indicator**

When the TI-83 Plus is calculating or graphing, a vertical moving line is displayed as a busy indicator in the top-right corner of the screen. When you pause a graph or a program, the busy indicator becomes a vertical moving dotted line.

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TI-83 Plus Operating the TI-83 Plus Silver Edition 12

**Display Cursors**

In most cases, the appearance of the cursor indicates what will happen when you press the next key or select the next menu item to be pasted as a character.

**Cursor** **Appearance** **Effect of Next Keystroke**

Entry Solid rectangle $

A character is entered at the cursor; any existing character is overwritten

Insert Underline **__**

A character is inserted in front of the cursor location

Second Reverse arrow

A 2nd character (yellow on the keyboard) is entered or a 2nd operation is executed

Alpha Reverse A

An alpha character (green on the keyboard) is entered or **SOLVE** is executed

Full Checkerboard rectangle #

No entry; the maximum characters are entered at a prompt or memory is full

If you press during an insertion, the cursor becomes an underlined **A** (**A**). If you press y during an insertion, the underlined cursor becomes an underlined **#** (**#**).

Graphs and editors sometimes display additional cursors, which are described in other chapters.

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TI-83 Plus Operating the TI-83 Plus Silver Edition 13

Entering Expressions and Instructions

**What Is an Expression?**

An expression is a group of numbers, variables, functions and their arguments, or a combination of these elements. An expression evaluates to a single answer. On the TI-83 Plus, you enter an expression in the same order as you would write it on paper. For example, pR2 is an expression.

You can use an expression on the home screen to calculate an answer. In most places where a value is required, you can use an expression to enter a value.

**Entering an Expression**

To create an expression, you enter numbers, variables, and functions from the keyboard and menus. An expression is completed when you press , regardless of the cursor location. The entire expression is evaluated according to Equation Operating System (EOS) rules, and the answer is displayed.

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TI-83 Plus Operating the TI-83 Plus Silver Edition 14

Most TI-83 Plus functions and operations are symbols comprising several characters. You must enter the symbol from the keyboard or a menu; do not spell it out. For example, to calculate the log of 45, you must press **45**. Do not enter the letters **L**, **O**, and **G**. If you enter **LOG**, the TI-83 Plus interprets the entry as implied multiplication of the variables **L**, **O**, and **G**.

Calculate 3.76 (L7.9 + 5) + 2 log 45.

**3** **76** **7** **9** y C **5** **2** **45**

**Multiple Entries on a Line**

To enter two or more expressions or instructions on a line, separate them with colons ( [:]). All instructions are stored together in last entry (**ENTRY**) .

**Entering a Number in Scientific Notation**

To enter a number in scientific notation, follow these steps.

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TI-83 Plus Operating the TI-83 Plus Silver Edition 15

1. Enter the part of the number that precedes the exponent. This value can be an expression.

2. Press y D. is pasted to the cursor location.

3. If the exponent is negative, press , and then enter the exponent, which can be one or two digits.

When you enter a number in scientific notation, the TI-83 Plus does not automatically display answers in scientific or engineering notation. The mode settings and the size of the number determine the display format.

**Functions**

A function returns a value. For example, , **L**, **+**, **(**, and **log(** are the functions in the example on the previous page. In general, the first letter of each function is lowercase on the TI-83 Plus. Most functions take at least one argument, as indicated by an open parenthesis ( **(** ) following the name. For example, **sin(** requires one argument, **sin(***value***)**.

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TI-83 Plus Operating the TI-83 Plus Silver Edition 16

**Instructions**

An instruction initiates an action. For example, **ClrDraw** is an instruction that clears any drawn elements from a graph. Instructions cannot be used in expressions. In general, the first letter of each instruction name is uppercase. Some instructions take more than one argument, as indicated by an open parenthesis ( **(** ) at the end of the name. For example, **Circle(** requires three arguments, **Circle(***X***,***Y***,***radius***)**.

**Interrupting a Calculation**

To interrupt a calculation or graph in progress, which is indicated by the busy indicator, press .

When you interrupt a calculation, a menu is displayed.

To return to the home screen, select **1:Quit**.

To go to the location of the interruption, select **2:Goto**.

When you interrupt a graph, a partial graph is displayed.

To return to the home screen, press or any nongraphing key.

To restart graphing, press a graphing key or select a graphing instruction.

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TI-83 Plus Operating the TI-83 Plus Silver Edition 17

TI-83 Plus Edit Keys

**Keystrokes** **Result**

~ or | Moves the cursor within an expression; these keys repeat.

} or Moves the cursor from line to line within an expression that occupies more than one line; these keys repeat.

On the top line of an expression on the home screen, } moves the cursor to the beginning of the expression.

On the bottom line of an expression on the home screen, moves the cursor to the end of the expression.

y | Moves the cursor to the beginning of an expression.

y ~ Moves the cursor to the end of an expression.

Evaluates an expression or executes an instruction.

On a line with text on the home screen, clears the current line.

On a blank line on the home screen, clears everything on the home screen.

In an editor, clears the expression or value where the cursor is located; it does not store a zero.

{ Deletes a character at the cursor; this key repeats.

y 6 Changes the cursor to an underline (**__**); inserts characters in front of the underline cursor; to end insertion, press y 6 or press |, }, ~, or .

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TI-83 Plus Operating the TI-83 Plus Silver Edition 18

**Keystrokes** **Result**

y Changes the cursor to ; the next keystroke performs a **2nd** operation (an operation in yellow above a key and to the left); to cancel **2nd**, press y again.

Changes the cursor to ; the next keystroke pastes an alpha character (a character in green above a key and to the right) or executes **SOLVE** (Chapters 10 and 11); to cancel , press or press |, }, ~, or .

y 7 Changes the cursor to ; sets alpha-lock; subsequent keystrokes (on an alpha key) paste alpha characters; to cancel alpha-lock, press . If you are prompted to enter a name such as for a group or a program, alpha-lock is set automatically.

Pastes an **X** in **Func** mode, a **T** in **Par** mode, a **q** in **Pol** mode, or an **n** in **Seq** mode with one keystroke.

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TI-83 Plus Operating the TI-83 Plus Silver Edition 19

Setting Modes

**Checking Mode Settings**

Mode settings control how the TI-83 Plus displays and interprets numbers and graphs. Mode settings are retained by the Constant Memory feature when the TI-83 Plus is turned off. All numbers, including elements of matrices and lists, are displayed according to the current mode settings.

To display the mode settings, press z. The current settings are highlighted. Defaults are highlighted below. The following pages describe the mode settings in detail.

**Normal Sci Eng** Numeric notation **Float 0123456789** Number of decimal places **Radian Degree** Unit of angle measure **Func Par Pol Seq** Type of graphing **Connected** ** Dot** Whether to connect graph points **Sequential** ** Simul** Whether to plot simultaneously **Real a+b i re^qi** Real, rectangular complex, or polar complex

**Full Horiz G-T**Full screen, two split-screen modes

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TI-83 Plus Operating the TI-83 Plus Silver Edition 20

**Changing Mode Settings**

To change mode settings, follow these steps.

1. Press or } to move the cursor to the line of the setting that you want to change.

2. Press ~ or | to move the cursor to the setting you want.

3. Press .

**Setting a Mode from a Program**

You can set a mode from a program by entering the name of the mode as an instruction; for example, **Func** or **Float**. From a blank program command line, select the mode setting from the mode screen; the instruction is pasted to the cursor location.

**Normal, Sci, Eng**

Notation modes only affect the way an answer is displayed on the home screen. Numeric answers can be displayed with up to 10 digits and a two-digit exponent. You can enter a number in any format.

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TI-83 Plus Operating the TI-83 Plus Silver Edition 21

**Normal** notation mode is the usual way we express numbers, with digits to the left and right of the decimal, as in **12345.67**.

**Sci** (scientific) notation mode expresses numbers in two parts. The significant digits display with one digit to the left of the decimal. The appropriate power of 10 displays to the right of **E**, as in **1.234567E4**.

**Eng** (engineering) notation mode is similar to scientific notation. However, the number can have one, two, or three digits before the decimal; and the power-of-10 exponent is a multiple of three, as in **12.34567E3**.

**Note**: If you select **Normal** notation, but the answer cannot display in 10 digits (or the absolute value is less than .001), the TI-83 Plus expresses the answer in scientific notation.

**Float, 0123456789**

**Float** (floating) decimal mode displays up to 10 digits, plus the sign and decimal.

**0123456789** (fixed) decimal mode specifies the number of digits (**0** through **9**) to display to the right of the decimal. Place the cursor on the desired number of decimal digits, and then press .

The decimal setting applies to **Normal**, **Sci**, and **Eng** notation modes.

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TI-83 Plus Operating the TI-83 Plus Silver Edition 22

The decimal setting applies to these numbers:

An answer displayed on the home screen

Coordinates on a graph (Chapters 3, 4, 5, and 6)

The **Tangent(** **DRAW** instruction equation of the line, **x**, and **dy/dx** values (Chapter 8)

Results of **CALCULATE** operations (Chapters 3, 4, 5, and 6)

The regression equation stored after the execution of a regression model (Chapter 12)

**Radian, Degree**

Angle modes control how the TI-83 Plus interprets angle values in trigonometric functions and polar/rectangular conversions.

**Radian** mode interprets angle values as radians. Answers display in radians.

**Degree** mode interprets angle values as degrees. Answers display in degrees.

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TI-83 Plus Operating the TI-83 Plus Silver Edition 23

**Func, Par, Pol, Seq**

Graphing modes define the graphing parameters. Chapters 3, 4, 5, and 6 describe these modes in detail.

**Func** (function) graphing mode plots functions, where **Y** is a function of **X** (Chapter 3).

**Par** (parametric) graphing mode plots relations, where **X** and **Y** are functions of **T** (Chapter 4).

**Pol** (polar) graphing mode plots functions, where **r** is a function of **q** (Chapter 5).

**Seq** (sequence) graphing mode plots sequences (Chapter 6).

**Connected, Dot**

**Connected** plotting mode draws a line connecting each point calculated for the selected functions.

**Dot** plotting mode plots only the calculated points of the selected functions.

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TI-83 Plus Operating the TI-83 Plus Silver Edition 24

**Sequential, Simul**

**Sequential** graphing-order mode evaluates and plots one function completely before the next function is evaluated and plotted.

**Simul** (simultaneous) graphing-order mode evaluates and plots all selected functions for a single value of **X** and then evaluates and plots them for the next value of **X**.

**Note:** Regardless of which graphing mode is selected, the TI-83 Plus will sequentially graph all stat plots before it graphs any functions.

**Real, a+b i, re^qi**

**Real** mode does not display complex results unless complex numbers are entered as input.

Two complex modes display complex results.

**a+b i** (rectangular complex mode) displays complex numbers in the form a+b

*i*.

**re^**q** i** (polar complex mode) displays complex numbers in the form re^q

**.**

*i*Page 28

TI-83 Plus Operating the TI-83 Plus Silver Edition 25

**Full, Horiz, G.T**

**Full** screen mode uses the entire screen to display a graph or edit screen.

Each split-screen mode displays two screens simultaneously.

**Horiz** (horizontal) mode displays the current graph on the top half of the screen; it displays the home screen or an editor on the bottom half (Chapter 9).

**G.T** (graph-table) mode displays the current graph on the left half of the screen; it displays the table screen on the right half (Chapter 9).

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TI-83 Plus Operating the TI-83 Plus Silver Edition 26

Using TI-83 Plus Variable Names

**Variables and Defined Items**

On the TI-83 Plus you can enter and use several types of data, including real and complex numbers, matrices, lists, functions, stat plots, graph databases, graph pictures, and strings.

The TI-83 Plus uses assigned names for variables and other items saved in memory. For lists, you also can create your own five-character names.

**Variable Type** **Names**

Real numbers **A**, **B**, ... , **Z**

Complex numbers **A**, **B**, ... , **Z**

Matrices **A, B, C**, ... , **J**

Lists **L1**, **L2**, **L3**, **L4**, **L5**, **L6**, and user-defined names

Functions **Y1**, **Y2**, . . . , **Y9**, **Y0**

Parametric equations **X1T** and **Y1T**, . . . , **X6T** and **Y6T**

Polar functions **r1**, **r2**, **r3**, **r4**, **r5**, **r6**

Sequence functions **u**, **v**, **w**

Stat plots **Plot1, Plot2, Plot3**

Graph databases **GDB1**, **GDB2**, . . . , **GDB9**, **GDB0**

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TI-83 Plus Operating the TI-83 Plus Silver Edition 27

**Variable Type** **Names**

Graph pictures **Pic1**, **Pic2**, ... , **Pic9**, **Pic0**

Strings **Str1**, **Str2**, ... , **Str9**, **Str0**

Apps Applications

AppVars Application variables

Groups Grouped variables

System variables **Xmin**, **Xmax**, and others

**Notes about Variables**

You can create as many list names as memory will allow (Chapter 11).

Programs have user-defined names and share memory with variables (Chapter 16).

From the home screen or from a program, you can store to matrices (Chapter 10), lists (Chapter 11), strings (Chapter 15), system variables such as** Xmax** (Chapter 1), **TblStart** (Chapter 7), and all **Y=** functions (Chapters 3, 4, 5, and 6).

From an editor, you can store to matrices, lists, and **Y= **functions (Chapter 3).

From the home screen, a program, or an editor, you can store a value to a matrix element or a list element.

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TI-83 Plus Operating the TI-83 Plus Silver Edition 28

You can use **DRAW STO** menu items to store and recall graph databases and pictures (Chapter 8).

Although most variables can be archived, system variables including r, t, x, y, and **q** cannot be archived (Chapter 18)

**Apps** are independent applications.which are stored in Flash ROM. **AppVars** is a variable holder used to store variables created by independent applications. You cannot edit or change variables in **AppVars** unless you do so through the application which created them.

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TI-83 Plus Operating the TI-83 Plus Silver Edition 29

Storing Variable Values

**Storing Values in a Variable**

Values are stored to and recalled from memory using variable names. When an expression containing the name of a variable is evaluated, the value of the variable at that time is used.

To store a value to a variable from the home screen or a program using the key, begin on a blank line and follow these steps.

1. Enter the value you want to store. The value can be an expression.

2. Press . ! is copied to the cursor location.

3. Press and then the letter of the variable to which you want to store the value.

4. Press . If you entered an expression, it is evaluated. The value is stored to the variable.

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TI-83 Plus Operating the TI-83 Plus Silver Edition 30

**Displaying a Variable Value**

To display the value of a variable, enter the name on a blank line on the home screen, and then press .

**Archiving Variables (Archive, Unarchive)**

You can archive data, programs, or other variables in a section of memory called user data archive where they cannot be edited or deleted inadvertently. Archived variables are indicated by asterisks (*) to the left of the variable names. Archived variables cannot be edited or executed. They can only be seen and unarchived. For example, if you archive list L1, you will see that L1 exists in memory but if you select it and paste the name L1 to the home screen, you wont be able to see its contents or edit it until they are unarchived.

.

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TI-83 Plus Operating the TI-83 Plus Silver Edition 31

Recalling Variable Values

**Using Recall (RCL)**

To recall and copy variable contents to the current cursor location, follow these steps. To leave **RCL**, press .

1. Press y RCL. **RCL** and the edit cursor are displayed on the bottom line of the screen.

2. Enter the name of the variable in any of five ways.

Press and then the letter of the variable.

Press y LIST, and then select the name of the list, or press y [L*n*].

Press y >, and then select the name of the matrix.

Press to display the **VARS** menu or ~ to display the **VARS Y.VARS** menu; then select the type and then the name of the variable or function.

Press |, and then select the name of the program (in the program editor only).

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TI-83 Plus Operating the TI-83 Plus Silver Edition 32

The variable name you selected is displayed on the bottom line and the cursor disappears.

3. Press . The variable contents are inserted where the cursor was located before you began these steps.

**Note:** You can edit the characters pasted to the expression without affecting the value in memory.

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TI-83 Plus Operating the TI-83 Plus Silver Edition 33

ENTRY (Last Entry) Storage Area

**Using ENTRY (Last Entry)**

When you press on the home screen to evaluate an expression or execute an instruction, the expression or instruction is placed in a storage area called **ENTRY** (last entry). When you turn off the TI-83 Plus, **ENTRY** is retained in memory.

To recall **ENTRY**, press y [. The last entry is pasted to the current cursor location, where you can edit and execute it. On the home screen or in an editor, the current line is cleared and the last entry is pasted to the line.

Because the TI-83 Plus updates **ENTRY** only when you press , you can recall the previous entry even if you have begun to enter the next expression.

**5** **7** y [

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TI-83 Plus Operating the TI-83 Plus Silver Edition 34

**Accessing a Previous Entry**

The TI-83 Plus retains as many previous entries as possible in **ENTRY**, up to a capacity of 128 bytes. To scroll those entries, press y [ repeatedly. If a single entry is more than 128 bytes, it is retained for **ENTRY**, but it cannot be placed in the **ENTRY** storage area.

**1** **A** **2 ** **B** y [

If you press y [ after displaying the oldest stored entry, the newest stored entry is displayed again, then the next-newest entry, and so on.

y [

**Reexecuting the Previous Entry**

After you have pasted the last entry to the home screen and edited it (if you chose to edit it), you can execute the entry. To execute the last entry, press .

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TI-83 Plus Operating the TI-83 Plus Silver Edition 35

To reexecute the displayed entry, press again. Each reexecution displays an answer on the right side of the next line; the entry itself is not redisplayed.

**0** **N** **N** **1** **N ** : **N**

**Multiple Entry Values on a Line**

To store to **ENTRY** two or more expressions or instructions, separate each expression or instruction with a colon, then press . All expressions and instructions separated by colons are stored in **ENTRY**.

When you press y [, all the expressions and instructions separated by colons are pasted to the current cursor location. You can edit any of the entries, and then execute all of them when you press .

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TI-83 Plus Operating the TI-83 Plus Silver Edition 36

For the equation A=pr2, use trial and error to find the radius of a circle that covers 200 square centimeters. Use 8 as your first guess.

**8** **R** [:] y B **R** y [

y | **7** y 6 **95**

Continue until the answer is as accurate as you want.

**Clearing ENTRY**

**Clear Entries** (Chapter 18) clears all data that the TI-83 Plus is holding in the **ENTRY** storage area.

**Using Ans in an Expression**

When an expression is evaluated successfully from the home screen or from a program, the TI-83 Plus stores the answer to a storage area called **Ans** (last answer). **Ans** may be a real or complex number, a list, a matrix, or a string. When you turn off the TI-83 Plus, the value in **Ans** is retained in memory.

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TI-83 Plus Operating the TI-83 Plus Silver Edition 37

You can use the variable **Ans** to represent the last answer in most places. Press y Z to copy the variable name **Ans** to the cursor location. When the expression is evaluated, the TI-83 Plus uses the value of **Ans** in the calculation.

Calculate the area of a garden plot 1.7 meters by 4.2 meters. Then calculate the yield per square meter if the plot produces a total of 147 tomatoes.

**1** **7** **4** **2** **147** y Z

**Continuing an Expression**

You can use **Ans** as the first entry in the next expression without entering the value again or pressing y Z. On a blank line on the home screen, enter the function. The TI-83 Plus pastes the variable name **Ans** to the screen, then the function.

**5** **2** **9** **9**

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**Storing Answers**

To store an answer, store **Ans** to a variable before you evaluate another expression.

Calculate the area of a circle of radius 5 meters. Next, calculate the volume of a cylinder of radius 5 meters and height 3.3 meters, and then store the result in the variable V.

y B **5** **3** **3** **V**

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TI-83 Plus Menus

**Using a TI-83 Plus Menu**

You can access most TI-83 Plus operations using menus. When you press a key or key combination to display a menu, one or more menu names appear on the top line of the screen.

The menu name on the left side of the top line is highlighted. Up to seven items in that menu are displayed, beginning with item **1**, which also is highlighted.

A number or letter identifies each menu items place in the menu. The order is **1** through **9**, then **0**, then **A**, **B**, **C**, and so on. The **LIST NAMES**, **PRGM EXEC**, and **PRGM EDIT** menus only label items **1 **through **9** and **0**.

When the menu continues beyond the displayed items, a down arrow ($) replaces the colon next to the last displayed item.

When a menu item ends in an ellipsis (...), the item displays a secondary menu or editor when you select it.

When an asterisk (*) appears to the left of a menu item, that item is stored in user data archive (Chapter 18).

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To display any other menu listed on the top line, press ~ or | until that menu name is highlighted. The cursor location within the initial menu is irrelevant. The menu is displayed with the cursor on the first item.

**Note:** The Menu Map in Appendix A shows each menu, each operation under each menu, and the key or key combination you press to display each menu.

**Displaying a Menu**

While using your TI-83 Plus, you often will need to access items from its menus.

When you press a key that displays a menu, that menu temporarily replaces the screen where you are working. For example, when you press , the **MATH** menu is displayed as a full screen.

After you select an item from a menu, the screen where you are working usually is displayed again.

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**Moving from One Menu to Another**

Some keys access more than one menu. When you press such a key, the names of all accessible menus are displayed on the top line. When you highlight a menu name, the items in that menu are displayed. Press ~ and | to highlight each menu name.

**Scrolling a Menu**

To scroll down the menu items, press . To scroll up the menu items, press }.

To page down six menu items at a time, press . To page up six menu items at a time, press }. The green arrows on the calculator, between and }, are the page-down and page-up symbols.

To wrap to the last menu item directly from the first menu item, press }. To wrap to the first menu item directly from the last menu item, press .

**Selecting an Item from a Menu**

You can select an item from a menu in either of two ways.

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Press the number or letter of the item you want to select. The cursor can be anywhere on the menu, and the item you select need not be displayed on the screen.

Press or } to move the cursor to the item you want, and then press .

After you select an item from a menu, the TI-83 Plus typically displays the previous screen.

**Note:** On the **LIST NAMES**, **PRGM EXEC**, and **PRGM EDIT** menus, only items **1** through **9** and **0** are labeled in such a way that you can select them by pressing the appropriate number key. To move the cursor to the first item beginning with any alpha character or q, press the key combination for that alpha character or q. If no items begin with that character, the cursor moves beyond it to the next item.

Calculate 327.

**27**

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**Leaving a Menu without Making a Selection**

You can leave a menu without making a selection in any of four ways.

Press y 5 to return to the home screen.

Press to return to the previous screen.

Press a key or key combination for a different menu, such as or y 9.

Press a key or key combination for a different screen, such as o or y 0.

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VARS and VARS Y**.**VARS Menus

**VARS Menu**

You can enter the names of functions and system variables in an expression or store to them directly.

To display the **VARS** menu, press . All **VARS** menu items display secondary menus, which show the names of the system variables. **1:Window**, **2:Zoom**, and **5:Statistics** each access more than one secondary menu.

**VARS** ** Y-VARS** **1:** **Window...** **X/Y**, **T/q**, and **U/V/W** variables **2:** **Zoom...** **ZX/ZY**, **ZT/Zq**, and **ZU** variables **3:** **GDB...** **Graph database **variables **4:** **Picture...** **Picture** variables **5:** **Statistics...** **XY**, **G**, **EQ**, **TEST**, and **PTS** variables **6:** **Table...** **TABLE **variables **7:** **String...** **String **variables

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**Selecting a Variable from the VARS Menu or VARS Y.VARS Menu**

To display the **VARS Y.VARS** menu, press ~. **1:Function**, **2:Parametric**, and **3:Polar** display secondary menus of the **Y=** function variables.

**VARS** **Y-VARS**

**1:** **Function...** **Y***n* functions **2:** **Parametric...** **X***n***T**, **Y***n***T** functions **3:** **Polar...** **r***n* functions **4:** **On/Off...** Lets you select/deselect functions

**Note:** The sequence variables (**u**, **v**, **w**) are located on the keyboard as the second functions of , , and .

To select a variable from the **VARS** or **VARS Y.VARS** menu, follow these steps.

1. Display the **VARS** or **VARS Y.VARS** menu.

Press to display the **VARS** menu.

Press ~ to display the **VARS Y.VARS** menu.

2. Select the type of variable, such as **2:Zoom** from the **VARS** menu or **3:Polar** from the **VARS Y.VARS** menu. A secondary menu is displayed.

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3. If you selected **1:Window**, **2:Zoom**, or **5:Statistics **from the** VARS** menu, you can press ~ or | to display other secondary menus.

4. Select a variable name from the menu. It is pasted to the cursor location.

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Equation Operating System (EOS)

**Order of Evaluation**

The Equation Operating System (EOS) defines the order in which functions in expressions are entered and evaluated on the TI-83 Plus. EOS lets you enter numbers and functions in a simple, straightforward sequence.

EOS evaluates the functions in an expression in this order.

**Order Number** **Function**

1 Functions that precede the argument, such as **(**, **sin(**, or **log(**

2 Functions that are entered after the argument, such as **2**, **M1**, **!**, , **r**, and conversions

3 Powers and roots, such as **2^5** or **5x32**

4 Permutations (**nPr**) and combinations (**nCr**)

5 Multiplication, implied multiplication, and division

6 Addition and subtraction

7 Relational functions, such as **>** or

8 Logic operator **and**

9 Logic operators **or** and **xor**

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**Note:** Within a priority level, EOS evaluates functions from left to right. Calculations within parentheses are evaluated first.

**Implied Multiplication**

The TI-83 Plus recognizes implied multiplication, so you need not press to express multiplication in all cases. For example, the TI-83 Plus interprets **2p**, **4sin(46)**, **5(1+2)**, and **(25)7** as implied multiplication.

**Note:** TI-83 Plus implied multiplication rules, although like theTI.83, differ from those of the TI.82. For example, the TI-83 Plus evaluates **12X** as **(12)X**, while the TI.82 evaluates **12X** as **1/(2X)** (Chapter 2).

**Parentheses**

All calculations inside a pair of parentheses are completed first. For example, in the expression **4(1+2)**, EOS first evaluates the portion inside the parentheses, **1+2**, and then multiplies the answer, **3**, by **4**.

You can omit the close parenthesis ( **)** ) at the end of an expression. All open parenthetical elements are closed automatically at the end of an expression. This is also true for open parenthetical elements that precede the store or display-conversion instructions.

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**Note:** An open parenthesis following a list name, matrix name, or **Y=** function name does not indicate implied multiplication. It specifies elements in the list (Chapter 11) or matrix (Chapter 10) and specifies a value for which to solve the **Y=** function.

**Negation**

To enter a negative number, use the negation key. Press and then enter the number. On the TI-83 Plus, negation is in the third level in the EOS hierarchy. Functions in the first level, such as squaring, are evaluated before negation.

For example, **MX2**, evaluates to a negative number (or 0). Use parentheses to square a negative number.

**Note:** Use the key for subtraction and the key for negation. If you press to enter a negative number, as in **9** **7**, or if you press to indicate subtraction, as in **9** **7**, an error occurs. If you press **A** **B**, it is interpreted as implied multiplication (**AMB**).

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Special Features of the TI-83 Plus

**Flash Electronic Upgradability**

The TI-83 Plus uses Flash technology, which lets you upgrade to future software versions without buying a new calculator.

**For details, refer to:** Chapter 19

As new functionality becomes available, you can electronically upgrade your TI-83 Plus from the Internet. Future software versions include maintenance upgrades that will be released free of charge, as well as new applications and major software upgrades that will be available for purchase from the TI web site: **education.ti.com**

**1.56 Megabytes (M) of Available Memory**

1.56 M of available memory are built into the TI-83 Plus. About 24 kilobytes (K) of RAM (random access memory) are available for you to compute and store functions, programs, and data.

**For details, refer to:** Chapter 18

About 1.54 M of user data archive allow you to store data, programs, applications, or any other variables to a safe location where they cannot

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be edited or deleted inadvertently. You can also free up RAM by archiving variables to user data

**Applications**

Applications can be installed to customize the TI-83 Plus to your classroom needs. The big 1.54 M archive space lets you store up to 94 applications at one time. Applications can also be stored on a computer for later use or linked unit-to-unit.

**For details, refer to:** Chapter 18

**Archiving**

You can store variables in the TI-83 Plus user data archive, a protected area of memory separate from RAM. The user data archive lets you:

**For details, refer to:** Chapter 18

Store data, programs, applications or any other variables to a safe location where they cannot be edited or deleted inadvertently.

Create additional free RAM by archiving variables.

By archiving variables that do not need to be edited frequently, you can free up RAM for applications that may require additional memory.

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**Calculator-Based Laboratory (CBL 2, CBL) and** **Calculator-Based Ranger (CBR)**

The TI-83 Plus comes with the CBL/CBR application already installed. When coupled with the (optional) CBL 2/CBL or CBR accessories, you can use the TI-83 Plus to analyze real world data.

**For details, refer to:** Chapter 14

CBL 2/CBL and CBR let you explore mathematical and scientific relationships among distance, velocity, acceleration, and time using data collected from activities you perform.

CBL 2/CBL and CBR differ in that CBL 2/CBL allows you to collect data using several different probes analyzing temperature, light, voltage, or sonic (motion) data. CBR collects data using a built-in Sonic probe. CBL 2/CBL and CBR accessories can be linked together to collect more than one type of data at the same time. You can find more information on CBL 2/CBL and CBR in their user manuals.

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Other TI-83 Plus Features

Getting Started has introduced you to basic TI-83 Plus operations. This guidebook covers the other features and capabilities of the TI-83 Plus in greater detail.

**Graphing**

You can store, graph, and analyze up to 10 functions, up to six parametric functions, up to six polar functions, and up to three sequences. You can use **DRAW** instructions to annotate graphs.

**For graphing details,** **refer to:** Chapters 3, 4, 5, 6, 8

The graphing chapters appear in this order: **Function**, **Parametric**, **Polar**, **Sequence**, and **DRAW**.

**Sequences**

You can generate sequences and graph them over time. Or, you can graph them as web plots or as phase plots.

**For details, refer to:** Chapter 6

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**Tables**

You can create function evaluation tables to analyze many functions simultaneously.

**For details, refer to:** Chapter 7

**Split Screen**

You can split the screen horizontally to display both a graph and a related editor (such as the **Y=** editor), the table, the stat list editor, or the home screen. Also, you can split the screen vertically to display a graph and its table simultaneously.

**For details, refer to:** Chapter 9

**Matrices**

You can enter and save up to 10 matrices and perform standard matrix operations on them.

**For details, refer to:** Chapter 10

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**Lists**

You can enter and save as many lists as memory allows for use in statistical analyses. You can attach formulas to lists for automatic computation. You can use lists to evaluate expressions at multiple values simultaneously and to graph a family of curves.

**For details, refer to:** Chapter 11

**Statistics**

You can perform one- and two-variable, list- based statistical analyses, including logistic and sine regression analysis. You can plot the data as a histogram, xyLine, scatter plot, modified or regular box-and-whisker plot, or normal probability plot. You can define and store up to three stat plot definitions.

**For details, refer to:** Chapter 12

**Inferential Statistics**

You can perform 16 hypothesis tests and confidence intervals and 15 distribution functions. You can display hypothesis test results graphically or numerically.

**For details, refer to:** Chapter 13

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**Applications**

You can use such applications as Finance or the CBL/CBR. With the Finance application you can use time-value-of-money (**TVM**) functions to analyze financial instruments such as annuities,

**For details, refer to:** Chapter 14

loans, mortgages, leases, and savings. You can analyze the value of money over equal time periods using cash flow functions. You can amortize loans with the amortization functions. With the CBL/CBR applications and CBL 2/CBL or CBR (optional) accessories, you can use a variety of probes to collect real world data.

Your TI-83 Plus includes Flash applications in addition to the ones mentioned above. Press to see the complete list of applications that came with your calculator.

Documentation for TI Flash applications is on the TI Resource CD. Visit education.ti.com/calc/guides for additional Flash application guidebooks.

**CATALOG**

The **CATALOG** is a convenient, alphabetical list of all functions and instructions on the TI-83 Plus. You can paste any function or instruction from the **CATALOG** to the current cursor location.

**For details, refer to:** Chapter 15

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**Programming**

You can enter and store programs that include extensive control and input/output instructions.

**For details, refer to:** Chapter 16

**Archiving**

Archiving allows you to store data, programs, or other variables to user data archive where they cannot be edited or deleted inadvertently. Archiving also allows you to free up RAM for variables that may require additional memory.

**For details, refer to:** Chapter 16

Archived variables are indicated by asterisks (*) to the left of the variable names.

**Communication Link**

The TI-83 Plus has a port to connect and communicate with another TI-83 Plus, a TI-83 Plus, a TI.83, a TI-82, a TI-73, CBL 2/CBL, or a CBR System.

**For details, refer to:** Chapter 19

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With the **TI Connect** or **TI-GRAPH LINK** software and **a TI-GRAPH LINK** cable, you can also link the TI-83 Plus to a personal computer.

As future software upgrades become available on the TI web site, you can download the software to your PC and then use the **TI Connect** or **TI-GRAPH LINK **software and a **TI-GRAPH LINK** cable to upgrade your TI-83 Plus.

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Error Conditions

**Diagnosing an Error**

The TI-83 Plus detects errors while performing these tasks.

Evaluating an expression

Executing an instruction

Plotting a graph

Storing a value

When the TI-83 Plus detects an error, it returns an error message as a menu title, such as **ERR:SYNTAX** or **ERR:DOMAIN**. Appendix B describes each error type and possible reasons for the error.

If you select **1:Quit** (or press y 5 or ), then the home screen is displayed.

If you select **2:Goto**, then the previous screen is displayed with the cursor at or near the error location.

**Note**: If a syntax error occurs in the contents of a **Y=** function during program execution, then the **Goto** option returns to the **Y=** editor, not to the program.

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**Correcting an Error**

To correct an error, follow these steps.

1. Note the error type (**ERR:***error type*).

2. Select **2:Goto**, if it is available. The previous screen is displayed with the cursor at or near the error location.

3. Determine the error. If you cannot recognize the error, refer to Appendix B.

4. Correct the expression.

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Chapter 2: Math, Angle, and Test Operations

Getting Started: Coin Flip

**Getting Started is a fast-paced introduction. Read the chapter for details.**

**Suppose you want to model flipping a fair coin 10 times. You want to track how** **many of those 10 coin flips result in heads. You want to perform this simulation** **40 times. With a fair coin, the probability of a coin flip resulting in heads is 0.5** **and the probability of a coin flip resulting in tails is 0.5.**

1. Begin on the home screen. Press | to display the **MATH PRB** menu. Press **7** to select **7:randBin(** (random Binomial). **randBin(** is pasted to the home screen. Press **10** to enter the number of coin flips. Press . Press ** 5 **to enter the probability of heads. Press . Press **40 **to enter the number of simulations. Press .

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2. Press to evaluate the expression. A list of 40 elements is generated with the first 7 displayed. The list contains the count of heads resulting from each set of 10 coin flips. The list has 40 elements because this simulation was performed 40 times. In this example, the coin came up heads five times in the first set of 10 coin flips, five times in the second set of 10 coin flips, and so on.

3. Press ~ or | to view the additional counts in the list. Ellipses (**...**) indicate that the list continues beyond the screen.

4. Press y L1 to store the data to the list name **L1**. You then can use the data for another activity, such as plotting a histogram (Chapter 12).

**Note:** Since **randBin(** generates random numbers, your list elements may differ from those in the example.

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Keyboard Math Operations

**Using Lists with Math Operations**

Math operations that are valid for lists return a list calculated element by element. If you use two lists in the same expression, they must be the same length.

**+ (Addition), N (Subtraction), (Multiplication), (Division)**

You can use **+** (addition, ), **N** (subtraction, ), (multiplication, ), and (division, ) with real and complex numbers, expressions, lists, and matrices. You cannot use with matrices.

*valueA***+***valueB* *valueA* **N ***valueB* *valueA**valueB* *valueA *** ***valueB*

**Trigonometric Functions**

You can use the trigonometric (trig) functions (sine, ; cosine, ; and tangent, ) with real numbers, expressions, and lists. The current angle mode setting affects interpretation. For example, **sin(30)** in **Radian** mode returns **L.9880316241**; in **Degree** mode it returns **.5**.

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**sin(***value***)** **cos(***value***)** **tan(***value***)**

You can use the inverse trig functions (arcsine, y ?; arccosine, y @; and arctangent, y A) with real numbers, expressions, and lists. The current angle mode setting affects interpretation.

**sinL1(***value***)** **cosL1(***value***)** **tanL1(***value***)**

**Note:** The trig functions do not operate on complex numbers.

**^ (Power), 2 (Square), ( (Square Root)**

You can use **^** (power, ), **2** (square, ), and **(** (square root, y C) with real and complex numbers, expressions, lists, and matrices. You cannot use **(** with matrices.

*value***^***power* *value***2** **(***value***)**

L**1 (Inverse)**

You can use **L1** (inverse, ) with real and complex numbers, expressions, lists, and matrices. The multiplicative inverse is equivalent to the reciprocal, 1*x*.

*value***L1**

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**log(, 10^(, ln(**

You can use **log(** (logarithm, ), **10^(** (power of 10, y G), and **ln(** (natural log, ) with real or complex numbers, expressions, and lists.

**log(***value***)** **10^(***power***)** **ln(***value***)**

**e^( (Exponential)**

**e^(** (exponential, y J) returns the constant **e** raised to a power. You can use **e^(** with real or complex numbers, expressions, and lists.

**e^(***power***)**

**e (Constant)**

**e** (constant, y [e]) is stored as a constant on the TI-83 Plus. Press y [e] to copy **e **to the cursor location. In calculations, the TI-83 Plus uses 2.718281828459 for **e**.

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**L (Negation)**

**M** (negation, ) returns the negative of *value*. You can use **M** with real or complex numbers, expressions, lists, and matrices.

**M***value*

EOS rules (Chapter 1) determine when negation is evaluated. For example, **LA2** returns a negative number, because squaring is evaluated before negation. Use parentheses to square a negated number, as in **(LA)2**.

**Note:** On the TI-83 Plus, the negation symbol (**M**) is shorter and higher than the subtraction sign (**N**), which is displayed when you press .

**p (Pi)**

**p** (Pi, y B) is stored as a constant in the TI-83 Plus. In calculations, the TI-83 Plus uses 3.1415926535898 for **p**.

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MATH Operations

**MATH Menu**

To display the **MATH** menu, press .

**MATH** ** NUM CPX PRB**

**1:** **4Frac** Displays the answer as a fraction. **2:** **4Dec** Displays the answer as a decimal. **3:** **3** Calculates the cube. **4:** **3(** Calculates the cube root. **5:** **x** Calculates the* xth* root. **6:** **fMin(** Finds the minimum of a function. **7:** **fMax(** Finds the maximum of a function. **8:** **nDeriv(** Computes the numerical derivative. **9:** **fnInt(** Computes the function integral. **0:** **Solver...** Displays the equation solver.

**4Frac, 4Dec**

**4Frac **(display as a fraction) displays an answer as its rational equivalent. You can use **4Frac** with real or complex numbers, expressions, lists, and matrices. If the answer cannot be simplified or the resulting denominator is more than three digits, the decimal equivalent is returned. You can only use **4Frac** following *value*.

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*value* **4Frac**

**4Dec** (display as a decimal) displays an answer in decimal form. You can use **4Dec** with real or complex numbers, expressions, lists, and matrices. You can only use **4Dec** following *value*.

*value* **4Dec**

**3(Cube), 3( (Cube Root)**

**3** (cube) returns the cube of *value*. You can use **3** with real or complex numbers, expressions, lists, and square matrices.

*value***3**

**3(** (cube root) returns the cube root of *value*. You can use **3(** with real or complex numbers, expressions, and lists.

**3(***value***)**

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**x (Root)**

**x** (*xth* root) returns the *xth root* of *value*. You can use **x** with real or complex numbers, expressions, and lists.

*xthroot***x***value*

**fMin(, fMax(**

**fMin(** (function minimum) and **fMax(** (function maximum) return the value at which the local minimum or local maximum value of *expression* with respect to *variable* occurs, between *lower* and *upper* values for *variable*. **fMin(** and **fMax(** are not valid in *expression*. The accuracy is controlled by *tolerance* (if not specified, the default is 1L5).

**fMin(***expression***,***variable***,***lower***,***upper*[**,***tolerance*]**)** **fMax(***expression***,***variable***,***lower***,***upper*[**,***tolerance*]**)**

**Note:** In this guidebook, optional arguments and the commas that accompany them are enclosed in brackets ([ ]).

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**nDeriv(**

**nDeriv(** (numerical derivative) returns an approximate derivative of *expression* with respect to *variable*, given the *value* at which to calculate the derivative and H (if not specified, the default is 1L3). **nDeriv(** is valid only for real numbers.

**nDeriv(***expression***,***variable***,***value*[**,**H]**)**

**nDeriv(** uses the symmetric difference quotient method, which approximates the numerical derivative value as the slope of the secant line through these points.

2

)(()( )('

+= *xfxf* *xf*

As H becomes smaller, the approximation usually becomes more accurate.

You can use **nDeriv(** once in *expression*. Because of the method used to calculate **nDeriv(**, the TI-83 Plus can return a false derivative value at a nondifferentiable point.

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**fnInt(**

**fnInt(** (function integral) returns the numerical integral (Gauss-Kronrod method) of *expression* with respect to *variable*, given *lower* limit, *upper* limit, and a *tolerance* (if not specified, the default is 1L5). **fnInt(** is valid only for real numbers.

**fnInt(***expression***,***variable***,***lower***,***upper*[**,***tolerance*]**)**

**Tip:** To speed the drawing of integration graphs (when **fnInt(** is used in a Y= equation), increase the value of the **Xres** window variable before you press s.

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Using the Equation Solver

**Solver**

**Solver** displays the equation solver, in which you can solve for any variable in an equation. The equation is assumed to be equal to zero. **Solver** is valid only for real numbers.

When you select **Solver**, one of two screens is displayed.

The equation editor (see step 1 picture below) is displayed when the equation variable **eqn** is empty.

The interactive solver editor is displayed when an equation is stored in **eqn**.

**Entering an Expression in the Equation Solver**

To enter an expression in the equation solver, assuming that the variable **eqn** is empty, follow these steps.

1. Select **0:Solver** from the **MATH** menu to display the equation editor.

2. Enter the expression in any of three ways.

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Enter the expression directly into the equation solver.

Paste a **Y=** variable name from the **VARS Y.VARS** menu to the equation solver.

Press y K, paste a **Y=** variable name from the **VARS Y.VARS**

menu, and press . The expression is pasted to the equation solver.

The expression is stored to the variable **eqn** as you enter it.

3. Press or . The interactive solver editor is displayed.

The equation stored in **eqn** is set equal to zero and displayed on the top line.

Variables in the equation are listed in the order in which they appear in the equation. Any values stored to the listed variables also are displayed.

The default lower and upper bounds appear in the last line of the editor (**bound={L199,199}**).

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A **$** is displayed in the first column of the bottom line if the editor continues beyond the screen.

**Tip:** To use the solver to solve an equation such as **K=.5MV2**, enter **eqn:0=KN.5MV2** in the equation editor.

**Entering and Editing Variable Values**

When you enter or edit a value for a variable in the interactive solver editor, the new value is stored in memory to that variable.

You can enter an expression for a variable value. It is evaluated when you move to the next variable. Expressions must resolve to real numbers at each step during the iteration.

You can store equations to any **VARS Y.VARS** variables, such as **Y1** or **r6**, and then reference the variables in the equation. The interactive solver editor displays all variables of all **Y=** functions referenced in the equation.

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**Solving for a Variable in the Equation Solver**

To solve for a variable using the equation solver after an equation has been stored to **eqn**, follow these steps.

1. Select **0:Solver** from the **MATH** menu to display the interactive solver editor, if not already displayed.

2. Enter or edit the value of each known variable. All variables, except the unknown variable, must contain a value. To move the cursor to the next variable, press or .

3. Enter an initial guess for the variable for which you are solving. This is optional, but it may help find the solution more quickly. Also, for equations with multiple roots, the TI-83 Plus will attempt to display the solution that is closest to your guess.

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TI-83 Plus Math, Angle, and Test Operations 76

The default guess is calculated as *(upper+lower)*

2 .

4. Edit **bound={***lower***,***upper***}**. *lower* and* upper* are the bounds between which the TI-83 Plus searches for a solution. This is optional, but it may help find the solution more quickly. The default is **bound={L199,199}**.

5. Move the cursor to the variable for which you want to solve and press \ (above the key).

The solution is displayed next to the variable for which you solved. A solid square in the first column marks the variable for which you solved and indicates that the equation is balanced. An ellipsis shows that the value continues beyond the screen. **Note:** When a number continues beyond the screen, be sure to press ~ to scroll to the end of the number to see whether it ends with a negative or positive exponent. A very small number may appear to be a large number until you scroll right to see the exponent.

The values of the variables are updated in memory.

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**leftNrt=***diff* is displayed in the last line of the editor. *diff* is the difference between the left and right sides of the equation. A solid square in the first column next to **leftNrt=** indicates that the equation has been evaluated at the new value of the variable for which you solved.

**Editing an Equation Stored to eqn**

To edit or replace an equation stored to **eqn** when the interactive equation solver is displayed, press } until the equation editor is displayed. Then edit the equation.

**Equations with Multiple Roots**

Some equations have more than one solution. You can enter a new initial guess or new bounds to look for additional solutions.

**Further Solutions**

After you solve for a variable, you can continue to explore solutions from the interactive solver editor. Edit the values of one or more variables. When you edit any variable value, the solid squares next to the previous solution and **leftNrt=***diff* disappear. Move the cursor to the variable for which you now want to solve and press \.

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**Controlling the Solution for Solver or solve(**

The TI-83 Plus solves equations through an iterative process. To control that process, enter bounds that are relatively close to the solution and enter an initial guess within those bounds. This will help to find a solution more quickly. Also, it will define which solution you want for equations with multiple solutions.

**Using solve( on the Home Screen or from a Program**

The function **solve(** is available only from **CATALOG** or from within a program. It returns a solution (root) of *expression* for *variable*, given an initial *guess*, and *lower* and *upper* bounds within which the solution is sought. The default for *lower* is L199. The default for *upper* is 199. **solve(** is valid only for real numbers.

**solve(***expression***,***variable***,***guess*[**,{***lower***,***upper***}**]**)**

*expression* is assumed equal to zero. The value of *variable* will not be updated in memory. *guess* may be a value or a list of two values. Values must be stored for every variable in *expression*, except *variable*, before *expression* is evaluated. *lower* and *upper* must be entered in list format.

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MATH NUM (Number) Operations

**MATH NUM Menu**

To display the **MATH NUM** menu, press ~.

**MATH** **NUM** ** CPX PRB** **1:** **abs(** Absolute value **2:** **round(** Round **3:** **iPart(** Integer part **4:** **fPart(** Fractional part **5:** **int(** Greatest integer **6:** **min(** Minimum value **7:** **max(** Maximum value **8:** **lcm(** Least common multiple **9:** **gcd(** Greatest common divisor

**abs(**

**abs(** (absolute value) returns the absolute value of real or complex (modulus) numbers, expressions, lists, and matrices.

**abs(***value***)**

**Note:** **abs(** is also available on the **MATH CPX** menu.

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**round(**

**round(** returns a number, expression, list, or matrix rounded to *#decimals* (9). If *#decimals* is omitted, *value* is rounded to the digits that are displayed, up to 10 digits.

**round(***value*[**,***#decimals*]**)**

**iPart(, fPart(**

**iPart(** (integer part) returns the integer part or parts of real or complex numbers, expressions, lists, and matrices.

**iPart(***value***)**

**fPart(** (fractional part) returns the fractional part or parts of real or complex numbers, expressions, lists, and matrices.

**fPart(***value***)**

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**int(**

**int(** (greatest integer) returns the largest integer real or complex numbers, expressions, lists, and matrices.

**int(***value***)**

**Note:** For a given *value*, the result of **int(** is the same as the result of **iPart(** for nonnegative numbers and negative integers, but one integer less than the result of **iPart(** for negative noninteger numbers.

**min(, max(**

**min(** (minimum value) returns the smaller of *valueA* and *valueB* or the smallest element in *list*. If *listA* and *listB* are compared, **min(** returns a list of the smaller of each pair of elements. If *list* and *value* are compared, **min(** compares each element in *list* with *value*.

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**max(** (maximum value) returns the larger of *valueA* and *valueB* or the largest element in *list*. If *listA* and *listB* are compared, **max(** returns a list of the larger of each pair of elements. If *list* and *value* are compared, **max(** compares each element in *list* with *value*.

**min(***valueA***,***valueB***)** **max(***valueA***,***valueB***)** **min(***list***)** **max(***list***)** **min(***listA***,***listB***)** **max(***listA***,***listB***)** **min(***list***,***value***)** **max(***list***,***value***)**

**Note:** **min(** and **max(** also are available on the **LIST MATH** menu.

**lcm(, gcd(**

**lcm(** returns the least common multiple of *valueA* and *valueB*, both of which must be nonnegative integers. When *listA* and *listB* are specified, **lcm(** returns a list of the lcm of each pair of elements. If *list* and *value* are specified, **lcm(** finds the lcm of each element in *list* and *value*.

**gcd(** returns the greatest common divisor of *valueA* and *valueB*, both of which must be nonnegative integers. When *listA* and *listB* are specified, **gcd(** returns a list of the gcd of each pair of elements. If *list* and *value* are specified, **gcd(** finds the gcd of each element in *list* and *value*.

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TI-83 Plus Math, Angle, and Test Operations 83

**lcm(***valueA***,***valueB***)** **gcd(***valueA***,***valueB***)** **lcm(***listA***,***listB***)** **gcd(***listA***,***listB***)** **lcm(***list***,***value***)** **gcd(***list***,***value***)**

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Entering and Using Complex Numbers

**Complex-Number Modes**

The TI-83 Plus displays complex numbers in rectangular form and polar form. To select a complex-number mode, press z, and then select either of the two modes.

**a+b i**

*(rectangular-complex mode)*

**re^q**(polar-complex mode)

*i*On the TI-83 Plus, complex numbers can be stored to variables. Also, complex numbers are valid list elements.

In **Real** mode, complex-number results return an error, unless you entered a complex number as input. For example, in **Real** mode **ln(L1)** returns an error; in **a+b i** mode

**ln(L1)**returns an answer.

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TI-83 Plus Math, Angle, and Test Operations 85

**Real **mode **a+b i **mode

**$** **$**

**Entering Complex Numbers**

Complex numbers are stored in rectangular form, but you can enter a complex number in rectangular form or polar form, regardless of the mode setting. The components of complex numbers can be real numbers or expressions that evaluate to real numbers; expressions are evaluated when the command is executed.

**Note about Radian Versus Degree Mode**

Radian mode is recommended for complex number calculations. Internally, the TI-83 Plus converts all entered trigonometric values to radians, but it does not convert values for exponential, logarithmic, or hyperbolic functions.

In degree mode, complex identities such as *e*^(** i**q) = cos(q) +

**sin(q) are not generally true because the values for cos and sin are converted to radians, while those for e^() are not. For example,**

*i**e*^(

**45) = cos(45) +**

*i***sin(45) is treated internally as**

*i**e*^(

**45) = cos(p/4) +**

*i***sin(p/4). Complex identities are always true in radian mode.**

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**Interpreting Complex Results**

Complex numbers in results, including list elements, are displayed in either rectangular or polar form, as specified by the mode setting or by a display conversion instruction. In the example below, polar-complex (**re^q***i*) and **Radian** modes are set.

**Rectangular-Complex Mode**

Rectangular-complex mode recognizes and displays a complex number in the form **a+b i**, where

**a**is the real component,

**b**is the imaginary component, and

**is a constant equal to -1.**

*i*To enter a complex number in rectangular form, enter the value of *a* (*real* *component*), press or , enter the value of *b* (*imaginary component*), and press y V (constant).

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*real component*(**+** or **N**)*imaginary component i*

**Polar-Complex Mode**

Polar-complex mode recognizes and displays a complex number in the form *re^*q** i**, where

*r*is the magnitude,

*e*is the base of the natural log, q is the angle, and

**is a constant equal to -1.**

*i*To enter a complex number in polar form, enter the value of *r* (*magnitude*), press y J (exponential function), enter the value of q (*angle*), press y V (constant), and then press .

*magnitude***e^(***angle i*

**)**

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MATH CPX (Complex) Operations

**MATH CPX Menu**

To display the **MATH CPX** menu, press ~ ~.

**MATH** **NUM** **CPX** ** PRB** **1:** **conj(** Returns the complex conjugate. **2:** **real(** Returns the real part. **3:** **imag(** Returns the imaginary part. **4:** **angle(** Returns the polar angle. **5:** **abs(** Returns the magnitude (modulus). **6:** **4Rect** Displays the result in rectangular form. **7:** **4Polar** Displays the result in polar form.

**conj(**

**conj(** (conjugate) returns the complex conjugate of a complex number or list of complex numbers.

**conj(***a***+***b i*

**)**returns

*a*N

*b*in

**i****a+b**

*i*mode.

**conj(**

*r*

**e^(**q

**returns**

*i*))*r*

**e^(**Lq

**in**

*i*)**re^q**mode.

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TI-83 Plus Math, Angle, and Test Operations 89

**real(**

**real(** (real part) returns the real part of a complex number or list of complex numbers.

**real(***a***+***b i*

**)**returns

*a*.

**real(**

*r*

**e^(**q

**returns**

*i*))*r*

*cos*(q).

**imag(**

**imag(** (imaginary part) returns the imaginary (nonreal) part of a complex number or list of complex numbers.

**imag(***a***+***b i*

**)**returns

*b*.

**imag(**

*r*

**e^(**q

**returns**

*i*))*r*

*sin*(q).

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**angle(**

**angle(** returns the polar angle of a complex number or list of complex numbers, calculated as tanL1 (b/a), where b is the imaginary part and a is the real part. The calculation is adjusted by +p in the second quadrant or Np in the third quadrant.

**angle(***a***+***bi***)** returns *tan*L1*(b/a)*. **angle(***r***e^(**q*i***))** returns q, where Lp

**abs(**

**abs(** (absolute value) returns the magnitude (modulus), *(real2+imag2) *, of a complex number or list of complex numbers.

**abs(***a***+***b i*

**)**returns

*(a2+b2)*.

**abs(**

*r*

**e^(**q

**returns**

*i*))*r*(magnitude).

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**4Rect**

**4Rect** (display as rectangular) displays a complex result in rectangular form. It is valid only at the end of an expression. It is not valid if the result is real.

*complex result***8Rect** returns *a*+*b i*.

**4Polar**

**4Polar** (display as polar) displays a complex result in polar form. It is valid only at the end of an expression. It is not valid if the result is real.

*complex result***8Polar** returns *r***e^(**q** i)**.

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MATH PRB (Probability) Operations

**MATH PRB Menu**

To display the **MATH PRB** menu, press |.

**MATH NUM CPX** **PRB**

**1:** **rand** Random-number generator **2:** **nPr** Number of permutations **3:** **nCr** Number of combinations **4:** **!** Factorial **5:** **randInt(** Random-integer generator **6:** **randNorm(** Random # from Normal distribution **7:** **randBin(** Random # from Binomial distribution

**rand**

**rand** (random number) generates and returns one or more random numbers > 0 and < 1. To generate a list of random-numbers, specify an integer > 1 for *numtrials* (number of trials). The default for *numtrials* is 1.

**rand**[**(***numtrials***)**]

**Tip:** To generate random numbers beyond the range of 0 to 1, you can include **rand** in an expression. For example, **rand5** generates a random number > 0 and < 5.

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With each **rand** execution, the TI-83 Plus generates the same random- number sequence for a given seed value. The TI-83 Plus factory-set seed value for **rand** is **0**. To generate a different random-number sequence, store any nonzero seed value to **rand**. To restore the factory- set seed value, store **0** to **rand** or reset the defaults (Chapter 18).

**Note:** The seed value also affects **randInt(**, **randNorm(**, and **randBin(** instructions.

**nPr, nCr**

**nPr** (number of permutations) returns the number of permutations of *items* taken *number* at a time. *items* and *number* must be nonnegative integers. Both *items* and *number* can be lists.

*items* **nPr** *number*

**nCr** (number of combinations) returns the number of combinations of *items* taken *number* at a time. *items* and *number* must be nonnegative integers. Both *items* and *number* can be lists.

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*items* **nCr** *number*

**! (Factorial)**

**!** (factorial) returns the factorial of either an integer or a multiple of .5. For a list, it returns factorials for each integer or multiple of .5. *value* must be L.5 and 69.

*value***!**

**Note:** The factorial is computed recursively using the relationship (n+1)! = nn!, until n is reduced to either 0 or L1/2. At that point, the definition 0!=1 or the definition (L12)!=p is used to complete the calculation. Hence:

n!=n(nN1)(nN2) ... 21, if n is an integer 0 n!= n(nN1)(nN2) ... 12p, if n+12 is an integer 0 n! is an error, if neither n nor n+12 is an integer 0.

(The variable n equals *value* in the syntax description above.)

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TI-83 Plus Math, Angle, and Test Operations 95

**randInt(**

**randInt(** (random integer) generates and displays a random integer within a range specified by *lower* and *upper* integer bounds. To generate a list of random numbers, specify an integer >1 for *numtrials* (number of trials); if not specified, the default is 1.

**randInt(***lower***,***upper*[**,***numtrials*]**)**

**randNorm(**

**randNorm(** (random Normal) generates and displays a random real number from a specified Normal distribution. Each generated value could be any real number, but most will be within the interval [mN3(s), m+3(s)]. To generate a list of random numbers, specify an integer > 1 for *numtrials* (number of trials); if not specified, the default is 1.

**randNorm(**m**,**s[**,***numtrials*]**)**

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TI-83 Plus Math, Angle, and Test Operations 96

**randBin(**

**randBin(** (random Binomial) generates and displays a random integer from a specified Binomial distribution. *numtrials* (number of trials) must be 1. *prob* (probability of success) must be 0 and 1. To generate a list of random numbers, specify an integer > 1 for* numsimulations* (number of simulations); if not specified, the default is 1.

**randBin(***numtrials***,***prob*[**,***numsimulations*]**)**

**Note:** The seed value stored to **rand** also affects **randInt(**, **randNorm(**, and **randBin(** instructions.

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ANGLE Operations

**ANGLE Menu**

To display the **ANGLE** menu, press y [ANGLE]. The **ANGLE** menu displays angle indicators and instructions. The **Radian**/**Degree** mode setting affects the TI-83 Pluss interpretation of **ANGLE** menu entries.

**ANGLE**

**1:** Degree notation **2:** **'** DMS minute notation **3:** **r** Radian notation **4:** **8DMS** Displays as degree/minute/second **5:** **R8Pr(** Returns **r**, given **X** and **Y** **6:** **R8Pq(** Returns **q**, given **X** and **Y** **7:** **P8Rx(** Returns **x**, given **R** and **q**

**8:** **P8Ry(** Returns **y**, given **R** and **q**

**Entry Notation**

DMS (degrees/minutes/seconds) entry notation comprises the degree symbol (), the minute symbol (**'**), and the second symbol (**"**). *degrees* must be a real number; *minutes* and *seconds* must be real numbers 0.

*degrees**minutes***'***seconds***"**

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TI-83 Plus Math, Angle, and Test Operations 98

For example, enter for 30 degrees, 1 minute, 23 seconds. If the angle mode is not set to **Degree**, you must use so that the TI-83 Plus can interpret the argument as degrees, minutes, and seconds.

**Degree** mode **Radian** mode

** (Degree)**

(degree) designates an angle or list of angles as degrees, regardless of the current angle mode setting. In **Radian** mode, you can use to convert degrees to radians.

*value*

**{***value1***,***value2***,***value3***,***value4***,**...**,***value n***}**

also designates *degrees* (D) in DMS format. **'** (minutes) designates *minutes* (M) in DMS format. **"** (seconds) designates *seconds* (S) in DMS format.

**Note:** **"** is not on the **ANGLE** menu. To enter **"**, press [].

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TI-83 Plus Math, Angle, and Test Operations 99

**r (Radians)**

**r** (radians) designates an angle or list of angles as radians, regardless of the current angle mode setting. In **Degree** mode, you can use **r** to convert radians to degrees.

*value***r**

**Degree** mode

**8DMS**

**8DMS** (degree/minute/second) displays *answer* in DMS format. The mode setting must be **Degree** for *answer* to be interpreted as degrees, minutes, and seconds. **8DMS** is valid only at the end of a line.

*answer***8DMS**

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TI-83 Plus Math, Angle, and Test Operations 100

**R8Pr(, R8Pq(, P8Rx(, P8Ry(**

**R8Pr(** converts rectangular coordinates to polar coordinates and returns **r**. **R8Pq(** converts rectangular coordinates to polar coordinates and returns **q**. *x* and *y* can be lists.

**R8Pr(***x***,***y***), R8Pq(***x***,***y***)**

**Note:** **Radian** mode is set.

**P8Rx(** converts polar coordinates to rectangular coordinates and returns **x**. **P8Ry(** converts polar coordinates to rectangular coordinates and returns **y**. *r* and q can be lists.

**P8Rx(***r***,**q**), P8Ry(***r***,**q**)**

**Note:** **Radian** mode is set.

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TI-83 Plus Math, Angle, and Test Operations 101

TEST (Relational) Operations

**TEST Menu**

To display the **TEST** menu, press y :.

**This operator...** **Returns 1 (true) if...** **TEST** ** LOGIC**

**1:** **=** Equal **2:** Not equal to **3:** **>** Greater than **4:** Greater than or equal to **5:** **<** Less than **6:** Less than or equal to

**=, , >, , <, **

Relational operators compare *valueA* and *valueB* and return **1** if the test is true or **0** if the test is false. *valueA* and *valueB* can be real numbers, expressions, or lists. For **=** and only, *valueA* and *valueB* also can be matrices or complex numbers. If *valueA* and *valueB* are matrices, both must have the same dimensions.

Relational operators are often used in programs to control program flow and in graphing to control the graph of a function over specific values.

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TI-83 Plus Math, Angle, and Test Operations 102

*valueA***=***valueB* *valueA**valueB* *valueA***>***valueB* *valueA**valueB* *valueA***<***valueB* *valueA**valueB*

**Using Tests**

Relational operators are evaluated after mathematical functions according to EOS rules (Chapter 1).

The expression **2+2=2+3** returns **0**. The TI-83 Plus performs the addition first because of EOS rules, and then it compares 4 to 5.

The expression **2+(2=2)+3** returns **6**. The TI-83 Plus performs the relational test first because it is in parentheses, and then it adds 2, 1, and 3.

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TI-83 Plus Math, Angle, and Test Operations 103

TEST LOGIC (Boolean) Operations

**TEST LOGIC Menu**

To display the **TEST LOGIC** menu, press y TEST ~.

**This operator...** **Returns a 1 (true) if...** **TEST** **LOGIC**

**1:** **and** Both values are nonzero (true). **2:** **or** At least one value is nonzero (true). **3:** **xor** Only one value is zero (false). **4:** **not(** The value is zero (false).

**Boolean Operators**

Boolean operators are often used in programs to control program flow and in graphing to control the graph of the function over specific values. Values are interpreted as zero (false) or nonzero (true).

**and, or, xor**

**and**, **or**, and **xor** (exclusive or) return a value of **1** if an expression is true or **0** if an expression is false, according to the table below. *valueA* and *valueB* can be real numbers, expressions, or lists.

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TI-83 Plus Math, Angle, and Test Operations 104

*valueA ***and ***valueB* *valueA ***or ***valueB* *valueA ***xor ***valueB*

**valueA** **valueB** **and** **or** **xor**

0 0 returns 1 1 0

0 0 returns 0 1 1

0 0 returns 0 1 1

0 0 returns 0 0 0

**not(**

**not(** returns** 1** if *value* (which can be an expression) is **0**.

**not(***value***)**

**Using Boolean Operations**

Boolean logic is often used with relational tests. In the following program, the instructions store **4** into **C**.

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TI-83 Plus Function Graphing 105

Chapter 3: Function Graphing

Getting Started: Graphing a Circle

**Getting Started is a fast-paced introduction. Read the chapter for details.**

**Graph a circle of radius 10, centered on the origin in the standard viewing** **window. To graph this circle, you must enter separate formulas for the upper and** **lower portions of the circle. Then use ZSquare (zoom square) to adjust the** **display and make the functions appear as a circle.**

1. In **Func** mode, press o to display the **Y= **editor. Press y **100** to enter the expression Y=(100NX2), which defines the top half of the circle.

The expression Y=L(100NX2) defines the bottom half of the circle. On the TI-83 Plus, you can define one function in terms of another. To define **Y2=LY1**, press to enter the negation sign. Press ~ to display the **VARS Y.VARS**

menu. Then press to select **1:Function**. The **FUNCTION** secondary menu is displayed. Press **1** to select **1:Y1**.

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TI-83 Plus Function Graphing 106

2. Press q **6** to select **6:ZStandard**. This is a quick way to reset the window variables to the standard values. It also graphs the functions; you do not need to press .

Notice that the functions appear as an ellipse in the standard viewing window.

3. To adjust the display so that each pixel represents an equal width and height, press q **5** to select **5:ZSquare**. The functions are replotted and now appear as a circle on the display.

4. To see the **ZSquare** window variables, press p and notice the new values for **Xmin**, **Xmax**, **Ymin**, and **Ymax**.

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TI-83 Plus Function Graphing 107

Defining Graphs

**TI-83 PlusGraphing Mode Similarities**

Chapter 3 specifically describes function graphing, but the steps shown here are similar for each TI-83 Plus graphing mode. Chapters 4, 5, and 6 describe aspects that are unique to parametric graphing, polar graphing, and sequence graphing.

**Defining a Graph**

To define a graph in any graphing mode, follow these steps. Some steps are not always necessary.

1. Press z and set the appropriate graph mode.

2. Press o and enter, edit, or select one or more functions in the **Y=** editor.

3. Deselect stat plots, if necessary.

4. Set the graph style for each function.

5. Press p and define the viewing window variables.

6. Press y . and select the graph format settings.

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TI-83 Plus Function Graphing 108

**Displaying and Exploring a Graph**

After you have defined a graph, press to display it. Explore the behavior of the function or functions using the TI-83 Plus tools described in this chapter.

**Saving a Graph for Later Use**

You can store the elements that define the current graph to any of 10 graph database variables (**GDB1** through **GDB9**, and **GDB0**; Chapter 8). To recreate the current graph later, simply recall the graph database to which you stored the original graph.

These types of information are stored in a **GDB**.

**Y=** functions

Graph style settings

Window settings

Format settings

You can store a picture of the current graph display to any of 10 graph picture variables (**Pic1** through **Pic9**, and **Pic0**; Chapter 8). Then you can superimpose one or more stored pictures onto the current graph.

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TI-83 Plus Function Graphing 109

Setting the Graph Modes

**Checking and Changing the Graphing Mode**

To display the mode screen, press z. The default settings are highlighted below. To graph functions, you must select **Func** mode before you enter values for the window variables and before you enter the functions.

The TI-83 Plus has four graphing modes.

**Func** (function graphing)

**Par** (parametric graphing; Chapter 4)

**Pol** (polar graphing; Chapter 5)

**Seq** (sequence graphing; Chapter 6)

Other mode settings affect graphing results. Chapter 1 describes each mode setting.

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TI-83 Plus Function Graphing 110

**Float** or **0123456789** (fixed) decimal mode affects displayed graph coordinates.

**Radian** or **Degree** angle mode affects interpretation of some functions.

**Connected** or **Dot** plotting mode affects plotting of selected functions.

**Sequential** or **Simul** graphing-order mode affects function plotting when more than one function is selected.

**Setting Modes from a Program**

To set the graphing mode and other modes from a program, begin on a blank line in the program editor and follow these steps.

1. Press z to display the mode settings.

2. Press , ~, |, and } to place the cursor on the mode that you want to select.

3. Press to paste the mode name to the cursor location.

The mode is changed when the program is executed.

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Defining Functions

**Displaying Functions in the Y= Editor**

To display the **Y=** editor, press o. You can store up to 10 functions to the function variables **Y1** through **Y9**, and **Y0**. You can graph one or more defined functions at once. In this example, functions **Y1** and **Y2** are defined and selected.

**Defining or Editing a Function**

To define or edit a function, follow these steps.

1. Press o to display the **Y=** editor.

2. Press to move the cursor to the function you want to define or edit. To erase a function, press .

3. Enter or edit the expression to define the function.

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You may use functions and variables (including matrices and lists) in the expression. When the expression evaluates to a nonreal number, the value is not plotted; no error is returned.

The independent variable in the function is **X**. **Func** mode defines as **X**. To enter **X**, press or press [X].

When you enter the first character, the **=** is highlighted, indicating that the function is selected.

As you enter the expression, it is stored to the variable **Y**n as a user- defined function in the **Y=** editor.

4. Press or to move the cursor to the next function.

**Defining a Function from the Home Screen or a Program**

To define a function from the home screen or a program, begin on a blank line and follow these steps.

1. Press [], enter the expression, and then press [] again.

2. Press .

3. Press ~ **1** to select **1:Function** from the **VARS Y.VARS** menu.

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4. Select the function name, which pastes the name to the cursor location on the home screen or program editor.

5. Press to complete the instruction.

**"***expression***"!Y***n*

When the instruction is executed, the TI-83 Plus stores the expression to the designated variable **Y**n, selects the function, and displays the message **Done**.

**Evaluating Y= Functions in Expressions**

You can calculate the value of a **Y=** function **Y***n* at a specified *value* of **X**. A list of *values* returns a list.

**Y***n***(***value***)** **Y***n***({***value1,value2,value3, . . .,value n***})**

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Selecting and Deselecting Functions

**Selecting and Deselecting a Function**

You can select and deselect (turn on and turn off) a function in the **Y=** editor. A function is selected when the **=** sign is highlighted. The TI-83 Plus graphs only the selected functions. You can select any or all functions **Y1** through **Y9**, and **Y0**.

To select or deselect a function in the **Y=** editor, follow these steps.

1. Press o to display the **Y=** editor.

2. Move the cursor to the function you want to select or deselect.

3. Press | to place the cursor on the functions **=** sign.

4. Press to change the selection status.

When you enter or edit a function, it is selected automatically. When you clear a function, it is deselected.

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**Turning On or Turning Off a Stat Plot in the Y= Editor**

To view and change the on/off status of a stat plot in the **Y=** editor, use **Plot1 Plot2 Plot3** (the top line of the **Y=** editor). When a plot is on, its name is highlighted on this line.

To change the on/off status of a stat plot from the **Y= **editor, press } and ~ to place the cursor on **Plot1**, **Plot2**, or **Plot3**, and then press .

**Selecting and Deselecting Functions from the Home Screen or a** **Program**

To select or deselect a function from the home screen or a program, begin on a blank line and follow these steps.

1. Press ~ to display the **VARS Y.VARS** menu.

2. Select **4:On/Off** to display the **ON/OFF** secondary menu.

**Plot1** is turned on. **Plot2** and **Plot3** are turned off.

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3. Select **1:FnOn** to turn on one or more functions or **2:FnOff** to turn off one or more functions. The instruction you select is copied to the cursor location.

4. Enter the number (**1** through **9**, or **0**; not the variable **Y***n*) of each function you want to turn on or turn off.

If you enter two or more numbers, separate them with commas.

To turn on or turn off all functions, do not enter a number after **FnOn** or **FnOff**.

**FnOn**[*function#,function#, . . .,function n*] **FnOff**[*function#,function#, . . .,function n*]

5. Press . When the instruction is executed, the status of each function in the current mode is set and **Done** is displayed.

For example, in **Func** mode, **FnOff :FnOn 1,3** turns off all functions in the **Y=** editor, and then turns on **Y1** and **Y3**.

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Setting Graph Styles for Functions

**Graph Style Icons in the Y= Editor**

This table describes the graph styles available for function graphing. Use the styles to visually differentiate functions to be graphed together. For example, you can set **Y1** as a solid line, **Y2** as a dotted line, and **Y3** as a thick line.

**Icon** **Style** **Description**

Line A solid line connects plotted points; this is the default in **Connected** mode

Thick A thick solid line connects plotted points

Above Shading covers the area above the graph

Below Shading covers the area below the graph

Path A circular cursor traces the leading edge of the graph and draws a path

Animate A circular cursor traces the leading edge of the graph without drawing a path

Dot A small dot represents each plotted point; this is the default in **Dot** mode

**Note:** Some graph styles are not available in all graphing modes. Chapters 4, 5, and 6 list the styles for **Par**, **Pol**, and **Seq** modes.

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**Setting the Graph Style**

To set the graph style for a function, follow these steps.

1. Press o to display the **Y=** editor.

2. Press and } to move the cursor to the function.

3. Press | | to move the cursor left, past the **=** sign, to the graph style icon in the first column. The insert cursor is displayed. (Steps 2 and 3 are interchangeable.)

4. Press repeatedly to rotate through the graph styles. The seven styles rotate in the same order in which they are listed in the table above.

5. Press ~, }, or when you have selected a style.

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**Shading Above and Below**

When you select or for two or more functions, the TI-83 Plus rotates through four shading patterns.

Vertical lines shade the first function with a or graph style.

Horizontal lines shade the second.

Negatively sloping diagonal lines shade the third.

Positively sloping diagonal lines shade the fourth.

The rotation returns to vertical lines for the fifth or function, repeating the order described above.

When shaded areas intersect, the patterns overlap.

**Note:** When or is selected for a Y= function that graphs a family of curves, such as **Y1={1,2,3}X**, the four shading patterns rotate for each member of the family of curves.

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**Setting a Graph Style from a Program**

To set the graph style from a program, select **H:GraphStyle(** from the **PRGM CTL** menu. To display this menu, press while in the program editor. *function#* is the number of the **Y=** function name in the current graphing mode. *graphstyle#* is an integer from **1** to **7** that corresponds to the graph style, as shown below.

**1** = (line) **2** = (thick) **3** = (above) **4** = (below) **5 **= (path) **6** = (animate) **7** = (dot)

**GraphStyle(***function#,graphstyle#***)**

For example, when this program is executed in **Func** mode, **GraphStyle(1,3)** sets **Y1** to (above).

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Setting the Viewing Window Variables

**The TI-83 Plus Viewing Window**

The viewing window is the portion of the coordinate plane defined by **Xmin**, **Xmax**, **Ymin**, and **Ymax**. **Xscl** (X scale) defines the distance between tick marks on the x-axis. **Yscl** (Y scale) defines the distance between tick marks on the y-axis. To turn off tick marks, set **Xscl=0** and **Yscl=0**.

Xmax

Ymin

Ymax

Xscl

Yscl

Xmin

**Displaying the Window Variables**

To display the current window variable values, press p. The window editor above and to the right shows the default values in **Func** graphing mode and **Radian** angle mode. The window variables differ from one graphing mode to another.

**Xres** sets pixel resolution (**1** through **8**) for function graphs only. The default is **1**.

At **Xres=1**, functions are evaluated and graphed at each pixel on the x-axis.

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At **Xres=8**, functions are evaluated and graphed at every eighth pixel along the x-axis.

**Tip:** Small **Xres** values improve graph resolution but may cause the TI-83 Plus to draw graphs more slowly.

**Changing a Window Variable Value**

To change a window variable value from the window editor, follow these steps.

1. Press or } to move the cursor to the window variable you want to change.

2. Edit the value, which can be an expression.

Enter a new value, which clears the original value.

Move the cursor to a specific digit, and then edit it.

3. Press , , or }. If you entered an expression, the TI-83 Plus evaluates it. The new value is stored.

**Note:** **Xmin**<**Xmax** and **Ymin**<**Ymax** must be true in order to graph.

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**Storing to a Window Variable from the Home Screen or a Program**

To store a value, which can be an expression, to a window variable, begin on a blank line and follow these steps.

1. Enter the value you want to store.

2. Press .

3. Press to display the **VARS** menu.

4. Select **1:Window** to display the **Func** window variables (**X/Y** secondary menu).

Press ~ to display the **Par** and **Pol** window variables (**T/q**

secondary menu).

Press ~ ~ to display the **Seq** window variables (**U/V/W** secondary menu).

5. Select the window variable to which you want to store a value. The name of the variable is pasted to the current cursor location.

6. Press to complete the instruction.

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When the instruction is executed, the TI-83 Plus stores the value to the window variable and displays the value.

**@X and @Y**

The variables **@X** and **@Y** (items **8** and **9** on the **VARS** (**1:Window**) **X/Y**

secondary menu) define the distance from the center of one pixel to the center of any adjacent pixel on a graph (graphing accuracy). **@X** and **@Y** are calculated from **Xmin**, **Xmax**, **Ymin**, and **Ymax** when you display a graph.

**@X** = **(Xmax N Xmin)**

**94** ** @Y** = **(Ymax N Ymin)**

**62**

You can store values to **@X** and **@Y**. If you do, **Xmax** and **Ymax** are calculated from **@X**, **Xmin**, **@Y**, and **Ymin**.

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Setting the Graph Format

**Displaying the Format Settings**

To display the format settings, press y .. The default settings are highlighted below.

**RectGC** ** PolarGC** Sets cursor coordinates. **CoordOn** ** CoordOff** Sets coordinates display on or off. **GridOff** ** GridOn** Sets grid off or on. **AxesOn** ** AxesOff** Sets axes on or off. **LabelOff** ** LabelOn** Sets axes label off or on. **ExprOn** ** ExprOff** Sets expression display on or off.

Format settings define a graphs appearance on the display. Format settings apply to all graphing modes. **Seq** graphing mode has an additional mode setting (Chapter 6).

**Changing a Format Setting**

To change a format setting, follow these steps.

1. Press , ~, }, and | as necessary to move the cursor to the setting you want to select.

2. Press to select the highlighted setting.

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**RectGC, PolarGC**

**RectGC** (rectangular graphing coordinates) displays the cursor location as rectangular coordinates **X** and **Y**.

**PolarGC** (polar graphing coordinates) displays the cursor location as polar coordinates **R** and **q**.

The **RectGC**/**PolarGC** setting determines which variables are updated when you plot the graph, move the free-moving cursor, or trace.

**RectGC** updates **X** and **Y**; if **CoordOn **format is selected, **X** and **Y** are displayed.

**PolarGC** updates **X**, **Y**, **R**, and **q**; if **CoordOn **format is selected, **R** and **q** are displayed.

**CoordOn, CoordOff**

**CoordOn** (coordinates on) displays the cursor coordinates at the bottom of the graph. If **ExprOff** format is selected, the function number is displayed in the top-right corner.

**CoordOff** (coordinates off) does not display the function number or coordinates.

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**GridOff, GridOn**

Grid points cover the viewing window in rows that correspond to the tick marks on each axis.

**GridOff** does not display grid points.

**GridOn** displays grid points.

**AxesOn, AxesOff**

**AxesOn** displays the axes.

**AxesOff** does not display the axes.

This overrides the **LabelOff**/**LabelOn** format setting.

**LabelOff, LabelOn**

**LabelOff** and **LabelOn** determine whether to display labels for the axes (**X** and **Y**), if **AxesOn** format is also selected.

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**ExprOn, ExprOff**

**ExprOn** and **ExprOff** determine whether to display the **Y=** expression when the trace cursor is active. This format setting also applies to stat plots.

When **ExprOn** is selected, the expression is displayed in the top-left corner of the graph screen.

When **ExprOff** and** CoordOn** both are selected, the number in the top-right corner specifies which function is being traced.

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Displaying Graphs

**Displaying a New Graph**

To display the graph of the selected function or functions, press . **TRACE**, **ZOOM** instructions, and **CALC** operations display the graph automatically. As the TI-83 Plus plots the graph, the busy indicator is on. As the graph is plotted, **X** and **Y** are updated.

**Pausing or Stopping a Graph**

While plotting a graph, you can pause or stop graphing.

Press to pause; then press to resume.

Press to stop; then press to redraw.

**Smart Graph**

Smart Graph is a TI-83 Plus feature that redisplays the last graph immediately when you press , but only if all graphing factors that would cause replotting have remained the same since the graph was last displayed.

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If you performed any of these actions since the graph was last displayed, the TI-83 Plus will replot the graph based on new values when you press s.

Changed a mode setting that affects graphs

Changed a function in the current picture

Selected or deselected a function or stat plot

Changed the value of a variable in a selected function

Changed a window variable or graph format setting

Cleared drawings by selecting **ClrDraw**

Changed a stat plot definition

**Overlaying Functions on a Graph**

On the TI-83 Plus, you can graph one or more new functions without replotting existing functions. For example, store **sin(X)** to **Y1** in the **Y= **editor and press . Then store **cos(X)** to **Y2** and press again. The function **Y2** is graphed on top of **Y1**, the original function.

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**Graphing a Family of Curves**

If you enter a list (Chapter 11) as an element in an expression, the TI-83 Plus plots the function for each value in the list, thereby graphing a family of curves. In **Simul** graphing-order mode, it graphs all functions sequentially for the first element in each list, and then for the second, and so on.

**{2,4,6}sin(X)** graphs three functions: **2 sin(X)**, **4 sin(X)**, and **6 sin(X)**.

**{2,4,6}sin({1,2,3}X)** graphs **2 sin(X)**,** 4 sin(2X)**, and** 6 sin(3X)**.

**Note:** When using more than one list, the lists must have the same dimensions.

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Exploring Graphs with the Free-Moving Cursor

**Free-Moving Cursor**

When a graph is displayed, press |, ~, }, or to move the cursor around the graph. When you first display the graph, no cursor is visible. When you press |, ~, }, or , the cursor moves from the center of the viewing window.

As you move the cursor around the graph, the coordinate values of the cursor location are displayed at the bottom of the screen if **CoordOn** format is selected. The **Float**/**Fix** decimal mode setting determines the number of decimal digits displayed for the coordinate values.

To display the graph with no cursor and no coordinate values, press or . When you press |, ~, }, or , the cursor moves from the same position.

**Graphing Accuracy**

The free-moving cursor moves from pixel to pixel on the screen. When you move the cursor to a pixel that appears to be on the function, the cursor may be near, but not actually on, the function. The coordinate

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value displayed at the bottom of the screen actually may not be a point on the function. To move the cursor along a function, use r.

The coordinate values displayed as you move the cursor approximate actual math coordinates, *accurate to within the width and height of the pixel. As **Xmin**, **Xmax**, **Ymin**, and **Ymax** get closer together (as in a **Zoom** **In**) graphing accuracy increases, and the coordinate values more closely approximate the math coordinates.

Free- moving cursor on the curve

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Exploring Graphs with TRACE

**Beginning a Trace**

Use **TRACE** to move the cursor from one plotted point to the next along a function. To begin a trace, press r. If the graph is not displayed already, press r to display it. The trace cursor is on the first selected function in the **Y= **editor, at the middle **X** value on the screen. The cursor coordinates are displayed at the bottom of the screen if **CoordOn** format is selected. The **Y= **expression is displayed in the top-left corner of the screen, if **ExprOn** format is selected.

**Moving the Trace Cursor**

**To move the TRACE cursor** **do this:**

To the previous or next plotted point, press | or ~.

Five plotted points on a function (**Xres** affects this), press y | or y ~.

To any valid **X** value on a function, enter a value, and then press .

From one function to another, press } or .

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When the trace cursor moves along a function, the **Y** value is calculated from the **X** value; that is, **Y**=**Y**n**(X)**. If the function is undefined at an **X** value, the **Y** value is blank.

If you move the trace cursor beyond the top or bottom of the screen, the coordinate values at the bottom of the screen continue to change appropriately.

**Moving the Trace Cursor from Function to Function**

To move the trace cursor from function to function, press and }. The cursor follows the order of the selected functions in the **Y=** editor. The trace cursor moves to each function at the same **X** value. If **ExprOn** format is selected, the expression is updated.

**Moving the Trace Cursor to Any Valid X Value**

To move the trace cursor to any valid **X** value on the current function, enter the value. When you enter the first digit, an **X=** prompt and the number you entered are displayed in the bottom-left corner of the screen. You can enter an expression at the **X=** prompt. The value must

Trace cursor on the curve

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be valid for the current viewing window. When you have completed the entry, press to move the cursor.

**Note:** This feature does not apply to stat plots.

**Panning to the Left or Right**

If you trace a function beyond the left or right side of the screen, the viewing window automatically pans to the left or right. **Xmin** and **Xmax** are updated to correspond to the new viewing window.

**Quick Zoom**

While tracing, you can press to adjust the viewing window so that the cursor location becomes the center of the new viewing window, even if the cursor is above or below the display. This allows panning up and down. After Quick Zoom, the cursor remains in **TRACE**.

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**Leaving and Returning to TRACE**

When you leave and return to **TRACE**, the trace cursor is displayed in the same location it was in when you left **TRACE**, unless Smart Graph has replotted the graph.

**Using TRACE in a Program**

On a blank line in the program editor, press r. The instruction **Trace** is pasted to the cursor location. When the instruction is encountered during program execution, the graph is displayed with the trace cursor on the first selected function. As you trace, the cursor coordinate values are updated. When you finish tracing the functions, press to resume program execution.

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Exploring Graphs with the ZOOM Instructions

**ZOOM Menu**

To display the **ZOOM** menu, press q. You can adjust the viewing window of the graph quickly in several ways. All **ZOOM** instructions are accessible from programs.

**ZOOM** ** MEMORY**

**1:ZBox** Draws a box to define the viewing window. **2:Zoom In** Magnifies the graph around the cursor. **3:Zoom Out** Views more of a graph around the cursor. **4:ZDecimal** Sets @**X** and @**Y** to 0.1. **5:ZSquare** Sets equal-size pixels on the **X** and **Y** axes. **6:ZStandard** Sets the standard window variables. **7:ZTrig** Sets the built-in trig window variables. **8:ZInteger** Sets integer values on the **X** and **Y** axes. **9:ZoomStat** Sets the values for current stat lists. **0:ZoomFit** Fits** YMin** and **YMax** between **XMin** and **XMax**.

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**Zoom Cursor**

When you select **1:ZBox**, **2:Zoom In**, or **3:Zoom Out**, the cursor on the graph becomes the zoom cursor (**+**), a smaller version of the free-moving cursor (**+**).

**ZBox**

To define a new viewing window using **ZBox**, follow these steps.

1. Select **1:ZBox** from the **ZOOM** menu. The zoom cursor is displayed at the center of the screen.

2. Move the zoom cursor to any spot you want to define as a corner of the box, and then press . When you move the cursor away from the first defined corner, a small, square dot indicates the spot.

3. Press |, }, ~, or . As you move the cursor, the sides of the box lengthen or shorten proportionately on the screen.

**Note:** To cancel **ZBox** before you press , press .

4. When you have defined the box, press to replot the graph.

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To use **ZBox** to define another box within the new graph, repeat steps 2 through 4. To cancel **ZBox**, press .

**Zoom In, Zoom Out**

**Zoom In** magnifies the part of the graph that surrounds the cursor location. **Zoom Out** displays a greater portion of the graph, centered on the cursor location. The **XFact** and **YFact** settings determine the extent of the zoom.

To zoom in on a graph, follow these steps.

1. Check **XFact** and **YFact**; change as needed.

2. Select **2:Zoom In** from the **ZOOM** menu. The zoom cursor is displayed.

3. Move the zoom cursor to the point that is to be the center of the new viewing window.

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4. Press . The TI-83 Plus adjusts the viewing window by **XFact** and **YFact**; updates the window variables; and replots the selected functions, centered on the cursor location.

5. Zoom in on the graph again in either of two ways.

To zoom in at the same point, press .

To zoom in at a new point, move the cursor to the point that you want as the center of the new viewing window, and then press .

To zoom out on a graph, select **3:Zoom Out** and repeat steps 3 through 5.

To cancel **Zoom In** or **Zoom Out**, press .

**ZDecimal**

**ZDecimal** replots the functions immediately. It updates the window variables to preset values, as shown below. These values set **@X** and **@Y** equal to **0.1** and set the **X** and **Y** value of each pixel to one decimal place.

**Xmin=L4.7** **Ymin=L3.1** **Xmax=4.7** **Ymax=3.1** **Xscl=1** **Yscl=1**

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**ZSquare**

**ZSquare** replots the functions immediately. It redefines the viewing window based on the current values of the window variables. It adjusts in only one direction so that **@X=@Y**, which makes the graph of a circle look like a circle. **Xscl** and **Yscl** remain unchanged. The midpoint of the current graph (not the intersection of the axes) becomes the midpoint of the new graph.

**ZStandard**

**ZStandard** replots the functions immediately. It updates the window variables to the standard values shown below.

**Xmin=L10** **Ymin=L10** **Xres=1** **Xmax=10** **Ymax=10** **Xscl=1** **Yscl=1**

**ZTrig**

**ZTrig** replots the functions immediately. It updates the window variables to preset values that are appropriate for plotting trig functions. Those preset values in **Radian** mode are shown below.

**Xmin=L(4724)p** **Ymin=L4** **Xmax=(4724)p** **Ymax=4** **Xscl=p/2** **Yscl=1**

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**ZInteger**

**ZInteger** redefines the viewing window to the dimensions shown below. To use **ZInteger**, move the cursor to the point that you want to be the center of the new window, and then press ; **ZInteger** replots the functions.

**@X=1** **Xscl=10** **@Y=1** **Yscl=10**

**ZoomStat**

**ZoomStat** redefines the viewing window so that all statistical data points are displayed. For regular and modified box plots, only **Xmin** and **Xmax** are adjusted.

**ZoomFit**

**ZoomFit** replots the functions immediately. **ZoomFit **recalculates **YMin** and **YMax** to include the minimum and maximum **Y** values of the selected functions between the current **XMin** and **XMax**. **XMin** and **XMax** are not changed.

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Using ZOOM MEMORY

**ZOOM MEMORY Menu**

To display the** ZOOM MEMORY** menu, press q ~.

**ZOOM** **MEMORY**

**1:** **ZPrevious** Uses the previous viewing window. **2:** **ZoomSto** Stores the user-defined window. **3:** **ZoomRcl** Recalls the user-defined window. **4:** **SetFactors...** Changes **Zoom In** and **Zoom Out** factors.

**ZPrevious**

**ZPrevious** replots the graph using the window variables of the graph that was displayed before you executed the last **ZOOM** instruction.

**ZoomSto**

**ZoomSto** immediately stores the current viewing window. The graph is displayed, and the values of the current window variables are stored in the user-defined **ZOOM** variables **ZXmin**, **ZXmax**, **ZXscl**, **ZYmin**, **ZYmax**, **ZYscl**, and **ZXres**.

These variables apply to all graphing modes. For example, changing the value of **ZXmin** in **Func** mode also changes it in **Par** mode.

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**ZoomRcl**

**ZoomRcl** graphs the selected functions in a user-defined viewing window. The user-defined viewing window is determined by the values stored with the **ZoomSto** instruction. The window variables are updated with the user-defined values, and the graph is plotted.

**ZOOM FACTORS**

The zoom factors, **XFact** and **YFact**, are positive numbers (not necessarily integers) greater than or equal to 1. They define the magnification or reduction factor used to **Zoom In** or **Zoom Out** around a point.

**Checking XFact and YFact**

To display the **ZOOM FACTORS** screen, where you can review the current values for **XFact** and **YFact**, select **4:SetFactors** from the **ZOOM MEMORY**

menu. The values shown are the defaults.

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**Changing XFact and YFact**

You can change **XFact** and **YFact** in either of two ways.

Enter a new value. The original value is cleared automatically when you enter the first digit.

Place the cursor on the digit you want to change, and then enter a value or press { to delete it.

**Using ZOOM MEMORY Menu Items from the Home Screen or a** **Program**

From the home screen or a program, you can store directly to any of the user-defined **ZOOM** variables.

From a program, you can select the **ZoomSto** and **ZoomRcl** instructions from the **ZOOM MEMORY** menu.

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Using the CALC (Calculate) Operations

**CALCULATE Menu**

To display the **CALCULATE** menu, press y CALC. Use the items on this menu to analyze the current graph functions.

**CALCULATE** **1:value** Calculates a function **Y** value for a given **X**. **2:zero** Finds a zero (x-intercept) of a function. **3:minimum** Finds a minimum of a function. **4:maximum** Finds a maximum of a function. **5:intersect** Finds an intersection of two functions. **6:dy/dx** Finds a numeric derivative of a function. **7:f(x)dx** Finds a numeric integral of a function.

**value**

**value** evaluates one or more currently selected functions for a specified value of **X**.

**Note:** When a value is displayed for **X**, press to clear the value. When no value is displayed, press to cancel the **value** operation.

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To evaluate a selected function at **X**, follow these steps.

1. Select **1:value** from the **CALCULATE** menu. The graph is displayed with **X=** in the bottom-left corner.

2. Enter a real value, which can be an expression, for **X** between **Xmin** and **Xmax**.

3. Press .

The cursor is on the first selected function in the **Y= **editor at the **X** value you entered, and the coordinates are displayed, even if **CoordOff** format is selected.

To move the cursor from function to function at the entered **X** value, press } or . To restore the free-moving cursor, press | or ~.

**zero**

**zero** finds a zero (x-intercept or root) of a function using **solve(**. Functions can have more than one x-intercept value; **zero** finds the zero closest to your guess.

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The time **zero** spends to find the correct zero value depends on the accuracy of the values you specify for the left and right bounds and the accuracy of your guess.

To find a zero of a function, follow these steps.

1. Select **2:zero** from the **CALCULATE** menu. The current graph is displayed with **Left Bound?** in the bottom-left corner.

2. Press } or to move the cursor onto the function for which you want to find a zero.

3. Press | or ~ (or enter a value) to select the x-value for the left bound of the interval, and then press . A **4** indicator on the graph screen shows the left bound. **Right Bound?** is displayed in the bottom-left corner. Press | or ~ (or enter a value) to select the x-value for the right bound, and then press . A **3** indicator on the graph screen shows the right bound. **Guess?** is then displayed in the bottom-left corner.

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4. Press | or ~ (or enter a value) to select a point near the zero of the function, between the bounds, and then press .

The cursor is on the solution and the coordinates are displayed, even if **CoordOff** format is selected. To move to the same x-value for other selected functions, press } or . To restore the free-moving cursor, press | or ~.

**minimum, maximum**

**minimum** and **maximum** find a minimum or maximum of a function within a specified interval to a tolerance of 1L5.

To find a minimum or maximum, follow these steps.

1. Select **3:minimum** or **4:maximum** from the **CALCULATE** menu. The current graph is displayed.

2. Select the function and set left bound, right bound, and guess as described for **zero**.

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The cursor is on the solution, and the coordinates are displayed, even if you have selected **CoordOff** format; **Minimum** or **Maximum** is displayed in the bottom-left corner.

To move to the same x-value for other selected functions, press } or . To restore the free-moving cursor, press | or ~.

**intersect**

**intersect** finds the coordinates of a point at which two or more functions intersect using **solve(**. The intersection must appear on the display to use **intersect**.

To find an intersection, follow these steps.

1. Select **5:intersect** from the **CALCULATE** menu. The current graph is displayed with **First curve?** in the bottom-left corner.

2. Press or }, if necessary, to move the cursor to the first function, and then press . **Second curve?** is displayed in the bottom-left corner.

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3. Press or }, if necessary, to move the cursor to the second function, and then press .

4. Press ~ or | to move the cursor to the point that is your guess as to location of the intersection, and then press .

The cursor is on the solution and the coordinates are displayed, even if **CoordOff** format is selected. **Intersection** is displayed in the bottom-left corner. To restore the free-moving cursor, press |, }, ~, or .

**dy/dx**

**dy/dx** (numerical derivative) finds the numerical derivative (slope) of a function at a point, with H=1L3.

To find a functions slope at a point, follow these steps.

1. Select **6:dy/dx** from the **CALCULATE** menu. The current graph is displayed.

2. Press } or to select the function for which you want to find the numerical derivative.

3. Press | or ~ (or enter a value) to select the **X** value at which to calculate the derivative, and then press .

The cursor is on the solution and the numerical derivative is displayed.

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To move to the same x-value for other selected functions, press } or . To restore the free-moving cursor, press | or ~.

**f(x)dx**

**f(x)dx** (numerical integral) finds the numerical integral of a function in a specified interval. It uses the **fnInt(** function, with a tolerance of H=1L3.

To find the numerical derivative of a function, follow these steps.

1. Select **7:f(x)dx** from the **CALCULATE** menu. The current graph is displayed with **Lower Limit?** in the bottom-left corner.

2. Press } or to move the cursor to the function for which you want to calculate the integral.

3. Set lower and upper limits as you would set left and right bounds for **zero**. The integral value is displayed, and the integrated area is shaded.

**Note:** The shaded area is a drawing. Use **ClrDraw** (Chapter 8) or any action that invokes Smart Graph to clear the shaded area.

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Chapter 4: Parametric Graphing

Getting Started: Path of a Ball

**Getting Started is a fast-paced introduction. Read the chapter for details.**

**Graph the parametric equation that describes the path of a ball hit at an initial** **speed of 30 meters per second, at an initial angle of 25 degrees with the** **horizontal from ground level. How far does the ball travel? When does it hit the** **ground? How high does it go? Ignore all forces except gravity.**

**For initial velocity v0 and angle q, the position of the ball as a function of time has** **horizontal and vertical components.**

**Horizontal:** **X1(t)=tv0cos(q)** **Vertical: Y1(t)=tv0sin(q)N ** **1** **2 gt2**

**The vertical and horizontal vectors of the balls motion also will be graphed.**

**Vertical vector:** **X2(t)=0** **Y2(t)=Y1(t)** **Horizontal vector:** **X3(t)=X1(t)** **Y3(t)=0** **Gravity constant:** **g=9.8 m/sec2**

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1. Press z. Press ~ to select **Par** mode. Press ~ to select **Simul** for simultaneous graphing of all three parametric equations in this example.

2. Press o. Press **30** **25** y ; **1** (to select ) to define **X1T** in terms of **T**.

3. Press **30** **25** y ; **1** **9.8** **2** to define **Y1T**.

The vertical component vector is defined by **X2T**

and **Y2T**.

4. Press **0** to define **X2T**.

5. Press ~ to display the **VARS Y.VARS** menu. Press **2** to display the **PARAMETRIC** secondary menu. Press **2** to define **Y2T**.

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The horizontal component vector is defined by **X3T** and **Y3T**.

6. Press ~ **2**, and then press** 1** to define **X3T**. Press **0** to define **Y3T**.

7. Press | | } to change the graph style to for **X3T** and **Y3T**. Press } to change the graph style to for **X2T** and **Y2T**. Press } to change the graph style to for **X1T** and **Y1T**. (These keystrokes assume that all graph styles were set to originally.)

8. Press p. Enter these values for the window variables.

**Tmin=0** **Xmin=L10** **Ymin=L5** **Tmax=5** **Xmax=100** **Ymax=15** **Tstep=.1** **Xscl=50** **Yscl=10**

9. Press y . ~ to set **AxesOff**, which turns off the axes.

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10.Press . The plotting action simultaneously shows the ball in flight and the vertical and horizontal component vectors of the motion.

**Tip:** To simulate the ball flying through the air, set graph style to (animate) for **X1T** and **Y1T**.

11.Press r to obtain numerical results and answer the questions at the beginning of this section.

Tracing begins at **Tmin** on the first parametric equation (**X1T** and **Y1T**). As you press ~ to trace the curve, the cursor follows the path of the ball over time. The values for **X** (distance), **Y** (height), and **T** (time) are displayed at the bottom of the screen.

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Defining and Displaying Parametric Graphs

** TI-83 Plus Graphing Mode Similarities**

The steps for defining a parametric graph are similar to the steps for defining a function graph. Chapter 4 assumes that you are familiar with Chapter 3: Function Graphing. Chapter 4 details aspects of parametric graphing that differ from function graphing.

**Setting Parametric Graphing Mode**

To display the mode screen, press z. To graph parametric equations, you must select **Par** graphing mode before you enter window variables and before you enter the components of parametric equations.

**Displaying the Parametric Y= Editor**

After selecting **Par** graphing mode, press o to display the parametric **Y=** editor.

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In this editor, you can display and enter both the **X** and **Y** components of up to six equations, **X1T** and **Y1T** through **X6T** and **Y6T**. Each is defined in terms of the independent variable **T**. A common application of parametric graphs is graphing equations over time.

**Selecting a Graph Style**

The icons to the left of **X1T** through **X6T** represent the graph style of each parametric equation (Chapter 3). The default in **Par** mode is (line), which connects plotted points. Line, (thick), (path), (animate), and (dot) styles are available for parametric graphing.

**Defining and Editing Parametric Equations**

To define or edit a parametric equation, follow the steps in Chapter 3 for defining a function or editing a function. The independent variable in a parametric equation is **T**. In **Par** graphing mode, you can enter the parametric variable **T** in either of two ways.

Press .

Press T.

Two components, **X** and **Y**, define a single parametric equation. You must define both of them.

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**Selecting and Deselecting Parametric Equations**

The TI-83 Plus graphs only the selected parametric equations. In the **Y=** editor, a parametric equation is selected when the **=** signs of both the **X** and **Y** components are highlighted. You may select any or all of the equations **X1T** and **Y1T** through **X6T** and **Y6T**.

To change the selection status, move the cursor onto the **=** sign of either the **X** or **Y** component and press . The status of both the **X **and **Y** components is changed.

**Setting Window Variables**

To display the window variable values, press p. These variables define the viewing window. The values below are defaults for **Par** graphing in **Radian** angle mode.

**Tmin=0** Smallest **T** value to evaluate **Tmax=6.2831853...** Largest **T** value to evaluate (2p) **Tstep=.1308996...** **T** value increment (p24) **Xmin=L10** Smallest **X** value to be displayed **Xmax=10** Largest **X** value to be displayed **Xscl=1** Spacing between the **X** tick marks **Ymin=L10** Smallest **Y** value to be displayed **Ymax=10** Largest **Y** value to be displayed **Yscl=1** Spacing between the **Y** tick marks

**Note:** To ensure that sufficient points are plotted, you may want to change the **T** window variables.

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**Setting the Graph Format**

To display the current graph format settings, press y .. Chapter 3 describes the format settings in detail. The other graphing modes share these format settings; **Seq** graphing mode has an additional axes format setting.

**Displaying a Graph**

When you press , the TI-83 Plus plots the selected parametric equations. It evaluates the **X** and **Y** components for each value of **T** (from **Tmin** to **Tmax** in intervals of **Tstep**), and then plots each point defined by **X** and **Y**. The window variables define the viewing window.

As the graph is plotted, **X**, **Y**, and **T** are updated.

Smart Graph applies to parametric graphs (Chapter 3).

**Window Variables and Y.VARS Menus**

You can perform these actions from the home screen or a program.

Access functions by using the name of the** X **or **Y** component of the equation as a variable.

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Store parametric equations.

Select or deselect parametric equations.

Store values directly to window variables.

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Exploring Parametric Graphs

**Free-Moving Cursor**

The free-moving cursor in **Par** graphing works the same as in **Func** graphing.

In **RectGC** format, moving the cursor updates the values of **X** and **Y**; if **CoordOn** format is selected, **X** and **Y** are displayed.

In **PolarGC** format, **X**, **Y**, **R**, and **q** are updated; if **CoordOn** format is selected, **R** and **q** are displayed.

**TRACE**

To activate **TRACE**, press r. When **TRACE** is active, you can move the trace cursor along the graph of the equation one **Tstep** at a time. When you begin a trace, the trace cursor is on the first selected function at **Tmin**. If **ExprOn** is selected, then the function is displayed.

In **RectGC** format, **TRACE** updates and displays the values of **X**, **Y**, and **T** if **CoordOn** format is on.

In **PolarGC** format, **X**, **Y**, **R**, **q** and **T** are updated; if **CoordOn** format is selected, **R**, **q**, and **T** are displayed. The **X** and **Y** (or **R** and **q**) values are calculated from **T**.

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To move five plotted points at a time on a function, press y | or y ~. If you move the cursor beyond the top or bottom of the screen, the coordinate values at the bottom of the screen continue to change appropriately.

Quick Zoom is available in **Par** graphing; panning is not (Chapter 3).

**Moving the Trace Cursor to Any Valid T Value**

To move the trace cursor to any valid **T** value on the current function, enter the number. When you enter the first digit, a **T=** prompt and the number you entered are displayed in the bottom-left corner of the screen. You can enter an expression at the **T=** prompt. The value must be valid for the current viewing window. When you have completed the entry, press to move the cursor.

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**ZOOM**

**ZOOM** operations in **Par** graphing work the same as in **Func** graphing. Only the **X** (**Xmin**, **Xmax**, and **Xscl**) and **Y** (**Ymin**, **Ymax**, and **Yscl**) window variables are affected.

The **T** window variables (**Tmin**, **Tmax**, and **Tstep**) are only affected when you select **ZStandard**. The **VARS ZOOM** secondary menu **ZT/Zq** items **1:ZTmin**, **2:ZTmax**, and **3:ZTstep** are the zoom memory variables for **Par** graphing.

**CALC**

**CALC** operations in **Par** graphing work the same as in **Func** graphing. The **CALCULATE** menu items available in **Par** graphing are **1:value**, **2:dy/dx**, **3:dy/dt**, and **4:dx/dt**.

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Chapter 5: Polar Graphing

Getting Started: Polar Rose

**Getting Started is a fast-paced introduction. Read the chapter for details.**

**The polar equation R=Asin(Bq) graphs a rose. Graph the rose for A=8 and B=2.5,** **and then explore the appearance of the rose for other values of A and B.**

1. Press z to display the mode screen. Press ~ ~ to select **Pol** graphing mode. Select the defaults (the options on the left) for the other mode settings.

2. Press o to display the polar **Y=** editor. Press **8** **2.5** to define **r1**.

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3. Press q **6** to select **6:ZStandard** and graph the equation in the standard viewing window. The graph shows only five petals of the rose, and the rose does not appear to be symmetrical. This is because the standard window sets **qmax=2p** and defines the window, rather than the pixels, as square.

4. Press p to display the window variables. Press **4** y B to increase the value of **qmax** to 4p.

5. Press q **5** to select **5:ZSquare** and plot the graph.

6. Repeat steps 2 through 5 with new values for the variables **A** and **B** in the polar equation **r1=Asin(Bq)**. Observe how the new values affect the graph.

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Defining and Displaying Polar Graphs

**TI-83 Plus Graphing Mode Similarities**

The steps for defining a polar graph are similar to the steps for defining a function graph. Chapter 5 assumes that you are familiar with Chapter 3: Function Graphing. Chapter 5 details aspects of polar graphing that differ from function graphing.

**Setting Polar Graphing Mode**

To display the mode screen, press z. To graph polar equations, you must select **Pol** graphing mode before you enter values for the window variables and before you enter polar equations.

**Displaying the Polar Y= Editor**

After selecting **Pol** graphing mode, press o to display the polar **Y=** editor.

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In this editor, you can enter and display up to six polar equations, **r1**

through **r6**. Each is defined in terms of the independent variable **q**.

**Selecting Graph Styles**

The icons to the left of **r1** through **r6** represent the graph style of each polar equation (Chapter 3). The default in **Pol** graphing mode is (line), which connects plotted points. Line, (thick), (path), (animate), and (dot) styles are available for polar graphing.

**Defining and Editing Polar Equations**

To define or edit a polar equation, follow the steps in Chapter 3 for defining a function or editing a function. The independent variable in a polar equation is **q**. In **Pol** graphing mode, you can enter the polar variable **q** in either of two ways.

Press .

Press q.

**Selecting and Deselecting Polar Equations**

The TI-83 Plus graphs only the selected polar equations. In the **Y=** editor, a polar equation is selected when the **=** sign is highlighted. You may select any or all of the equations.

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To change the selection status, move the cursor onto the **=** sign, and then press .

**Setting Window Variables**

To display the window variable values, press p. These variables define the viewing window. The values below are defaults for **Pol** graphing in **Radian** angle mode.

q**min=0** Smallest **q** value to evaluate q**max=6.2831853...** Largest **q** value to evaluate (2p) q**step=.1308996...** Increment between **q** values (p24) **Xmin=L10** Smallest **X** value to be displayed **Xmax=10** Largest **X** value to be displayed **Xscl=1** Spacing between the **X** tick marks **Ymin=L10** Smallest **Y** value to be displayed **Ymax=10** Largest **Y** value to be displayed **Yscl=1** Spacing between the **Y** tick marks

**Note:** To ensure that sufficient points are plotted, you may want to change the q window variables.

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**Setting the Graph Format**

To display the current graph format settings, press y .. Chapter 3 describes the format settings in detail. The other graphing modes share these format settings.

**Displaying a Graph**

When you press , the TI-83 Plus plots the selected polar equations. It evaluates **R** for each value of **q** (from **qmin** to **qmax** in intervals of **qstep**) and then plots each point. The window variables define the viewing window.

As the graph is plotted, **X**, **Y**, **R**, and **q** are updated.

Smart Graph applies to polar graphs (Chapter 3).

**Window Variables and Y.VARS Menus**

You can perform these actions from the home screen or a program.

Access functions by using the name of the equation as a variable.

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Store polar equations.

Select or deselect polar equations.

Store values directly to window variables.

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Exploring Polar Graphs

**Free-Moving Cursor**

The free-moving cursor in **Pol** graphing works the same as in **Func** graphing. In **RectGC** format, moving the cursor updates the values of **X** and **Y**; if **CoordOn** format is selected, **X** and **Y** are displayed. In **PolarGC** format, **X**, **Y**, **R**, and **q** are updated; if **CoordOn** format is selected, **R** and **q** are displayed.

**TRACE**

To activate **TRACE**, press r. When **TRACE** is active, you can move the trace cursor along the graph of the equation one **qstep** at a time. When you begin a trace, the trace cursor is on the first selected function at **qmin**. If **ExprOn** format is selected, then the equation is displayed.

In **RectGC** format, **TRACE** updates the values of **X**, **Y**, and **q**; if **CoordOn** format is selected, **X**, **Y**, and **q** are displayed. In **PolarGC** format, **TRACE**

updates **X**, **Y**, **R**, and **q**; if **CoordOn** format is selected, **R** and **q** are displayed.

To move five plotted points at a time on a function, press y | or y ~. If you move the trace cursor beyond the top or bottom of the

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screen, the coordinate values at the bottom of the screen continue to change appropriately.

Quick Zoom is available in **Pol** graphing mode; panning is not (Chapter 3).

**Moving the Trace Cursor to Any Valid q Value**

To move the trace cursor to any valid **q** value on the current function, enter the number. When you enter the first digit, a **q=** prompt and the number you entered are displayed in the bottom-left corner of the screen. You can enter an expression at the **q=** prompt. The value must be valid for the current viewing window. When you complete the entry, press to move the cursor.

**ZOOM**

**ZOOM** operations in **Pol** graphing work the same as in **Func** graphing. Only the **X** (**Xmin**, **Xmax**, and **Xscl**) and **Y** (**Ymin**, **Ymax**, and **Yscl**) window variables are affected.

The **q **window variables (**qmin**, **qmax**, and** qstep**) are not affected, except when you select **ZStandard**. The **VARS ZOOM** secondary menu **ZT/Zq** items **4:Zqmin**, **5:Zqmax**, and **6:Zqstep** are zoom memory variables for **Pol** graphing.

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**CALC**

**CALC** operations in **Pol** graphing work the same as in **Func** graphing. The **CALCULATE** menu items available in **Pol** graphing are **1:value**, **2:dy/dx**, and **3:dr/dq**.

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Chapter 6: Sequence Graphing

Getting Started: Forest and Trees

**Getting Started is a fast-paced introduction. Read the chapter for details.**

**A small forest of 4,000 trees is under a new forestry plan. Each year 20 percent of** **the trees will be harvested and 1,000 new trees will be planted. Will the forest** **eventually disappear? Will the forest size stabilize? If so, in how many years and** **with how many trees?**

1. Press z. Press ~ ~ ~ to select **Seq** graphing mode.

2. Press y . and select **Time** axes format and **ExprOn** format if necessary.

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3. Press o. If the graph-style icon is not (dot), press | |, press until is displayed, and then press ~ ~.

4. Press ~ **3** to select **iPart(** (integer part) because only whole trees are harvested. After each annual harvest, 80 percent (.80) of the trees remain.

Press **8** y [u] **1** to define the number of trees after each harvest. Press **1000** to define the new trees. Press **4000** to define the number of trees at the beginning of the program.

5. Press p **0** to set **nMin=0**. Press **50** to set **nMax=50**. **nMin** and **nMax** evaluate forest size over 50 years. Set the other window variables.

**PlotStart=1** **Xmin=0** **Ymin=0** **PlotStep=1** **Xmax=50** **Ymax=6000**

**Xscl=10** **Yscl=1000**

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6. Press r. Tracing begins at **nMin** (the start of the forestry plan). Press ~ to trace the sequence year by year. The sequence is displayed at the top of the screen. The values for **n** (number of years), **X** (**X=n**, because **n** is plotted on the x-axis), and **Y** (tree count) are displayed at the bottom. When will the forest stabilize? With how many trees?

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Defining and Displaying Sequence Graphs

**TI-83 Plus Graphing Mode Similarities**

The steps for defining a sequence graph are similar to the steps for defining a function graph. Chapter 6 assumes that you are familiar with Chapter 3: Function Graphing. Chapter 6 details aspects of sequence graphing that differ from function graphing.

**Setting Sequence Graphing Mode**

To display the mode screen, press z. To graph sequence functions, you must select **Seq** graphing mode before you enter window variables and before you enter sequence functions.

Sequence graphs automatically plot in **Simul** mode, regardless of the current plotting-order mode setting.

** TI-83 Plus Sequence Functions u, v, and w**

The TI-83 Plus has three sequence functions that you can enter from the keyboard: **u**, **v**, and **w**. They are above the , , and keys.

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You can define sequence functions in terms of:

The independent variable **n**

The previous term in the sequence function, such as **u(nN1)**

The term that precedes the previous term in the sequence function, such as **u(nN2)**

The previous term or the term that precedes the previous term in another sequence function, such as **u(nN1)** or **u(nN2)** referenced in the sequence **v(n)**.

**Note:** Statements in this chapter about **u(n)** are also true for **v(n)** and **w(n)**; statements about **u(nN1)** are also true for **v(nN1)** and **w(nN1)**; statements about **u(nN2)** are also true for **v(nN2)** and **w(nN2)**.

**Displaying the Sequence Y= Editor**

After selecting **Seq** mode, press o to display the sequence **Y=** editor.

In this editor, you can display and enter sequences for **u(n)**, **v(n)**, and **w(n)**. Also, you can edit the value for **nMin**, which is the sequence window variable that defines the minimum **n** value to evaluate.

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The sequence **Y=** editor displays the **nMin** value because of its relevance to **u(nMin)**, **v(nMin)**, and **w(nMin)**, which are the initial values for the sequence equations **u(n)**, **v(n)**, and **w(n)**, respectively.

**nMin** in the** Y=** editor is the same as **nMin** in the window editor. If you enter a new value for **nMin** in one editor, the new value for **nMin** is updated in both editors.

**Note:** Use **u(nMin)**, **v(nMin)**, or **w(nMin)** only with a recursive sequence, which requires an initial value.

**Selecting Graph Styles**

The icons to the left of **u(n)**, **v(n)**, and **w(n)** represent the graph style of each sequence (Chapter 3). The default in **Seq** mode is (dot), which shows discrete values. Dot, (line), and (thick) styles are available for sequence graphing. Graph styles are ignored in **Web** format.

**Selecting and Deselecting Sequence Functions**

The TI-83 Plus graphs only the selected sequence functions. In the **Y=** editor, a sequence function is selected when the **=** signs of both **u(n)=** and **u(nMin)=** are highlighted.

To change the selection status of a sequence function, move the cursor onto the **=** sign of the function name, and then press . The status is changed for both the sequence function **u(n)** and its initial value **u(nMin)**.

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**Defining and Editing a Sequence Function**

To define or edit a sequence function, follow the steps in Chapter 3 for defining a function. The independent variable in a sequence is **n**.

In **Seq** graphing mode, you can enter the sequence variable in either of two ways.

Press .

Press y N [N].

You can enter the function name from the keyboard.

To enter the function name **u**, press y [u] (above ).

To enter the function name **v**, press y [v] (above ).

To enter the function name **w**, press y [w] (above ).

Generally, sequences are either nonrecursive or recursive. Sequences are evaluated only at consecutive integer values. **n** is always a series of consecutive integers, starting at zero or any positive integer.

**Nonrecursive Sequences**

In a nonrecursive sequence, the **n**th term is a function of the independent variable **n**. Each term is independent of all other terms.

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For example, in the nonrecursive sequence below, you can calculate **u(5)** directly, without first calculating **u(1)** or any previous term.

The sequence equation above returns the sequence **2**, **4**, **6**, **8**, **10**, for **n** = **1**, **2**,** 3**, **4**, **5**, ** .**

**Note:** You may leave blank the initial value **u(nMin)** when calculating nonrecursive sequences.

**Recursive Sequences**

In a recursive sequence, the **n**th term in the sequence is defined in relation to the previous term or the term that precedes the previous term, represented by **u(nN1)** and **u(nN2)**. A recursive sequence may also be defined in relation to **n**, as in **u(n)=u(nN1)+n.**

For example, in the sequence below you cannot calculate **u(5)** without first calculating **u(1)**, **u(2)**, **u(3)**, and **u(4)**.

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Using an initial value **u(nMin) = 1**, the sequence above returns **1**, **2**, **4**, **8**, **16**, . . .

**Tip:** On the TI-83 Plus, you must type each character of the terms. For example, to enter **u(nN1)**, press y [u] .

Recursive sequences require an initial value or values, since they reference undefined terms.

If each term in the sequence is defined in relation to the previous term, as in **u(nN1)**, you must specify an initial value for the first term.

If each term in the sequence is defined in relation to the term that precedes the previous term, as in **u(nN2)**, you must specify initial values for the first two terms. Enter the initial values as a list enclosed in braces ({ }) with commas separating the values.

The value of the first term is 0 and the value of the second term is 1 for the sequence **u(n)**.

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**Setting Window Variables**

To display the window variables, press p. These variables define the viewing window. The values below are defaults for **Seq** graphing in both **Radian** and **Degree** angle modes.

**nMin=1** Smallest **n** value to evaluate **nMax=10** Largest **n** value to evaluate **PlotStart=1** First term number to be plotted **PlotStep=1** Incremental **n** value (for graphing only) **Xmin=L10** Smallest **X** value to be displayed **Xmax=10** Largest **X** value to be displayed **Xscl=1** Spacing between the **X** tick marks **Ymin=L10** Smallest **Y** value to be displayed **Ymax=10** Largest **Y** value to be displayed **Yscl=1** Spacing between the **Y** tick marks

**nMin** must be an integer 0. **nMax**, **PlotStart**, and **PlotStep** must be integers 1.

**nMin** is the smallest **n** value to evaluate. **nMin** also is displayed in the sequence **Y=** editor. **nMax** is the largest **n** value to evaluate. Sequences are evaluated at **u(nMin)**, **u(nMin+1)**, **u(nMin+2)** , . . . , **u(nMax)**.

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**PlotStart** is the first term to be plotted. **PlotStart=1** begins plotting on the first term in the sequence. If you want plotting to begin with the fifth term in a sequence, for example, set **PlotStart=5**. The first four terms are evaluated but are not plotted on the graph.

**PlotStep** is the incremental **n** value for graphing only. **PlotStep** does not affect sequence evaluation; it only designates which points are plotted on the graph. If you specify **PlotStep=2**, the sequence is evaluated at each consecutive integer, but it is plotted on the graph only at every other integer.

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Selecting Axes Combinations

**Setting the Graph Format**

To display the current graph format settings, press y .. Chapter 3 describes the format settings in detail. The other graphing modes share these format settings. The axes setting on the top line of the screen is available only in **Seq** mode.

**Time** **Webuv** **vw** **uw** Type of sequence plot (axes) **RectGC** ** PolarGC** Rectangular or polar output **CoordOn** ** CoordOff** Cursor coordinate display on/off **GridOff** ** GridOn** Grid display off or on **AxesOn** ** AxesOff** Axes display on or off **LabelOff** ** LabelOn** Axes label display off or on **ExprOn** ** ExprOff** Expression display on or off

**Setting Axes Format**

For sequence graphing, you can select from five axes formats. The table below shows the values that are plotted on the x-axis and y-axis for each axes setting.

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**Axes Setting** **x-axis** **y-axis**

**Time** **n** **u(n)**, **v(n)**, **w(n)**

**Web** **u(nN1)**, **v(nN1)**, **w(nN1)** **u(n)**, **v(n)**, **w(n)**

**uv** **u(n)** **v(n)**

**vw** **v(n)** **w(n)**

**uw** **u(n)** **w(n)**

**Displaying a Sequence Graph**

To plot the selected sequence functions, press . As a graph is plotted, the TI-83 Plus updates **X**, **Y**, and **n**.

Smart Graph applies to sequence graphs (Chapter 3).

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Exploring Sequence Graphs

**Free-Moving Cursor**

The free-moving cursor in **Seq** graphing works the same as in **Func** graphing. In **RectGC** format, moving the cursor updates the values of **X** and **Y**; if **CoordOn** format is selected, **X** and **Y** are displayed. In **PolarGC** format, **X**, **Y**, **R**, and **q** are updated; if **CoordOn** format is selected, **R** and **q** are displayed.

**TRACE**

The axes format setting affects **TRACE**.

When **Time**, **uv**, **vw**, or **uw** axes format is selected, **TRACE** moves the cursor along the sequence one **PlotStep** increment at a time. To move five plotted points at once, press y ~ or y |.

When you begin a trace, the trace cursor is on the first selected sequence at the term number specified by **PlotStart**, even if it is outside the viewing window.

Quick Zoom applies to all directions. To center the viewing window on the current cursor location after you have moved the trace cursor, press . The trace cursor returns to **nMin**.

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In **Web** format, the trail of the cursor helps identify points with attracting and repelling behavior in the sequence. When you begin a trace, the cursor is on the x-axis at the initial value of the first selected function.

**Tip:** To move the cursor to a specified **n** during a trace, enter a value for **n**, and press . For example, to quickly return the cursor to the beginning of the sequence, paste **nMin** to the **n=** prompt and press .

**Moving the Trace Cursor to Any Valid n Value**

To move the trace cursor to any valid **n** value on the current function, enter the number. When you enter the first digit, an **n =** prompt and the number you entered are displayed in the bottom-left corner of the screen. You can enter an expression at the **n =** prompt. The value must be valid for the current viewing window. When you have completed the entry, press to move the cursor.

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**ZOOM**

**ZOOM** operations in **Seq** graphing work the same as in **Func** graphing. Only the **X** (**Xmin**, **Xmax**, and **Xscl**) and **Y** (**Ymin**, **Ymax**, and **Yscl**) window variables are affected.

**PlotStart**, **PlotStep**, **nMin**, and **nMax** are only affected when you select **ZStandard**. The **VARS Zoom** secondary menu **ZU** items **1** through **7** are the **ZOOM MEMORY** variables for **Seq** graphing.

**CALC**

The only **CALC** operation available in **Seq **graphing is** value**.

When **Time** axes format is selected, **value** displays **Y** (the **u(n)** value) for a specified **n** value.

When **Web** axes format is selected, **value** draws the web and displays **Y** (the **u(n)** value) for a specified **n** value.

When **uv**, **vw**, or **uw** axes format is selected, **value** displays **X** and **Y** according to the axes format setting. For example, for **uv** axes format, **X** represents **u(n)** and **Y** represents **v(n)**.

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**Evaluating u, v, and w**

To enter the sequence names **u**, **v,** or **w**, press y [u], [v], or [w]. You can evaluate these names in any of three ways.

Calculate the nth value in a sequence.

Calculate a list of values in a sequence.

Generate a sequence with **u(***nstart***,***nstop***[,***nstep***])**. *nstep* is optional; default is 1.

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Graphing Web Plots

**Graphing a Web Plot**

To select **Web** axes format, press y . ~ . A web plot graphs **u(n)** versus **u(nN1)**, which you can use to study long-term behavior (convergence, divergence, or oscillation) of a recursive sequence. You can see how the sequence may change behavior as its initial value changes.

**Valid Functions for Web Plots**

When **Web** axes format is selected, a sequence will not graph properly or will generate an error.

It must be recursive with only one recursion level (**u(nN1)** but not **u(nN2)**).

It cannot reference **n** directly.

It cannot reference any defined sequence except itself.

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**Displaying the Graph Screen**

In **Web** format, press to display the graph screen. The TI-83 Plus:

Draws a **y=x** reference line in **AxesOn** format.

Plots the selected sequences with **u(nN1)** as the independent variable.

**Note:** A potential convergence point occurs whenever a sequence intersects the y=x reference line. However, the sequence may or may not actually converge at that point, depending on the sequences initial value.

**Drawing the Web**

To activate the trace cursor, press r. The screen displays the sequence and the current **n**, **X**, and **Y** values (**X** represents **u(nN1)** and **Y** represents **u(n)**). Press ~ repeatedly to draw the web step by step, starting at **nMin**. In **Web** format, the trace cursor follows this course.

1. It starts on the x-axis at the initial value **u(nMin)** (when **PlotStart=1**).

2. It moves vertically (up or down) to the sequence.

3. It moves horizontally to the **y=x** reference line.

4. It repeats this vertical and horizontal movement as you continue to press ~.

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Using Web Plots to Illustrate Convergence

**Example: Convergence**

1. Press o in **Seq** mode to display the sequence **Y=** editor. Make sure the graph style is set to (dot), and then define **nMin**, **u(n)** and **u(nMin)** as shown below.

2. Press y . to set **Time** axes format.

3. Press p and set the variables as shown below. **nMin=1** **Xmin=0** **Ymin=L10** **nMax=25** **Xmax=25** **Ymax=10** **PlotStart=1** **Xscl=1** **Yscl=1** **PlotStep=1**

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4. Press to graph the sequence.

5. Press y . and select the **Web** axes setting.

6. Press p and change the variables below. **Xmin=L10** **Xmax=10**

7. Press to graph the sequence.

8. Press r, and then press ~ to draw the web. The displayed cursor coordinates **n**, **X** (**u(nN1)**), and **Y** (**u(n)**) change accordingly. When you press ~, a new **n** value is displayed, and the trace cursor is on the sequence. When you press ~ again, the **n** value remains the same, and the cursor moves to the **y=x** reference line. This pattern repeats as you trace the web.

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Graphing Phase Plots

**Graphing with uv, vw, and uw**

The phase-plot axes settings **uv**, **vw**, and **uw** show relationships between two sequences. To select a phase-plot axes setting, press y ., press ~ until the cursor is on **uv**,** vw**, or **uw**, and then press .

**Axes Setting** **x-axis** **y-axis**

**uv** **u(n)** **v(n)**

**vw** **v(n)** **w(n)**

**uw** **u(n)** **w(n)**

**Example: Predator-Prey Model**

Use the predator-prey model to determine the regional populations of a predator and its prey that would maintain population equilibrium for the two species.

This example uses the model to determine the equilibrium populations of foxes and rabbits, with initial populations of 200 rabbits (**u(nMin)**) and 50 foxes (**v(nMin)**).

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These are the variables (given values are in parentheses):

R = number of rabbits M = rabbit population growth rate without foxes (.05) K = rabbit population death rate with foxes (.001) W = number of foxes G = fox population growth rate with rabbits (.0002) D = fox population death rate without rabbits (.03) **n** = time (in months) Rn = RnN1(1+MNKWnN1) Wn = WnN1(1+GRnN1ND)

1. Press o in **Seq** mode to display the sequence **Y=** editor. Define the sequences and initial values for Rn and Wn as shown below. Enter the sequence Rn as **u(n)** and enter the sequence Wn as **v(n)**.

2. Press y . to select **Time** axes format.

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3. Press p and set the variables as shown below. **nMin=0** **Xmin=0** **Ymin=0** **nMax=400** **Xmax=400** **Ymax=300** **PlotStart=1** **Xscl=100** **Yscl=100** **PlotStep=1**

4. Press to graph the sequence.

5. Press r ~ to individually trace the number of rabbits (**u(n)**) and foxes (**v(n)**) over time (**n**).

**Tip:** Press a number, and then press to jump to a specific **n** value (month) while in **TRACE**.

6. Press y . ~ ~ to select **uv** axes format.

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7. Press p and change these variables as shown below. **Xmin=84** **Ymin=25** **Xmax=237** **Ymax=75** **Xscl=50** **Yscl=10**

8. Press r. Trace both the number of rabbits (**X**) and the number of foxes (**Y**) through 400 generations.

**Note:** When you press r, the equation for **u** is displayed in the top-left corner. Press } or to see the equation for **v**.

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Comparing TI-83 Plus and TI-82 Sequence Variables

**Sequences and Window Variables**

Refer to the table if you are familiar with the TI-82. It shows TI-83 Plus sequences and sequence window variables, as well as their TI-82 counterparts.

**TI-83 Plus** **TI.82**

In the **Y=** editor:

**u(n)** **Un**

**u(nMin)** **UnStart **(window variable)

**v(n)** **Vn**

**v(nMin)** **VnStart **(window variable)

**w(n)** not available

**w(nMin)** not available

In the window editor:

**nMin** **nStart**

**nMax** **nMax**

**PlotStart** **nMin**

**PlotStep** not available

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Keystroke Differences Between TI-83 Plus and TI-82

**Sequence Keystroke Changes**

Refer to the table if you are familiar with the TI-82. It compares TI-83 Plus sequence-name syntax and variable syntax with TI.82 sequence-name syntax and variable syntax.

**TI-83 Plus / TI-82** **On TI-83 Plus, press:** **On TI-82, press:**

**n / n** y [n]

**u(n)** **/** **Un** y [u]

y

**v(n) / Vn** y [v]

y

**w(n)** y [w]

not available

**u(nN1) / UnN1** y [u]

y

**v(nN1) / VnN1** y [v]

y

**w(nN1)** y [w]

not available

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Chapter 7: Tables

Getting Started: Roots of a Function **Getting Started is a fast-paced introduction. Read the chapter for details.**

**Evaluate the function Y = X3 N 2X at each integer between L10 and 10. How many** **sign changes occur, and at what X values?**

1. Press z to set **Func** graphing mode.

2. Press o. Press **3** to select **3**. Then press **2** to enter the function **Y1=X3N2X**.

3. Press y - to display the **TABLE SETUP**

screen. Press **10** to set **TblStart=L10**. Press **1** to set **@Tbl=1**.

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Press to select **Indpnt: Auto** (automatically generated independent values). Press to select **Depend: Auto** (automatically generated dependent values).

4. Press y 0 to display the table screen.

5. Press until you see the sign changes in the value of **Y1**. How many sign changes occur, and at what **X** values?

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Setting Up the Table

**TABLE SETUP Screen**

To display the **TABLE SETUP** screen, press y -.

**TblStart, @Tbl**

**TblStart** (table start) defines the initial value for the independent variable. **TblStart** applies only when the independent variable is generated automatically (when** Indpnt: Auto** is selected).

**@Tbl** (table step) defines the increment for the independent variable.

**Note:** In **Seq** mode, both** TblStart** and **@Tbl** must be integers.

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**Indpnt: Auto, Indpnt: Ask, Depend: Auto, Depend: Ask**

**Selections** **Table Characteristics**

**Indpnt: Auto** **Depend: Auto**

Values are displayed automatically in both the independent-variable column and in all dependent- variable columns.

**Indpnt: Ask** **Depend: Auto**

The table is empty; when you enter a value for the independent variable, all corresponding dependent- variable values are calculated and displayed automatically.

**Indpnt: Auto** **Depend: Ask**

Values are displayed automatically for the independent variable; to generate a value for a dependent variable, move the cursor to that cell and press .

**Indpnt: Ask** **Depend: Ask**

The table is empty; enter values for the independent variable; to generate a value for a dependent variable, move the cursor to that cell and press .

**Setting Up the Table from the Home Screen or a Program**

To store a value to **TblStart**, **@Tbl**, or **TblZnput** from the home screen or a program, select the variable name from the **VARS TABLE** secondary menu. **TblZnput** is a list of independent-variable values in the current table.

When you press y - in the program editor, you can select **IndpntAuto**, **IndpntAsk**, **DependAuto**, and **DependAsk**.

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Defining the Dependent Variables

**Defining Dependent Variables from the Y= Editor**

In the **Y=** editor, enter the functions that define the dependent variables. Only functions that are selected in the **Y=** editor are displayed in the table. The current graphing mode is used. In **Par** mode, you must define both components of each parametric equation (Chapter 4).

**Editing Dependent Variables from the Table Editor**

To edit a selected **Y=** function from the table editor, follow these steps.

1. Press y 0 to display the table, then press ~ or | to move the cursor to a dependent-variable column.

2. Press } until the cursor is on the function name at the top of the column. The function is displayed on the bottom line.

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3. Press . The cursor moves to the bottom line. Edit the function.

4. Press or . The new values are calculated. The table and the **Y=** function are updated automatically.

**Note:** You also can use this feature to view the function that defines a dependent variable without having to leave the table.

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Displaying the Table

**The Table**

To display the table, press y 0.

Current cell

Independent-variable values in the first column

Dependent-variable values in the second and third columns

Current cells full value

**Note:** The table abbreviates the values, if necessary.

**Independent and Dependent Variables**

The current graphing mode determines which independent and dependent variables are displayed in the table (Chapter 1). In the table above, for example, the independent variable **X** and the dependent variables **Y1** and **Y2** are displayed because **Func** graphing mode is set.

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**Graphing Mode** **Independent Variable** **Dependent Variable**

**Func** (function) **X** **Y1** through **Y9**, and **Y0**

**Par** (parametric) **T** **X1T**/**Y1T** through **X6T**/**Y6T**

**Pol** (polar) **q** **r1** through **r6**

**Seq** (sequence) **n** **u(n)**, **v(n)**, and **w(n)**

**Clearing the Table from the Home Screen or a Program**

From the home screen, select the **ClrTable** instruction from the **CATALOG**. To clear the table, press .

From a program, select **9:ClrTable** from the **PRGM I/O** menu or from the **CATALOG**. The table is cleared upon execution. If **IndpntAsk** is selected, all independent and dependent variable values on the table are cleared. If **DependAsk** is selected, all dependent variable values on the table are cleared.

**Scrolling Independent-Variable Values**

If **Indpnt: Auto** is selected, you can press } and in the independent- variable column to display more values. As you scroll the column, the corresponding dependent-variable values also are displayed. All dependent-variable values may not be displayed if **Depend: Ask** is selected.

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**Note:** You can scroll back from the value entered for **TblStart**. As you scroll, **TblStart** is updated automatically to the value shown on the top line of the table. In the example above, **TblStart=0** and **@Tbl=1** generates and displays values of **X=0**, , **6**; but you can press } to scroll back and display the table for **X=M1**, , **5**.

**Displaying Other Dependent Variables**

If you have defined more than two dependent variables, the first two selected **Y=** functions are displayed initially. Press ~ or | to display dependent variables defined by other selected **Y=** functions. The independent variable always remains in the left column, except during a trace with **Par** graphing mode and **G.T** split-screen mode set.

**Tip:** To simultaneously display two dependent variables on the table that are not defined as consecutive Y= functions, go to the Y= editor and deselect the Y= functions between the two you want to display. For example, to simultaneously display **Y4** and **Y7** on the table, go to the Y= editor and deselect **Y5** and **Y6**.

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Chapter 8: Draw Instructions

Getting Started: Drawing a Tangent Line

**Getting Started is a fast-paced introduction. Read the chapter for details.**

**Suppose you want to find the equation of the tangent line at X = 2/2 for the** **function Y = sin(X).**

Before you begin, select **Radian** and **Func** mode from the mode screen, if necessary.

1. Press o to display the **Y=** editor. Press to store **sin(X)** in **Y1**.

2. Press q **7 **to select **7:ZTrig**, which graphs the equation in the Zoom Trig window.

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3. Press y < **5** to select **5:Tangent(**. The tangent instruction is initiated.

4. Press y C **2** **2**.

5. Press . The tangent line is drawn; the **X** value and the tangent-line equation are displayed on the graph.

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Using the DRAW Menu

**DRAW Menu**

To display the **DRAW** menu, press y <. The TI-83 Pluss interpretation of these instructions depends on whether you accessed the menu from the home screen or the program editor or directly from a graph.

**DRAW** ** POINTS STO**

**1:ClrDraw** Clears all drawn elements. **2:Line(** Draws a line segment between 2 points. **3:Horizontal** Draws a horizontal line. **4:Vertical** Draws a vertical line. **5:Tangent(** Draws a line segment tangent to a function. **6:DrawF** Draws a function. **7:Shade(** Shades an area between two functions. **8:DrawInv** Draws the inverse of a function. **9:Circle(** Draws a circle. **0:Text(** Draws text on a graph screen. **A:Pen** Activates the free-form drawing tool.

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**Before Drawing on a Graph**

The **DRAW** instructions draw on top of graphs. Therefore, before you use the **DRAW** instructions, consider whether you want to perform one or more of the following actions.

Change the mode settings on the mode screen.

Change the format settings on the format screen.

Enter or edit functions in the **Y=** editor.

Select or deselect functions in the **Y=** editor.

Change the window variable values.

Turn stat plots on or off.

Clear existing drawings with **ClrDraw**.

**Note:** If you draw on a graph and then perform any of the actions listed above, the graph is replotted without the drawings when you display the graph again.

**Drawing on a Graph**

You can use any **DRAW** menu instructions except **DrawInv** to draw on **Func**, **Par**, **Pol**, and **Seq** graphs. **DrawInv** is valid only in **Func** graphing. The coordinates for all **DRAW** instructions are the displays x-coordinate and y-coordinate values.

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You can use most **DRAW** menu and **DRAW POINTS** menu instructions to draw directly on a graph, using the cursor to identify the coordinates. You also can execute these instructions from the home screen or from within a program. If a graph is not displayed when you select a **DRAW**

menu instruction, the home screen is displayed.

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Clearing Drawings

**Clearing Drawings When a Graph Is Displayed**

All points, lines, and shading drawn on a graph with **DRAW** instructions are temporary.

To clear drawings from the currently displayed graph, select **1:ClrDraw** from the **DRAW** menu. The current graph is replotted and displayed with no drawn elements.

**Clearing Drawings from the Home Screen or a Program**

To clear drawings on a graph from the home screen or a program, begin on a blank line on the home screen or in the program editor. Select **1:ClrDraw** from the **DRAW** menu. The instruction is copied to the cursor location. Press .

When **ClrDraw** is executed, it clears all drawings from the current graph and displays the message **Done**. When you display the graph again, all drawn points, lines, circles, and shaded areas will be gone.

**Note:** Before you clear drawings, you can store them with **StorePic**.

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Drawing Line Segments

**Drawing a Line Segment Directly on a Graph**

To draw a line segment when a graph is displayed, follow these steps.

1. Select **2:Line(** from the **DRAW** menu.

2. Place the cursor on the point where you want the line segment to begin, and then press .

3. Move the cursor to the point where you want the line segment to end. The line is displayed as you move the cursor. Press .

To continue drawing line segments, repeat steps 2 and 3. To cancel **Line(**, press .

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**Drawing a Line Segment from the Home Screen or a Program**

**Line(** also draws a line segment between the coordinates (*X1,Y1*) and (*X2,Y2*). The values may be entered as expressions.

**Line(***X1,Y1,X2,Y2***)**

To erase a line segment, enter **Line(***X1,Y1,X2,Y2,***0)**

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Drawing Horizontal and Vertical Lines

**Drawing a Line Directly on a Graph**

To draw a horizontal or vertical line when a graph is displayed, follow these steps.

1. Select **3:Horizontal** or **4:Vertical** from the **DRAW** menu. A line is displayed that moves as you move the cursor.

2. Place the cursor on the y-coordinate (for horizontal lines) or x-coordinate (for vertical lines) through which you want the drawn line to pass.

3. Press to draw the line on the graph.

To continue drawing lines, repeat steps 2 and 3.

To cancel **Horizontal** or **Vertical**, press .

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**Drawing a Line from the Home Screen or a Program**

**Horizontal** (horizontal line) draws a horizontal line at **Y=***y*.* y* can be an expression but not a list.

**Horizontal** *y*

**Vertical** (vertical line) draws a vertical line at **X**=*x*.* x* can be an expression but not a list.

**Vertical** *x*

To instruct the TI-83 Plus to draw more than one horizontal or vertical line, separate each instruction with a colon ( **:** ).

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Drawing Tangent Lines

**Drawing a Tangent Line Directly on a Graph**

To draw a tangent line when a graph is displayed, follow these steps.

1. Select **5:Tangent(** from the **DRAW** menu.

2. Press and } to move the cursor to the function for which you want to draw the tangent line. The current graphs **Y=** function is displayed in the top-left corner, if **ExprOn** is selected.

3. Press ~ and | or enter a number to select the point on the function at which you want to draw the tangent line.

4. Press . In **Func** mode, the **X** value at which the tangent line was drawn is displayed on the bottom of the screen, along with the equation of the tangent line. In all other modes, the **dy/dx** value is displayed.

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**Tip:** Change the fixed decimal setting on the mode screen if you want to see fewer digits displayed for **X** and the equation for **Y**.

**Drawing a Tangent Line from the Home Screen or a Program**

**Tangent(** (tangent line) draws a line tangent to *expression* in terms of **X**, such as **Y1** or **X2**, at point **X**=*value*.* ***X** can be an expression. *expression* is interpreted as being in **Func** mode.

**Tangent(***expression***,***value***)**

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Drawing Functions and Inverses

**Drawing a Function**

**DrawF** (draw function) draws *expression* as a function in terms of **X** on the current graph. When you select **6:DrawF** from the **DRAW** menu, the TI-83 Plus returns to the home screen or the program editor. **DrawF** is not interactive.

**DrawF** *expression*

**Note:** You cannot use a list in *expression* to draw a family of curves.

**Drawing an Inverse of a Function**

**DrawInv** (draw inverse) draws the inverse of *expression* by plotting **X** values on the y-axis and **Y** values on the x-axis. When you select **8:DrawInv** from the **DRAW** menu, the TI-83 Plus returns to the home screen or the program editor. **DrawInv** is not interactive. **DrawInv** works in **Func** mode only.

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**DrawInv** *expression*

**Note:** You cannot use a list in *expression* to draw a family of curves.

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Shading Areas on a Graph

**Shading a Graph**

To shade an area on a graph, select **7:Shade(** from the **DRAW** menu. The instruction is pasted to the home screen or to the program editor.

**Shade(** draws *lowerfunc* and *upperfunc* in terms of **X** on the current graph and shades the area that is specifically above *lowerfunc* and below *upperfunc*. Only the areas where *lowerfunc* < *upperfunc* are shaded.

*Xleft* and *Xright*, if included, specify left and right boundaries for the shading. *Xleft* and *Xright* must be numbers between **Xmin** and **Xmax**, which are the defaults.

*pattern* specifies one of four shading patterns.

*pattern*=**1** vertical (default) *pattern*=**2** horizontal *pattern*=**3** negativeslope 45 *pattern*=**4** positiveslope 45

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*patres* specifies one of eight shading resolutions.

*patres*=**1** shades every pixel (default) *patres*=**2** shades every second pixel *patres*=**3** shades every third pixel *patres*=**4** shades every fourth pixel *patres*=**5** shades every fifth pixel *patres*=**6** shades every sixth pixel *patres*=**7** shades every seventh pixel *patres*=**8** shades every eighth pixel

**Shade(***lowerfunc,upperfunc[,Xleft,Xright,pattern,patres*]**)**

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Drawing Circles

**Drawing a Circle Directly on a Graph**

To draw a circle directly on a displayed graph using the cursor, follow these steps.

1. Select **9:Circle(** from the **DRAW** menu.

2. Place the cursor at the center of the circle you want to draw. Press .

3. Move the cursor to a point on the circumference. Press to draw the circle on the graph.

**Note:** This circle is displayed as circular, regardless of the window variable values, because you drew it directly on the display. When you use the **Circle(** instruction from the home screen or a program, the current window variables may distort the shape.

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To continue drawing circles, repeat steps 2 and 3. To cancel **Circle(**, press .

**Drawing a Circle from the Home Screen or a Program**

**Circle(** draws a circle with center (*X,Y*) and *radius. *These values can be expressions.

**Circle(***X,Y,radius***)**

**Tip:** When you use **Circle( **on the home screen or from a program, the current window values may distort the drawn circle. Use **ZSquare** (Chapter 3) before drawing the circle to adjust the window variables and make the circle circular.

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Placing Text on a Graph

**Placing Text Directly on a Graph**

To place text on a graph when the graph is displayed, follow these steps.

1. Select **0:Text( **from the **DRAW** menu.

2. Place the cursor where you want the text to begin.

3. Enter the characters. Press or y 7 to enter letters and q. You may enter TI-83 Plus functions, variables, and instructions. The font is proportional, so the exact number of characters you can place on the graph varies. As you type, the characters are placed on top of the graph.

To cancel **Text(**, press .

**Placing Text on a Graph from the Home Screen or a Program**

**Text(** places on the current graph the characters comprising *value*, which can include TI-83 Plus functions and instructions. The top-left corner of the first character is at pixel (*row,column*), where *row* is an integer between 0 and 57 and *column* is an integer between 0 and 94. Both *row* and *column* can be expressions.

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**Text(***row,column,value,value***)**

*value* can be text enclosed in quotation marks ( **"** ), or it can be an expression. The TI-83 Plus will evaluate an expression and display the result with up to 10 characters.

**Split Screen**

On a **Horiz** split screen, the maximum value for *row* is 25. On a **G.T** split screen, the maximum value for *row* is 45, and the maximum value for *column* is 46.

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Using Pen to Draw on a Graph

**Using Pen to Draw on a Graph**

**Pen** draws directly on a graph only. You cannot execute **Pen** from the home screen or a program.

To draw on a displayed graph, follow these steps.

1. Select **A:Pen** from the **DRAW** menu.

2. Place the cursor on the point where you want to begin drawing. Press to turn on the pen.

3. Move the cursor. As you move the cursor, you draw on the graph, shading one pixel at a time.

4. Press to turn off the pen.

For example, **Pen** was used to create the arrow pointing to the local minimum of the selected function.

Note: To continue drawing on the graph, move the cursor to a new position where you want to begin drawing again, and then repeat steps 2, 3, and 4. To cancel **Pen**, press .

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Drawing Points on a Graph

**DRAW POINTS Menu**

To display the **DRAW POINTS** menu, press y < ~. The TI-83 Pluss interpretation of these instructions depends on whether you accessed this menu from the home screen or the program editor or directly from a graph.

**DRAW** **POINTS** ** STO** **1:Pt-On(** Turns on a point. **2:Pt-Off(** Turns off a point. **3:Pt-Change(** Toggles a point on or off. **4:Pxl-On(** Turns on a pixel. **5:Pxl-Off(** Turns off a pixel. **6:Pxl-Change(** Toggles a pixel on or off. **7:pxl-Test(** Returns 1 if pixel on, 0 if pixel off.

**Drawing Points Directly on a Graph with Pt**.**On(**

To draw a point on a graph, follow these steps.

1. Select **1:Pt.On(** from the** DRAW POINTS** menu.

2. Move the cursor to the position where you want to draw the point.

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3. Press to draw the point.

To continue drawing points, repeat steps 2 and 3. To cancel **Pt.On(**, press .

**Erasing Points with Pt.Off(**

To erase (turn off) a drawn point on a graph, follow these steps.

1. Select **2:Pt.Off(** (point off) from the** DRAW POINTS** menu.

2. Move the cursor to the point you want to erase.

3. Press to erase the point.

To continue erasing points, repeat steps 2 and 3. To cancel **Pt.Off(**, press .

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**Changing Points with Pt.Change(**

To change (toggle on or off) a point on a graph, follow these steps.

1. Select **3:Pt.Change(** (point change) from the** DRAW POINTS** menu.

2. Move the cursor to the point you want to change.

3. Press to change the points on/off status.

To continue changing points, repeat steps 2 and 3. To cancel **Pt.Change(**, press .

**Drawing Points from the Home Screen or a Program**

**Pt.On(** (point on) turns on the point at (**X**=*x*,**Y=***y*). **Pt.Off(** turns the point off. **Pt.Change(** toggles the point on or off. *mark* is optional; it determines the points appearance; specify **1**, **2**, or **3**, where:

**1** = (dot; default) **2** = (box) **3** = **+** (cross)

**Pt.On(***x,y[,mark*]**)** **Pt.Off(***x,y[,mark*]**)** **Pt.Change(***x,y***)**

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**Note:** If you specified *mark* to turn on a point with **Pt.On(**, you must specify *mark* when you turn off the point with** Pt.Off(. Pt.Change(** does not have the *mark* option.

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Drawing Pixels

** TI-83 Plus Pixels**

A pixel is a square dot on the TI-83 Plus display. The **Pxl.** (pixel) instructions let you turn on, turn off, or reverse a pixel (dot) on the graph using the cursor. When you select a pixel instruction from the **DRAW**

**POINTS** menu, the TI-83 Plus returns to the home screen or the program editor. The pixel instructions are not interactive.

**Turning On and Off Pixels with Pxl.On( and Pxl.Off(**

**Pxl.On(** (pixel on) turns on the pixel at (*row*,*column*), where *row* is an integer between 0 and 62 and *column* is an integer between 0 and 94.

**Pxl.Off(** turns the pixel off. **Pxl.Change(** toggles the pixel on and off.

**Pxl.On(***row,column***)** **Pxl.Off(***row,column***)** **Pxl.Change(***row,column***)**

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**Using pxl.Test(**

**pxl.Test(** (pixel test) returns 1 if the pixel at (*row,column*) is turned on or 0 if the pixel is turned off on the current graph. *row* must be an integer between 0 and 62. *column* must be an integer between 0 and 94.

**pxl.Test(***row***,***column***)**

**Split Screen**

On a **Horiz** split screen, the maximum value for *row* is 30 for **Pxl.On(**, **Pxl.Off(**, **Pxl.Change(**, and **pxl.Test(**.

On a **G.T** split screen, the maximum value for *row* is 50 and the maximum value for *column* is 46 for **Pxl.On(**, **Pxl.Off(**, **Pxl.Change(**, and **pxl.Test(**.

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Storing Graph Pictures (Pic)

**DRAW STO Menu**

To display the **DRAW STO** menu, press y < |. When you select an instruction from the** DRAW STO **menu, the TI-83 Plus returns to the home screen or the program editor. The picture and graph database instructions are not interactive.

**DRAW POINTS** **STO**

**1:** **StorePic** Stores the current picture. **2:** **RecallPic** Recalls a saved picture. **3:** **StoreGDB** Stores the current graph database. **4:** **RecallGDB** Recalls a saved graph database.

**Storing a Graph Picture**

You can store up to 10 graph pictures, each of which is an image of the current graph display, in picture variables **Pic1** through **Pic9**, or **Pic0**. Later, you can superimpose the stored picture onto a displayed graph from the home screen or a program.

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A picture includes drawn elements, plotted functions, axes, and tick marks. The picture does not include axes labels, lower and upper bound indicators, prompts, or cursor coordinates. Any parts of the display hidden by these items are stored with the picture.

To store a graph picture, follow these steps.

1. Select **1:StorePic **from the **DRAW STO** menu. **StorePic** is pasted to the current cursor location.

2. Enter the number (from **1** to **9**, or **0**) of the picture variable to which you want to store the picture. For example, if you enter **3**, the TI-83 Plus will store the picture to **Pic3**.

**Note: **You also can select a variable from the **PICTURE **secondary menu ( **4**). The variable is pasted next to **StorePic.**

3. Press to display the current graph and store the picture.

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Recalling Graph Pictures (Pic)

**Recalling a Graph Picture**

To recall a graph picture, follow these steps.

1. Select **2:RecallPic** from the **DRAW STO** menu. **RecallPic** is pasted to the current cursor location.

2. Enter the number (from **1** to **9**, or **0**) of the picture variable from which you want to recall a picture. For example, if you enter **3**, the TI-83 Plus will recall the picture stored to **Pic3**.

**Note: **You also can select a variable from the **PICTURE **secondary menu ( **4**). The variable is pasted next to **RecallPic**.

3. Press to display the current graph with the picture superimposed on it.

**Note:** Pictures are drawings. You cannot trace a curve that is part of a picture.

**Deleting a Graph Picture**

To delete graph pictures from memory, use the **MEMORY MANAGEMENT** **/DELETE **secondary menu(Chapter 18).

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Storing Graph Databases (GDB)

**What Is a Graph Database?**

A graph database (**GDB**) contains the set of elements that defines a particular graph. You can recreate the graph from these elements. You can store up to 10 **GDB**s in variables **GDB1** through **GDB9**, or **GDB0** and recall them to recreate graphs.

A **GDB** stores five elements of a graph.

Graphing mode Window variables Format settings All functions in the **Y=** editor and the selection status of each Graph style for each **Y= **function

**GDB**s do not contain drawn items or stat plot definitions.

**Storing a Graph Database**

To store a graph database, follow these steps.

1. Select **3:StoreGDB** from the **DRAW STO** menu. **StoreGDB** is pasted to the current cursor location.

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2. Enter the number (from **1** to **9**, or **0**) of the **GDB** variable to which you want to store the graph database. For example, if you enter **7**, the TI-83 Plus will store the **GDB** to **GDB7**.

**Note: **You also can select a variable from the **GDB** secondary menu ( **3**). The variable is pasted next to **StoreGDB.**

3. Press to store the current database to the specified **GDB**

variable.

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Recalling Graph Databases (GDB)

**Recalling a Graph Database**

**CAUTION:** When you recall a **GDB**, it replaces all existing **Y=** functions. Consider storing the current **Y=** functions to another database before recalling a stored **GDB**.

To recall a graph database, follow these steps.

1. Select **4:RecallGDB** from the **DRAW STO** menu. **RecallGDB** is pasted to the current cursor location.

2. Enter the number (from **1** to **9**, or **0**) of the **GDB** variable from which you want to recall a **GDB**. For example, if you enter **7**, the TI-83 Plus will recall the **GDB** stored to **GDB7**.

**Note: **You also can select a variable from the **GDB** secondary menu ( **3**). The variable is pasted next to **RecallGDB.**

3. Press to replace the current **GDB** with the recalled **GDB**. The new graph is not plotted. The TI-83 Plus changes the graphing mode automatically, if necessary.

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**Deleting a Graph Database**

To delete a **GDB** from memory, use the **MEMORY MANAGEMENT/DELETE** secondary menu (Chapter 18).

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Chapter 9: Split Screen

Getting Started: Exploring the Unit Circle

**Getting Started is a fast-paced introduction. Read the chapter for details.**

**Use** **G.T (graph-table) split-screen mode to explore the unit circle and its** **relationship to the numeric values for the commonly used trigonometric angles** **of 0****, 30****, 45****, 60****, 90****, and so on.**

1. Press z to display the mode screen. Press ~ to select **Degree **mode. Press ~ to select **Par** (parametric) graphing mode.

Press ~ ~ to select **G.T** (graph-table) split-screen mode.

2. Press y. to display the format screen. Press ~ to select **ExprOff**.

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3. Press o to display the **Y=** editor for **Par** graphing mode. Press to store **cos(T)** to **X1T**. Press to store **sin(T)** to **Y1T**.

4. Press p to display the window editor. Enter these values for the window variables.

**Tmin=0** **Xmin=L2.3** **Ymin=L2.5** **Tmax=360** **Xmax=2.3** **Ymax=2.5** **Tstep=15** **Xscl=1** **Yscl=1**

5. Press r. On the left, the unit circle is graphed parametrically in **Degree** mode and the trace cursor is activated. When **T=0** (from the graph trace coordinates), you can see from the table on the right that the value of **X1T** (**cos(T)**) is **1** and **Y1T** (**sin(T)**) is **0**. Press ~ to move the cursor to the next 15 angle increment. As you trace around the circle in steps of 15, an approximation of the standard value for each angle is highlighted in the table.

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Using Split Screen

**Setting a Split-Screen Mode**

To set a split-screen mode, press z, and then move the cursor to the bottom line of the mode screen.

Select **Horiz** (horizontal) to display the graph screen and another screen split horizontally.

Select **G.T** (graph-table) to display the graph screen and table screen split vertically.

$ $

The split screen is activated when you press any key that applies to either half of the split screen.

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Some screens are never displayed as split screens. For example, if you press z in **Horiz** or **G.T** mode, the mode screen is displayed as a full screen. If you then press a key that displays either half of a split screen, such as r, the split screen returns.

When you press a key or key combination in either **Horiz** or **G.T** mode, the cursor is placed in the half of the display for which that key applies. For example, if you press r, the cursor is placed in the half in which the graph is displayed. If you press y 0, the cursor is placed in the half in which the table is displayed.

The TI-83 Plus will remain in split-screen mode until you change back to **Full** screen mode.

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Horiz (Horizontal) Split Screen

**Horiz Mode**

In** Horiz** (horizontal) split-screen mode, a horizontal line splits the screen into top and bottom halves.

The top half displays the graph.

The bottom half displays any of these editors.

Home screen (four lines)

**Y=** editor (four lines)

Stat list editor (two rows)

Window editor (three settings)

Table editor (two rows)

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**Moving from Half to Half in Horiz Mode**

To use the top half of the split screen:

Press or .

Select a **ZOOM** or **CALC** operation.

To use the bottom half of the split screen:

Press any key or key combination that displays the home screen.

Press o (**Y=** editor).

Press (stat list editor).

Press p (window editor).

Press y 0 (table editor).

**Full Screens in Horiz Mode**

All other screens are displayed as full screens in **Horiz** split-screen mode.

To return to the **Horiz** split screen from a full screen when in **Horiz** mode, press any key or key combination that displays the graph, home screen, **Y=** editor, stat list editor, window editor, or table editor.

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G**.**T (Graph-Table) Split Screen

**G.T Mode**

In **G.T** (graph-table) split-screen mode, a vertical line splits the screen into left and right halves.

The left half displays the graph.

The right half displays the table.

**Moving from Half to Half in G.T Mode**

To use the left half of the split screen:

Press or .

Select a **ZOOM** or **CALC** operation.

To use the right half of the split screen, press y 0.

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**Using r in G.T Mode**

As you move the trace cursor along a graph in the split screens left half in **G.T** mode, the table on the right half automatically scrolls to match the current cursor values.

**Note:** When you trace in **Par** graphing mode, both components of an equation (**XnT** and **YnT**) are displayed in the two columns of the table. As you trace, the current value of the independent variable **T** is displayed on the graph.

**Full Screens in G.T Mode**

All screens other than the graph and the table are displayed as full screens in **G.T** split-screen mode.

To return to the **G.T** split screen from a full screen when in **G.T** mode, press any key or key combination that displays the graph or the table.

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TI-83 Plus Pixels in Horiz and G**.**T Modes

**TI-83 Plus Pixels in Horiz and G.T Modes**

**Note:** Each set of numbers in parentheses above represents the row and column of a corner pixel, which is turned on.

**DRAW POINTS Menu Pixel Instructions**

For **Pxl.On(**, **Pxl.Off(**, **Pxl.Change(**, and **pxl.Test(**:

In **Horiz** mode, *row* must be {30; *column* must be {94.

In **G.T** mode, *row* must be {50; *column* must be {46.

**Pxl.On(***row***,***column***)**

**DRAW Menu Text( Instruction**

For the **Text(** instruction:

In **Horiz** mode, *row* must be {25; *column* must be {94.

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In **G.T** mode, *row* must be {45; *column* must be {46.

**Text(***row,column,"text"***)**

**PRGM I/O Menu Output( Instruction**

For the **Output(** instruction:

In **Horiz** mode, *row* must be {4; *column* must be {16.

In **G.T** mode, *row* must be {8; *column* must be {16.

**Output(***row***,***column***,"***text***")**

**Setting a Split-Screen Mode from the Home Screen or a Program**

To set **Horiz** or **G.T** from a program, follow these steps.

1. Press z while the cursor is on a blank line in the program editor.

2. Select **Horiz** or **G.T**.

The instruction is pasted to the cursor location. The mode is set when the instruction is encountered during program execution. It remains in effect after execution.

**Note:** You also can paste **Horiz** or **G.T** to the home screen or program editor from the **CATALOG** (Chapter 15).

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Chapter 10: Matrices

Getting Started: Systems of Linear Equations

**Getting Started is a fast-paced introduction. Read the chapter for details.**

**Find the solution of X + 2Y + 3Z = 3 and 2X + 3Y + 4Z = 3. On the TI-83 Plus, you** **can solve a system of linear equations by entering the coefficients as elements in** **a matrix, and then using rref( to obtain the reduced row-echelon form.**

1. Press y >. Press ~ ~ to display the **MATRX EDIT** menu. Press **1** to select **1: [A]**

2. Press **2** **4** to define a 24 matrix. The rectangular cursor indicates the current element. Ellipses (**...**) indicate additional columns beyond the screen.

3. Press **1** to enter the first element. The rectangular cursor moves to the second column of the first row.

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4. Press **2** **3** **3** to complete the first row for X + 2Y + 3Z = 3.

5. Press **2** **3** **4** **3** to enter the second row for 2X + 3Y + 4Z = 3.

6. Press y 5 to return to the home screen. If necessary, press to clear the home screen. Press y > ~ to display the **MATRX MATH** menu. Press } to wrap to the end of the menu. Select **B:rref(** to copy **rref(** to the home screen.

7. Press y > **1** to select **1: [A]** from the **MATRX NAMES** menu. Press . The reduced row-echelon form of the matrix is displayed and stored in **Ans**.

1X N 1Z = L3 therefore X = L3 + Z 1Y + 2Z = 3 therefore Y = 3 N 2Z

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Defining a Matrix

**What Is a Matrix?**

A matrix is a two-dimensional array. You can display, define, or edit a matrix in the matrix editor. The TI-83 Plus has 10 matrix variables, **[A]** through **[J]**. You can define a matrix directly in an expression. A matrix, depending on available memory, may have up to 99 rows or columns. You can store only real numbers in TI-83 Plus matrices.

**Selecting a Matrix**

Before you can define or display a matrix in the editor, you first must select the matrix name. To do so, follow these steps.

1. Press y > | to display the **MATRX EDIT** menu. The dimensions of any previously defined matrices are displayed.

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2. Select the matrix you want to define. The **MATRX EDIT** screen is displayed.

**Accepting or Changing Matrix Dimensions**

The dimensions of the matrix (*row* *column*) are displayed on the top line. The dimensions of a new matrix are **1 1**. You must accept or change the dimensions each time you edit a matrix. When you select a matrix to define, the cursor highlights the row dimension.

To accept the row dimension, press .

To change the row dimension, enter the number of rows (up to **99**), and then press .

The cursor moves to the column dimension, which you must accept or change the same way you accepted or changed the row dimension. When you press , the rectangular cursor moves to the first matrix element.

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Viewing and Editing Matrix Elements

**Displaying Matrix Elements**

After you have set the dimensions of the matrix, you can view the matrix and enter values for the matrix elements. In a new matrix, all values are zero.

Select the matrix from the **MATRX EDIT** menu and enter or accept the dimensions. The center portion of the matrix editor displays up to seven rows and three columns of a matrix, showing the values of the elements in abbreviated form if necessary. The full value of the current element, which is indicated by the rectangular cursor, is displayed on the bottom line.

This is an 8 4 matrix. Ellipses in the left or right column indicate additional columns. **#** or **$** in the right column indicate additional rows.

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**Deleting a Matrix**

To delete matrices from memory, use the **MEMORY MANAGEMENT/DELETE**

secondary menu (Chapter 18).

**Viewing a Matrix**

The matrix editor has two contexts, viewing and editing. In viewing context, you can use the cursor keys to move quickly from one matrix element to the next. The full value of the highlighted element is displayed on the bottom line.

Select the matrix from the **MATRX EDIT** menu, and then enter or accept the dimensions.

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**Viewing-Context Keys**

**Key** **Function**

| or ~ Moves the rectangular cursor within the current row

or } Moves the rectangular cursor within the current column; on the top row, } moves the cursor to the column dimension; on the column dimension, } moves the cursor to the row dimension

Switches to editing context; activates the edit cursor on the bottom line

Switches to editing context; clears the value on the bottom line

Any entry character Switches to editing context; clears the value on the bottom line; copies the character to the bottom line

y 6 Nothing

{ Nothing

**Editing a Matrix Element**

In editing context, an edit cursor is active on the bottom line. To edit a matrix element value, follow these steps.

1. Select the matrix from the **MATRX EDIT** menu, and then enter or accept the dimensions.

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2. Press |, }, ~, and to move the cursor to the matrix element you want to change.

3. Switch to editing context by pressing , , or an entry key.

4. Change the value of the matrix element using the editing-context keys described below. You may enter an expression, which is evaluated when you leave editing context.

**Note:** You can press to restore the value at the rectangular cursor if you make a mistake.

5. Press , }, or to move to another element.

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**Editing-Context Keys**

**Key** **Function**

| or ~ Moves the edit cursor within the value

or } Stores the value displayed on the bottom line to the matrix element; switches to viewing context and moves the rectangular cursor within the column

Stores the value displayed on the bottom line to the matrix element; switches to viewing context and moves the rectangular cursor to the next row element

Clears the value on the bottom line

Any entry character Copies the character to the location of the edit cursor on the bottom line

y 6 Activates the insert cursor

{ Deletes the character under the edit cursor on the bottom line

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Using Matrices with Expressions

**Using a Matrix in an Expression**

To use a matrix in an expression, you can do any of the following.

Copy the name from the **MATRX NAMES** menu.

Recall the contents of the matrix into the expression with y K (Chapter 1).

Enter the matrix directly (see below).

**Entering a Matrix in an Expression**

You can enter, edit, and store a matrix in the matrix editor. You also can enter a matrix directly in an expression.

To enter a matrix in an expression, follow these steps.

1. Press y [ **[** ] to indicate the beginning of the matrix.

2. Press y [ **[** ] to indicate the beginning of a row.

3. Enter a value, which can be an expression, for each element in the row. Separate the values with commas.

4. Press y [ **]** ] to indicate the end of a row.

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5. Repeat steps 2 through 4 to enter all of the rows.

6. Press y [ **]** ] to indicate the end of the matrix.

**Note:** The closing **]]** are not necessary at the end of an expression or preceding **!**.

The resulting matrix is displayed in the form:

**[[***element1,1***,**...**,***element1,n***],**...**,[***elementm,1***,**...**,***elementm,n***]]**

Any expressions are evaluated when the entry is executed.

**Note:** The commas that you must enter to separate elements are not displayed on output.

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Displaying and Copying Matrices

**Displaying a Matrix**

To display the contents of a matrix on the home screen, select the matrix from the **MATRX NAMES** menu, and then press .

Ellipses in the left or right column indicate additional columns. **#** or **$** in the right column indicate additional rows. Press ~, |, , and } to scroll the matrix.

**Copying One Matrix to Another**

To copy a matrix, follow these steps.

1. Press y > to display the **MATRX NAMES** menu.

2. Select the name of the matrix you want to copy.

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3. Press .

4. Press y > again and select the name of the new matrix to which you want to copy the existing matrix.

5. Press to copy the matrix to the new matrix name.

**Accessing a Matrix Element**

On the home screen or from within a program, you can store a value to, or recall a value from, a matrix element. The element must be within the currently defined matrix dimensions. Select *matrix* from the **MATRX NAMES**

menu.

**[***matrix***](***row***,***column***)**

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Using Math Functions with Matrices

**Using Math Functions with Matrices**

You can use many of the math functions on the TI-83 Plus keyboard, the **MATH** menu, the **MATH NUM** menu, and the **MATH TEST** menu with matrices. However, the dimensions must be appropriate. Each of the functions below creates a new matrix; the original matrix remains the same.

**+ (Add), (Subtract), ** **(Multiply)**

To add () or subtract () matrices, the dimensions must be the same. The answer is a matrix in which the elements are the sum or difference of the individual corresponding elements.

*matrixA***+***matrixB* *matrixA***N***matrixB*

To multiply () two matrices together, the column dimension of *matrixA* must match the row dimension of *matrixB*.

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*matrixA**matrixB*

Multiplying a *matrix* by a *value* or a *value* by a *matrix* returns a matrix in which each element of *matrix* is multiplied by *value*.

*matrix**value* *value**matrix*

**L (Negation)**

Negating a matrix () returns a matrix in which the sign of every element is changed (reversed).

**L***matrix*

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**abs(**

**abs(** (absolute value, **MATH NUM** menu) returns a matrix containing the absolute value of each element of *matrix*.

**abs(***matrix***)**

**round(**

**round(** (**MATH NUM** menu) returns a matrix. It rounds every element in *matrix* to #*decimals* ( 9). If *#decimals* is omitted, the elements are rounded to 10 digits.

**round(***matrix*[**,***#decimals*]**)**

**M1 (Inverse)**

Use the **L1** function () to invert a matrix (**^L1** is not valid). *matrix* must be square. The determinant cannot equal zero.

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*matrix***L1**

**Powers**

To raise a matrix to a power, *matrix* must be square. You can use **2** (), **3** (**MATH** menu), or **^***power* () for integer *power* between **0** and **255**.

*matrix***2**

*matrix***3**

*matrix***^***power*

**Relational Operations**

To compare two matrices using the relational operations **=** and (**TEST**

menu), they must have the same dimensions. **=** and compare *matrixA* and *matrixB* on an element-by-element basis. The other relational operations are not valid with matrices.

*matrixA***=***matrixB* returns **1** if every comparison is true; it returns **0** if any comparison is false.

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*matrixA**matrixB* returns **1** if at least one comparison is false; it returns **0** if no comparison is false.

**iPart(, fPart(, int(**

**iPart(** (integer part), **fPart(** (fractional part), and **int(** (greatest integer) are on the **MATH NUM** menu.

**iPart(** returns a matrix containing the integer part of each element of *matrix*.

**fPart(** returns a matrix containing the fractional part of each element of *matrix*.

**int(** returns a matrix containing the greatest integer of each element of *matrix*.

**iPart(***matrix***)** **fPart(***matrix***)** **int(***matrix***)**

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Using the MATRX MATH Operations

**MATRX MATH Menu**

To display the **MATRX MATH** menu, press y > ~.

**NAMES** **MATH** ** EDIT** **1:** **det(** Calculates the determinant. **2:** **T** Transposes the matrix. **3:** **dim(** Returns the matrix dimensions. **4:** **Fill(** Fills all elements with a constant. **5:** **identity(** Returns the identity matrix. **6:** **randM(** Returns a random matrix. **7:** **augment(** Appends two matrices. **8:** **Matr4list(** Stores a matrix to a list. **9:** **List4matr(** Stores a list to a matrix. **0:** **c*msum(** Returns the cumulative sums of a matrix. **A:** **ref(** Returns the row-echelon form of a matrix. **B:** **rref(** Returns the reduced row-echelon form. **C:** **rowSwap(** Swaps two rows of a matrix. **D:** **row+(** Adds two rows; stores in the second row. **E:** **row(** Multiplies the row by a number. **F:** **row+(** Multiplies the row, adds to the second row.

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**det(**

**det(** (determinant) returns the determinant (a real number) of a square *matrix*.

**det(***matrix***)**

**T (Transpose)**

**T** (transpose) returns a matrix in which each element (row, column) is swapped with the corresponding element (column, row) of *matrix*.

*matrix***T**

**Accessing Matrix Dimensions with dim(**

**dim(** (dimension) returns a list containing the dimensions (**{***rows**columns***}**) of *matrix*.

**dim(***matrix***)**

**Note:** **dim(***matrix***)!L**n**:L**n**(1)** returns the number of rows. **dim(***matrix***)!L***n***:L***n***(2)** returns the number of columns.

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**Creating a Matrix with dim(**

Use** dim(** with to create a new *matrixname* of dimensions *rows* *columns* with **0** as each element.

**{***rows***,***columns***}!dim(***matrixname***)**

**Redimensioning a Matrix with dim(**

Use **dim(** with to redimension an existing *matrixname* to dimensions *rows * *columns*. The elements in the old *matrixname* that are within the new dimensions are not changed. Additional created elements are zeros. Matrix elements that are outside the new dimensions are deleted.

**{***rows***,***columns***}!dim(***matrixname***)**

**Fill(**

**Fill(** stores *value* to every element in *matrixname*.

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**Fill(***value***,***matrixname***)**

**identity(**

**identity(** returns the identity matrix of *dimension* rows *dimension* columns.

**identity(***dimension***)**

**randM(**

**randM(** (create random matrix) returns a *rows* *columns* random matrix of integers L9 and 9. The seed value stored to the **rand** function controls the values (Chapter 2).

**randM(***rows***,***columns***)**

**augment(**

**augment(** appends *matrixA* to *matrixB* as new columns. *matrixA* and *matrixB* both must have the same number of rows.

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**augment(***matrixA***,***matrixB***)**

**Matr4list(**

**Matr4list(** (matrix stored to list) fills each *listname* with elements from each column in *matrix*. **Matr4list(** ignores extra *listname* arguments. Likewise, **Matr4list(** ignores extra *matrix* columns.

**Matr4list(***matrix***,***listnameA***,**...,*listname n***)**

&

**Matr4list(** also fills a *listname* with elements from a specified *column#* in *matrix*. To fill a list with a specific column from *matrix*, you must enter *column#* after *matrix*.

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**Matr4list(***matrix***,***column#***,***listname***)**

&

**List4matr(**

**List4matr(** (lists stored to matrix) fills *matrixname* column by column with the elements from each *list*. If dimensions of all *lists* are not equal, **List4matr(** fills each extra *matrixname* row with **0**. Complex lists are not valid.

**List4matr(***listA***,**...,*list n***,***matrixname***)**

&

**c*msum(**

**c*msum(** returns cumulative sums of the elements in *matrix*, starting with the first element. Each element is the cumulative sum of the column from top to bottom.

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**c*msum(***matrix***)**

**Row Operations**

**MATRX MATH** menu items **A** through **F** are row operations. You can use a row operation in an expression. Row operations do not change *matrix* in memory. You can enter all row numbers and values as expressions. You can select the matrix from the **MATRX NAMES** menu.

**ref(, rref(**

**ref(** (row-echelon form) returns the row-echelon form of a real *matrix*. The number of columns must be greater than or equal to the number of rows.

**ref(***matrix***)**

**rref(** (reduced row-echelon form) returns the reduced row-echelon form of a real *matrix*. The number of columns must be greater than or equal to the number of rows.

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**rref(***matrix***)**

**rowSwap(**

**rowSwap(** returns a matrix. It swaps *rowA* and *rowB* of *matrix*.

**rowSwap(***matrix***,***rowA***,***rowB***)**

**row+(**

**row+(** (row addition) returns a matrix. It adds *rowA* and *rowB* of *matrix* and stores the results in *rowB*.

**row+(***matrix***,***rowA***,***rowB***)**

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**row(**

**row(** (row multiplication) returns a matrix. It multiplies *row* of *matrix* by *value* and stores the results in *row*.

**row(***value***,***matrix***,***row***)**

**row+(**

**row+( **(row multiplication and addition) returns a matrix. It multiplies *rowA* of *matrix* by *value*, adds it to *rowB*, and stores the results in *rowB*.

**row+(***value***,***matrix***,***rowA***,***rowB***)**

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Chapter 11: Lists

Getting Started: Generating a Sequence

**Getting Started is a fast-paced introduction. Read the chapter for details.**

**Calculate the first eight terms of the sequence 1/A2. Store the results to a user-** **created list. Then display the results in fraction form. Begin this example on a** **blank line on the home screen.**

1. Press y 9 ~ to display the **LIST OPS** menu.

2. Press **5** to select **5:seq(**, which pastes **seq(** to the current cursor location.

3. Press **1** [A] [A] **1** **8** **1** to enter the sequence.

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4. Press , and then press y to turn on alpha-lock. Press [S] [E] [Q], and then press to turn off alpha-lock. Press **1** to complete the list name.

5. Press to generate the list and store it in **SEQ1**. The list is displayed on the home screen. An ellipsis (**...**) indicates that the list continues beyond the viewing window. Press ~ repeatedly (or press and hold ~) to scroll the list and view all the list elements.

6. Press y 9 to display the **LIST NAMES** menu. Press **7** to select **7:seq(** to paste **SEQ1** to the current cursor location. (If **SEQ1** is not item **7** on your **LIST NAMES** menu, move the cursor to **SEQ1** before you press .)

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7. Press to display the **MATH** menu. Press **1** to select **1:4Frac**, which pastes **4Frac** to the current cursor location.

8. Press to show the sequence in fraction form. Press ~ repeatedly (or press and hold ~) to scroll the list and view all the list elements.

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Naming Lists

**Using TI-83 Plus List Names L1 through L6**

The TI-83 Plus has six list names in memory: **L1**, **L2**, **L3**, **L4**, **L5**, and **L6**. The list names **L1** through **L6** are on the keyboard above the numeric keys through . To paste one of these names to a valid screen, press y, and then press the appropriate key. **L1** through **L6** are stored in stat list editor columns **1** through **6** when you reset memory.

**Creating a List Name on the Home Screen**

To create a list name on the home screen, follow these steps.

1. Press y E, enter one or more list elements, and then press y F. Separate list elements with commas. List elements can be real numbers, complex numbers, or expressions.

2. Press .

3. Press [letter from A to Z or q] to enter the first letter of the name.

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4. Enter zero to four letters, q, or numbers to complete the name.

5. Press . The list is displayed on the next line. The list name and its elements are stored in memory. The list name becomes an item on the **LIST NAMES** menu.

**Note:** If you want to view a user-created list in the stat list editor, you must store it in the stat list editor (Chapter 12).

You also can create a list name in these four places.

At the **Name=** prompt in the stat list editor

At an **Xlist:**, **Ylist:**, or **Data List:** prompt in the stat plot editor

At a **List:**, **List1:**, **List2:**, **Freq:**, **Freq1:**, **Freq2:**, **XList:**, or **YList:** prompt in the inferential stat editors

On the home screen using **SetUpEditor**

You can create as many list names as your TI-83 Plus memory has space to store.

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Storing and Displaying Lists

**Storing Elements to a List**

You can store list elements in either of two ways.

Use braces and on the home screen.

Use the stat list editor (Chapter 12).

The maximum dimension of a list is 999 elements.

**Tip:** When you store a complex number to a list, the entire list is converted to a list of complex numbers. To convert the list to a list of real numbers, display the home screen, and then enter **real(***listname***)!***listname*.

**Displaying a List on the Home Screen**

To display the elements of a list on the home screen, enter the name of the list (preceded by , if necessary, and then press . An ellipsis indicates that the list continues beyond the viewing window. Press ~ repeatedly (or press and hold ~) to scroll the list and view all the list elements.

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**Copying One List to Another**

To copy a list, store it to another list.

**Accessing a List Element**

You can store a value to or recall a value from a specific list *element*. You can store to any element within the current list dimension or one element beyond.

*listname***(***element***)**

**Deleting a List from Memory**

To delete lists from memory, including **L1** through **L6**, use the **MEMORY MANAGEMENT/DELETE **secondary menu (Chapter 18). Resetting memory restores **L1** through **L6**. Removing a list from the stat list editor does not delete it from memory.

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**Using Lists in Graphing**

You can use lists to graph a family of curves (Chapter 3).

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Entering List Names

**Using the LIST NAMES Menu**

To display the **LIST NAMES** menu, press y 9. Each item is a user- created list name. **LIST NAMES** menu items are sorted automatically in alphanumerical order. Only the first 10 items are labeled, using **1** through **9**, then **0**. To jump to the first list name that begins with a particular alpha character or q, press [letter from A to Z or q].

**Tip:** From the top of a menu, press } to move to the bottom. From the bottom, press to move to the top.

**Note:** The **LIST NAMES** menu omits list names **L1** through **L6**. Enter **L1** through **L6** directly from the keyboard.

When you select a list name from the **LIST NAMES** menu, the list name is pasted to the current cursor location.

The list name symbol precedes a list name when the name is pasted where non-list name data also is valid, such as the home screen.

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The symbol does not precede a list name when the name is pasted where a list name is the only valid input, such as the stat list editors **Name=** prompt or the stat plot editors **XList:** and **YList:** prompts.

**Entering a User-Created List Name Directly**

To enter an existing list name directly, follow these steps.

1. Press y 9 ~ to display the **LIST OPS** menu.

2. Select **B:**, which pastes to the current cursor location. is not always necessary.

**Note:** You also can paste ** **to the current cursor location from the **CATALOG** (Chapter 15).

3. Enter the characters that comprise the list name.

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Attaching Formulas to List Names

**Attaching a Formula to a List Name**

You can attach a formula to a list name so that each list element is a result of the formula. When executed, the attached formula must resolve to a list.

When anything in the attached formula changes, the list to which the formula is attached is updated automatically.

When you edit an element of a list that is referenced in the formula, the corresponding element in the list to which the formula is attached is updated.

When you edit the formula itself, all elements in the list to which the formula is attached are updated.

For example, the first screen below shows that elements are stored to **L3**, and the formula **L3+10** is attached to the list name **ADD10**. The quotation marks designate the formula to be attached to **ADD10**. Each element of **ADD10** is the sum of an element in **L3** and 10.

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The next screen shows another list, **L4**. The elements of **L4** are the sum of the same formula that is attached to **L3**. However, quotation marks are not entered, so the formula is not attached to **L4**.

On the next line, **L6!L3(1):L3** changes the first element in **L3** to **L6**, and then redisplays **L3**.

The last screen shows that editing **L3** updated **ADD10**, but did not change **L4**. This is because the formula **L3+10** is attached to **ADD10**, but it is not attached to **L4**.

**Note:** To view a formula that is attached to a list name, use the stat list editor (Chapter 12).

**Attaching a Formula to a List on the Home Screen or in a Program**

To attach a formula to a list name from a blank line on the home screen or from a program, follow these steps.

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1. Press [], enter the formula (which must resolve to a list), and press [] again.

**Note:** When you include more than one list name in a formula, each list must have the same dimension.

2. Press .

3. Enter the name of the list to which you want to attach the formula.

Press y, and then enter a TI-83 Plus list name **L1** through **L6**.

Press y 9 and select a user.created list name from the **LIST NAMES** menu.

Enter a user.created list name directly using .

4. Press .

**Note:** The stat list editor displays a formula-lock symbol next to each list name that has an attached formula. Chapter 12 describes how to use the stat list editor to attach formulas to lists, edit attached formulas, and detach formulas from lists.

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**Detaching a Formula from a List**

You can detach (clear) an attached formula from a list in several ways.

For example:

Enter **""!***listname* on the home screen.

Edit any element of a list to which a formula is attached.

Use the stat list editor (Chapter 12).

Use **ClrList** or **ClrAllList** to detach a formula from a list (Chapter 18).

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Using Lists in Expressions

**Using a List in an Expression**

You can use lists in an expression in any of three ways. When you press , any expression is evaluated for each list element, and a list is displayed.

Use **L1****L6** or any user-created list name in an expression.

Enter the list elements directly.

Use y K to recall the contents of the list into an expression at the cursor location (Chapter 1).

&

**Note:** You must paste user-created list names to the **Rcl** prompt by selecting them from the **LIST NAMES** menu. You cannot enter them directly using .

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**Using Lists with Math Functions**

You can use a list to input several values for some math functions. Other chapters and Appendix A specify whether a list is valid. The function is evaluated for each list element, and a list is displayed.

When you use a list with a function, the function must be valid for every element in the list. In graphing, an invalid element, such as **L1** in **({1,0,L1})**, is ignored.

This returns an error.

This graphs **X(1)** and **X(0)**, but skips **X(L1)**.

When you use two lists with a two-argument function, the dimension of each list must be the same. The function is evaluated for corresponding elements.

When you use a list and a value with a two-argument function, the value is used with each element in the list.

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LIST OPS Menu

**LIST OPS Menu**

To display the **LIST OPS** menu, press y 9 ~.

**NAMES** **OPS** ** MATH** **1:** **SortA(** Sorts lists in ascending order. **2:** **SortD(** Sorts lists in descending order. **3:** **dim(** Sets the list dimension. **4:** **Fill(** Fills all elements with a constant. **5:** **seq(** Creates a sequence. **6:** **c*msum(** Returns a list of cumulative sums. **7:** **@List(** Returns difference of successive elements. **8:** **Select(** Selects specific data points. **9:** **augment(** Concatenates two lists. **0:** **List4matr(** Stores a list to a matrix. **A:** **Matr4list(** Stores a matrix to a list. **B:** Designates the list-name data type.

**SortA(, SortD(**

**SortA(** (sort ascending) sorts list elements from low to high values. **SortD(** (sort descending) sorts list elements from high to low values. Complex lists are sorted based on magnitude (modulus).

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With one list, **SortA(** and **SortD(** sort the elements of *listname* and update the list in memory.

**SortA(***listname***)** **SortD(***listname***)**

With two or more lists, **SortA(** and **SortD(** sort *keylistname*, and then sort each *dependlist* by placing its elements in the same order as the corresponding elements in *keylistname*. All lists must have the same dimension.

**SortA(***keylistname***,***dependlist1*[**,***dependlist2***,**...**,***dependlist n*]**)** **SortD(***keylistname***,***dependlist1*[**,***dependlist2***,**...**,***dependlist n*]**)**

**Note:** In the example, **5** is the first element in **L4**, and **1** is the first element in **L5**. After **SortA(L4,L5)**, **5** becomes the second element of **L4**, and likewise, **1** becomes the second element of **L5**.

**Note: SortA(** and **SortD(** are the same as **SortA(** and **SortD(** on the **STAT EDIT** menu (Chapter 12).

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**Using dim( to Find List Dimensions**

**dim(** (dimension) returns the length (number of elements) of *list*.

**dim(***list***)**

**Using dim( to Create a List**

You can use **dim(** with to create a new *listname* with dimension *length* from 1 to 999. The elements are zeros.

*length***!dim(***listname***)**

**Using dim( to Redimension a List**

You can use **dim** with to redimension an existing *listname* to dimension *length* from 1 to 999.

The elements in the old *listname* that are within the new dimension are not changed.

Extra list elements are filled by **0**.

Elements in the old list that are outside the new dimension are deleted.

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*length***!dim(***listname***)**

**Fill(**

**Fill(** replaces each element in *listname* with *value*.

**Fill(***value***,***listname***)**

**Note:** **dim(** and **Fill(** are the same as **dim(** and **Fill(** on the **MATRX MATH** menu (Chapter 10).

**seq(**

**seq(** (sequence) returns a list in which each element is the result of the evaluation of *expression* with regard to *variable* for the values ranging from *begin* to *end* at steps of *increment*. *variable* need not be defined in memory. *increment* can be negative; the default value for *increment* is 1. **seq(** is not valid within *expression*. Complex lists are not valid.

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**seq(***expression***,***variable***,***begin***,***end*[**,***increment*]**)**

**c*msum(**

**c*msum(** (cumulative sum) returns the cumulative sums of the elements in *list*, starting with the first element. *list* elements can be real or complex numbers.

**c*msum(***list***)**

**@List(**

**@List(** returns a list containing the differences between consecutive elements in *list*. **@List** subtracts the first element in *list* from the second element, subtracts the second element from the third, and so on. The list of differences is always one element shorter than the original *list*. *list* elements can be a real or complex numbers.

**@List(***list***)**

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**Select(**

**Select(** selects one or more specific data points from a scatter plot or xyLine plot (only), and then stores the selected data points to two new lists, *xlistname* and *ylistname*. For example, you can use **Select(** to select and then analyze a portion of plotted CBL 2/CBL or CBR data.

**Select(***xlistname***,***ylistname***)**

**Note:** Before you use **Select(**, you must have selected (turned on) a scatter plot or xyLine plot. Also, the plot must be displayed in the current viewing window.

**Before Using Select(**

Before using **Select(**, follow these steps.

1. Create two list names and enter the data.

2. Turn on a stat plot, select **"** (scatter plot) or (xyLine), and enter the two list names for **Xlist:** and **Ylist: **(Chapter 12).

3. Use **ZoomStat** to plot the data (Chapter 3).

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**Using Select( to Select Data Points from a Plot**

To select data points from a scatter plot or xyLine plot, follow these steps.

1. Press y 9 ~ **8** to select **8:Select(** from the **LIST OPS** menu. **Select(** is pasted to the home screen.

2. Enter *xlistname*, press , enter *ylistname*, and then press to designate list names into which you want the selected data to be stored.

3. Press . The graph screen is displayed with **Left Bound?** in the bottom-left corner.

4. Press } or (if more than one stat plot is selected) to move the cursor onto the stat plot from which you want to select data points.

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5. Press | and ~ to move the cursor to the stat plot data point that you want as the left bound.

6. Press . A **4** indicator on the graph screen shows the left bound. **Right Bound?** is displayed in the bottom-left corner.

7. Press | or ~ to move the cursor to the stat plot point that you want for the right bound, and then press .

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The x-values and y-values of the selected points are stored in *xlistname* and *ylistname*. A new stat plot of *xlistname* and *ylistname* replaces the stat plot from which you selected data points. The list names are updated in the stat plot editor.

**Note:** The two new lists (*xlistname* and *ylistname*) will include the points you select as left bound and right bound. Also, *left-bound x-value* *right-bound x-value* must be true.

**augment(**

**augment(** concatenates the elements of *listA* and *listB*. The list elements can be real or complex numbers.

**augment(***listA***,***listB***)**

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**List4matr(**

**List4matr(** (lists stored to matrix) fills *matrixname* column by column with the elements from each list. If the dimensions of all lists are not equal, then **List4matr(** fills each extra *matrixname* row with **0**. Complex lists are not valid.

**List4matr(***list1***,***list2***,** . . . **,***list n***,***matrixname***)**

**&**

**Matr4list(**

**Matr4list(** (matrix stored to lists) fills each *listname* with elements from each column in *matrix*. If the number of *listname* arguments exceeds the number of columns in *matrix*, then **Matr4list(** ignores extra *listname* arguments. Likewise, if the number of columns in *matrix* exceeds the number of *listname* arguments, then **Matr4list(** ignores extra *matrix* columns.

**Matr4list(***matrix***,***listname1***,***listname2***,** . . . **,***listname n***)**

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**&**

**Matr4list(** also fills a *listname* with elements from a specified *column#* in *matrix*. To fill a list with a specific column from *matrix*, you must enter a *column#* after *matrix*.

**Matr4list(***matrix***,***column#***,***listname***)**

**&**

preceding one to five characters identifies those characters as a user- created *listname*. *listname* may comprise letters, q, and numbers, but it must begin with a letter from A to Z or q.

*listname*

Generally, must precede a user-created list name when you enter a user-created list name where other input is valid, for example, on the home screen. Without the , the TI-83 Plus may misinterpret a user- created list name as implied multiplication of two or more characters.

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need not precede a user-created list name where a list name is the only valid input, for example, at the **Name=** prompt in the stat list editor or the **Xlist:** and **Ylist:** prompts in the stat plot editor. If you enter where it is not necessary, the TI-83 Plus will ignore the entry.

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LIST MATH Menu

**LIST MATH Menu**

To display the **LIST MATH** menu, press y 9 |.

**NAMES OPS** **MATH** **1:min(** Returns minimum element of a list. **2:max(** Returns maximum element of a list. **3:mean(** Returns mean of a list. **4:median(** Returns median of a list. **5:sum(** Returns sum of elements in a list. **6:prod(** Returns product of elements in list. **7:stdDev(** Returns standard deviation of a list. **8:variance(** Returns the variance of a list.

**min(, max(**

**min(** (minimum) and **max( **(maximum) return the smallest or largest element of *listA*. If two lists are compared, it returns a list of the smaller or larger of each pair of elements in *listA* and *listB*. For a complex list, the element with smallest or largest magnitude (modulus) is returned.

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**min(***listA*[**,***listB*]**)** **max(***listA*[**,***listB*]**)**

**Note:** **min( **and **max( **are the same as **min( **and **max( **on the **MATH NUM** menu.

**mean(, median(**

**mean(** returns the mean value of *list*. **median(** returns the median value of *list*. The default value for *freqlist *is 1. Each *freqlist* element counts the number of consecutive occurrences of the corresponding element in *list*. Complex lists are not valid.

**mean(***list*[**,***freqlist*]**)** **median(***list*[**,***freqlist*]**)**

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**sum(, prod(**

**sum(** (summation) returns the sum of the elements in *list*. *start* and *end* are optional; they specify a range of elements. *list* elements can be real or complex numbers.

**prod(** returns the product of all elements of *list*.* start* and *end* elements are optional; they specify a range of list elements. *list* elements can be real or complex numbers.

**sum(***list*[**,***start***,***end*]**)** **prod(***list*[**,***start***,***end*]**)**

**Sums and Products of Numeric Sequences**

You can combine **sum(** or **prod(** with **seq(** to obtain:

*upper* *upper*

**G ***expression(x)* *expression(x)*

*x=lower* *x=lower*

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To evaluate G 2(N1) from N=1 to 4:

**stdDev(, variance(**

**stdDev(** returns the standard deviation of the elements in *list*. The default value for *freqlist *is 1. Each *freqlist* element counts the number of consecutive occurrences of the corresponding element in *list*. Complex lists are not valid.

**variance(** returns the variance of the elements in *list*. The default value for *freqlist *is 1. Each *freqlist* element counts the number of consecutive occurrences of the corresponding element in *list*. Complex lists are not valid.

**stdDev(***list*[**,***freqlist*]**)** **variance(***list*[**,***freqlist*]**)**

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Chapter 12: Statistics

Getting Started: Pendulum Lengths and Periods

**Getting Started is a fast-paced introduction. Read the chapter for details.**

**A group of students is attempting to determine the mathematical relationship** **between the length of a pendulum and its period (one complete swing of a** **pendulum). The group makes a simple pendulum from string and washers and** **then suspends it from the ceiling. They record the pendulums period for each of** **12 string lengths.***

**Length (cm)** **Time (sec)** **Length (cm)** **Time (sec)** 6.5 0.51 24.4 1.01 11.0 0.68 26.6 1.08 13.2 0.73 30.5 1.13 15.0 0.79 34.3 1.26 18.0 0.88 37.6 1.28 23.1 0.99 41.5 1.32

*This example is quoted and adapted from Contemporary Precalculus Through Applications, by the North Carolina School of Science and Mathematics, by permission of Janson Publications, Inc., Dedham, MA. 1-800-322-MATH. 1992. All rights reserved.

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1. Press z to set **Func** graphing mode.

2. Press **5** to select **5:SetUpEditor**. **SetUpEditor** is pasted to the home screen.

Press . This removes lists from stat list editor columns **1** through **20**, and then stores lists **L1** through **L6** in columns **1** through **6**.

**Note:** Removing lists from the stat list editor does not delete them from memory.

3. Press **1** to select **1:Edit** from the **STAT**

**EDIT** menu. The stat list editor is displayed. If elements are stored in **L1** and **L2**, press } to move the cursor onto** L1**, and then press ~ } to clear both lists. Press | to move the rectangular cursor back to the first row in **L1**.

4. Press **6** **5** to store the first pendulum string length (6.5 cm) in **L1**. The rectangular cursor moves to the next row. Repeat this step to enter each of the 12 string length values in the table.

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5. Press ~ to move the rectangular cursor to the first row in **L2**.

Press **51** to store the first time measurement (.51 sec) in **L2**. The rectangular cursor moves to the next row. Repeat this step to enter each of the 12 time values in the table.

6. Press o to display the **Y=** editor.

If necessary, press to clear the function **Y1**. As necessary, press }, , and ~ to turn off **Plot1**, **Plot2**, and **Plot3** from the top line of the **Y=** editor (Chapter 3). As necessary, press , |, and to deselect functions.

7. Press y , **1** to select **1:Plot1** from the **STAT PLOTS** menu. The stat plot editor is displayed for plot 1.

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8. Press to select **On**, which turns on plot 1. Press to select " (scatter plot). Press y d to specify **Xlist:L1** for plot 1. Press y e to specify **Ylist:L2** for plot 1. Press ~ to select **+** as the **Mark** for each data point on the scatter plot.

9. Press q **9** to select **9:ZoomStat** from the **ZOOM** menu. The window variables are adjusted automatically, and plot 1 is displayed. This is a scatter plot of the time-versus-length data.

Since the scatter plot of time-versus-length data appears to be approximately linear, fit a line to the data.

10. Press ~ **4** to select **4:LinReg(ax+b)** (linear regression model) from the **STAT CALC** menu. **LinReg(ax+b)** is pasted to the home screen.

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11. Press y d y e . Press ~ **1** to display the **VARS Y.VARS FUNCTION** secondary menu, and then press **1** to select **1:Y1**. **L1**, **L2**, and **Y1** are pasted to the home screen as arguments to **LinReg(ax+b)**.

12. Press to execute **LinReg(ax+b)**. The linear regression for the data in **L1** and **L2** is calculated. Values for **a** and **b** are displayed on the home screen. The linear regression equation is stored in **Y1**. Residuals are calculated and stored automatically in the list name **RESID**, which becomes an item on the **LIST NAMES** menu.

13. Press . The regression line and the scatter plot are displayed.

The regression line appears to fit the central portion of the scatter plot well. However, a residual plot may provide more information about this fit.

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14. Press **1** to select **1:Edit**. The stat list editor is displayed.

Press ~ and } to move the cursor onto **L3**.

Press y 6. An unnamed column is displayed in column **3**; **L3**, **L4**, **L5**, and **L6** shift right one column. The **Name=** prompt is displayed in the entry line, and alpha-lock is on.

15. Press y 9 to display the **LIST NAMES** menu.

If necessary, press to move the cursor onto the list name **RESID**.

16. Press to select **RESID** and paste it to the stat list editors **Name=** prompt.

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17. Press . **RESID** is stored in column **3** of the stat list editor.

Press repeatedly to examine the residuals.

Notice that the first three residuals are negative. They correspond to the shortest pendulum string lengths in **L1**. The next five residuals are positive, and three of the last four are negative. The latter correspond to the longer string lengths in **L1**. Plotting the residuals will show this pattern more clearly.

18. Press y , **2** to select **2:Plot2** from the **STAT PLOTS** menu. The stat plot editor is displayed for plot 2.

19. Press to select **On**, which turns on plot 2.

Press to select **"** (scatter plot). Press y d to specify **Xlist:L1** for plot 2. Press [R] [E] [S] [I] [D] (alpha-lock is on) to specify **Ylist:RESID** for plot 2. Press to select as the mark for each data point on the scatter plot.

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20. Press o to display the **Y=** editor.

Press | to move the cursor onto the **=** sign, and then press to deselect **Y1**. Press } to turn off plot 1.

21. Press q **9** to select **9:ZoomStat** from the **ZOOM** menu. The window variables are adjusted automatically, and plot 2 is displayed. This is a scatter plot of the residuals.

Notice the pattern of the residuals: a group of negative residuals, then a group of positive residuals, and then another group of negative residuals.

The residual pattern indicates a curvature associated with this data set for which the linear model did not account. The residual plot emphasizes a downward curvature, so a model that curves down with the data would be more accurate. Perhaps a function such as square root would fit. Try a power regression to fit a function of the form y = a xb.

22. Press o to display the **Y=** editor.

Press to clear the linear regression equation from **Y1**. Press } to turn on plot 1. Press ~ to turn off plot 2.

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23. Press q **9** to select **9:ZoomStat** from the **ZOOM** menu. The window variables are adjusted automatically, and the original scatter plot of time-versus-length data (plot 1) is displayed.

24. Press ~ [A] to select **A:PwrReg** from the **STAT CALC** menu. **PwrReg** is pasted to the home screen.

Press y d y e . Press ~ **1** to display the **VARS Y.VARS FUNCTION** secondary menu, and then press **1** to select **1:Y1**. **L1**, **L2**, and **Y1** are pasted to the home screen as arguments to **PwrReg**.

25. Press to calculate the power regression. Values for **a** and **b** are displayed on the home screen. The power regression equation is stored in **Y1**. Residuals are calculated and stored automatically in the list name **RESID**.

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26. Press . The regression line and the scatter plot are displayed.

The new function y=.192x**.**522 appears to fit the data well. To get more information, examine a residual plot.

27. Press o to display the **Y=** editor.

Press | to deselect **Y1**.

Press } to turn off plot 1. Press ~ to turn on plot 2.

**Note:** Step 19 defined plot 2 to plot residuals (**RESID**) versus string length (**L1**).

28. Press q **9** to select **9:ZoomStat** from the **ZOOM** menu. The window variables are adjusted automatically, and plot 2 is displayed. This is a scatter plot of the residuals.

The new residual plot shows that the residuals are random in sign, with the residuals increasing in magnitude as the string length increases.

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To see the magnitudes of the residuals, continue with these steps.

29. Press r.

Press ~ and | to trace the data. Observe the values for **Y** at each point.

With this model, the largest positive residual is about 0.041 and the smallest negative residual is about L0.027. All other residuals are less than 0.02 in magnitude.

Now that you have a good model for the relationship between length and period, you can use the model to predict the period for a given string length. To predict the periods for a pendulum with string lengths of 20 cm and 50 cm, continue with these steps.

30. Press ~ **1** to display the **VARS Y.VARS**

**FUNCTION** secondary menu, and then press **1** to select **1:Y1**. **Y1** is pasted to the home screen.

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31. Press **20** to enter a string length of 20 cm.

Press to calculate the predicted time of about 0.92 seconds.

Based on the residual analysis, we would expect the prediction of about 0.92 seconds to be within about 0.02 seconds of the actual value.

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32. Press y [ to recall the Last Entry.

Press | | | **5** to change the string length to 50 cm.

33. Press to calculate the predicted time of about 1.48 seconds.

Since a string length of 50 cm exceeds the lengths in the data set, and since residuals appear to be increasing as string length increases, we would expect more error with this estimate.

**Note:** You also can make predictions using the table with the **TABLE SETUP** settings **Indpnt:Ask** and **Depend:Auto** (Chapter 7).

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Setting Up Statistical Analyses

**Using Lists to Store Data**

Data for statistical analyses is stored in lists, which you can create and edit using the stat list editor. The TI-83 Plus has six list variables in memory, **L1** through **L6**, to which you can store data for statistical calculations. Also, you can store data to list names that you create (Chapter 11).

**Setting Up a Statistical Analysis**

To set up a statistical analysis, follow these steps. Read the chapter for details.

1. Enter the statistical data into one or more lists.

2. Plot the data.

3. Calculate the statistical variables or fit a model to the data.

4. Graph the regression equation for the plotted data.

5. Graph the residuals list for the given regression model.

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**Displaying the Stat List Editor**

The stat list editor is a table where you can store, edit, and view up to 20 lists that are in memory. Also, you can create list names from the stat list editor.

To display the stat list editor, press , and then select **1:Edit** from the **STAT EDIT** menu.

The top line displays list names. **L1** through **L6** are stored in columns **1** through **6** after a memory reset. The number of the current column is displayed in the top-right corner.

The bottom line is the entry line. All data entry occurs on this line. The characteristics of this line change according to the current context.

The center area displays up to seven elements of up to three lists; it abbreviates values when necessary. The entry line displays the full value of the current element.

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Using the Stat List Editor

**Entering a List Name in the Stat List Editor**

To enter a list name in the stat list editor, follow these steps.

1. Display the **Name=** prompt in the entry line in either of two ways.

Move the cursor onto the list name in the column where you want to insert a list, and then press y 6. An unnamed column is displayed and the remaining lists shift right one column.

Press } until the cursor is on the top line, and then press ~ until you reach the unnamed column.

**Note:** If list names are stored to all 20 columns, you must remove a list name to make room for an unnamed column.

The **Name=** prompt is displayed and alpha-lock is on.

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2. Enter a valid list name in any of four ways.

Select a name from the **LIST NAMES** menu (Chapter 11).

Enter **L1**, **L2**, **L3**, **L4**, **L5**, or **L6** from the keyboard.

Enter an existing user-created list name directly from the keyboard.

Enter a new user-created list name.

3. Press or to store the list name and its elements, if any, in the current column of the stat list editor.

To begin entering, scrolling, or editing list elements, press . The rectangular cursor is displayed. **Note:** If the list name you entered in step 2 already was stored in another stat list editor column, then the list and its elements, if any, move to the current column from the previous column. Remaining list names shift accordingly.

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**Creating a Name in the Stat List Editor**

To create a name in the stat list editor, follow these steps.

1. Display the **Name=** prompt.

2. Press [letter from A to Z or q] to enter the first letter of the name. The first character cannot be a number.

3. Enter zero to four letters, q, or numbers to complete the new user- created list name. List names can be one to five characters long.

4. Press or to store the list name in the current column of the stat list editor. The list name becomes an item on the **LIST NAMES**

menu (Chapter 11).

**Removing a List from the Stat List Editor**

To remove a list from the stat list editor, move the cursor onto the list name and then press {. The list is not deleted from memory; it is only removed from the stat list editor.

**Note1:** To delete a list name from memory, use the **MEMORY MANAGEMENT/** **DELETE secondary menu** (Chapter 18).

**Note 2:** If you archive a list, it will be removed from the stat list editor.

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**Removing All Lists and Restoring L1 through L6**

You can remove all user-created lists from the stat list editor and restore list names **L1** through **L6** to columns **1** through **6** in either of two ways.

Use **SetUpEditor** with no arguments.

Reset all memory (Chapter 18).

**Clearing All Elements from a List**

You can clear all elements from a list in any of five ways.

Use **ClrList** to clear specified lists.

In the stat list editor, press } to move the cursor onto a list name, and then press .

In the stat list editor, move the cursor onto each element, and then press { one by one.

On the home screen or in the program editor, enter **0!dim(***listname***)** to set the dimension of *listname* to 0 (Chapter 11).

Use **ClrAllLists** to clear all lists in memory (Chapter 18).

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**Editing a List Element**

To edit a list element, follow these steps.

1. Move the rectangular cursor onto the element you want to edit.

2. Press to move the cursor to the entry line.

**Note:** If you want to replace the current value, you can enter a new value without first pressing . When you enter the first character, the current value is cleared automatically.

3. Edit the element in the entry line.

Press one or more keys to enter the new value. When you enter the first character, the current value is cleared automatically.

Press ~ to move the cursor to the character before which you want to insert, press y 6, and then enter one or more characters.

Press ~ to move the cursor to a character you want to delete, and then press { to delete the character.

To cancel any editing and restore the original element at the rectangular cursor, press .

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**Note:** You can enter expressions and variables for elements.

4. Press , }, or to update the list. If you entered an expression, it is evaluated. If you entered only a variable, the stored value is displayed as a list element.

When you edit a list element in the stat list editor, the list is updated in memory immediately.

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Attaching Formulas to List Names

**Attaching a Formula to a List Name in Stat List Editor**

You can attach a formula to a list name in the stat list editor, and then display and edit the calculated list elements. When executed, the attached formula must resolve to a list. Chapter 11 describes in detail the concept of attaching formulas to list names.

To attach a formula to a list name that is stored in the stat list editor, follow these steps.

1. Press to display the stat list editor.

2. Press } to move the cursor to the top line.

3. Press | or ~, if necessary, to move the cursor onto the list name to which you want to attach the formula.

**Note:** If a formula in quotation marks is displayed on the entry line, then a formula is already attached to the list name. To edit the formula, press , and then edit the formula.

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4. Press [], enter the formula, and press [].

**Note:** If you do not use quotation marks, the TI-83 Plus calculates and displays the same initial list of answers, but does not attach the formula for future calculations.

**Note:** Any user-created list name referenced in a formula must be preceded by an symbol (Chapter 11).

5. Press . The TI-83 Plus calculates each list element and stores it to the list name to which the formula is attached. A lock symbol is displayed in the stat list editor, next to the list name to which the formula is attached.

lock symbol

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**Using the Stat List Editor When Formula-Generated Lists Are** **Displayed**

When you edit an element of a list referenced in an attached formula, the TI-83 Plus updates the corresponding element in the list to which the formula is attached (Chapter 11).

When a list with a formula attached is displayed in the stat list editor and you edit or enter elements of another displayed list, then the TI-83 Plus takes slightly longer to accept each edit or entry than when no lists with formulas attached are in view.

**Tip:** To speed editing time, scroll horizontally until no lists with formulas are displayed, or rearrange the stat list editor so that no lists with formulas are displayed.

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**Handling Errors Resulting from Attached Formulas**

On the home screen, you can attach to a list a formula that references another list with dimension 0 (Chapter 11). However, you cannot display the formula-generated list in the stat list editor or on the home screen until you enter at least one element to the list that the formula references.

All elements of a list referenced by an attached formula must be valid for the attached formula. For example, if **Real** number mode is set and the attached formula is **log(L1)**, then each element of **L1** must be greater than 0, since the logarithm of a negative number returns a complex result.

**Tip:** If an error menu is returned when you attempt to display a formula- generated list in the stat list editor, you can select **2:Goto**, write down the formula that is attached to the list, and then press to detach (clear) the formula. You then can use the stat list editor to find the source of the error. After making the appropriate changes, you can reattach the formula to a list.

If you do not want to clear the formula, you can select **1:Quit**, display the referenced list on the home screen, and find and edit the source of the error. To edit an element of a list on the home screen, store the new value to *listname***(***element#***)** (Chapter 11).

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Detaching Formulas from List Names

**Detaching a Formula from a List Name**

You can detach (clear) a formula from a list name in several ways.

For example:

In the stat list editor, move the cursor onto the name of the list to which a formula is attached. Press . All list elements remain, but the formula is detached and the lock symbol disappears.

In the stat list editor, move the cursor onto an element of the list to which a formula is attached. Press , edit the element, and then press . The element changes, the formula is detached, and the lock symbol disappears. All other list elements remain.

Use **ClrList**. All elements of one or more specified lists are cleared, each formula is detached, and each lock symbol disappears. All list names remain.

Use **ClrAllLists** (Chapter 18). All elements of all lists in memory are cleared, all formulas are detached from all list names, and all lock symbols disappear. All list names remain.

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**Editing an Element of a Formula-Generated List**

As described above, one way to detach a formula from a list name is to edit an element of the list to which the formula is attached. The TI-83 Plus protects against inadvertently detaching the formula from the list name by editing an element of the formula-generated list.

Because of the protection feature, you must press before you can edit an element of a formula-generated list.

The protection feature does not allow you to delete an element of a list to which a formula is attached. To delete an element of a list to which a formula is attached, you must first detach the formula in any of the ways described above.

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Switching Stat List Editor Contexts

**Stat List Editor Contexts**

The stat list editor has four contexts.

View-elements context Edit-elements context

View-names context Enter-name context

The stat list editor is first displayed in view-elements context. To switch through the four contexts, select **1:Edit** from the **STAT EDIT** menu and follow these steps.

1. Press } to move the cursor onto a list name. You are now in view-names context. Press ~ and | to view list names stored in other stat list editor columns.

2. Press . You are now in edit-elements context. You may edit any element in a list. All elements of the current list are displayed in braces ( **{** **}** )in the entry line. Press ~ and | to view more list elements.

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3. Press again. You are now in view-elements context. Press ~, |, , and } to view other list elements. The current elements full value is displayed in the entry line.

4. Press again. You are now in edit-elements context. You may edit the current element in the entry line.

5. Press } until the cursor is on a list name, then press y 6. You are now in enter-name context.

6. Press . You are now in view-names context.

7. Press . You are now back in view-elements context.

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Stat List Editor Contexts

**View-Elements Context**

In view-elements context, the entry line displays the list name, the current elements place in that list, and the full value of the current element, up to 12 characters at a time. An ellipsis (**...**) indicates that the element continues beyond 12 characters.

To page down the list six elements, press . To page up six elements, press }. To delete a list element, press {. Remaining elements shift up one row. To insert a new element, press y 6. **0** is the default value for a new element.

**Edit-Elements Context**

In edit-elements context, the data displayed in the entry line depends on the previous context.

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When you switch to edit-elements context from view-elements context, the full value of the current element is displayed. You can edit the value of this element, and then press and } to edit other list elements.

**&**

When you switch to edit-elements context from view-names context, the full values of all elements in the list are displayed. An ellipsis indicates that list elements continue beyond the screen. You can press ~ and | to edit any element in the list.

**&**

**Note:** In edit-elements context, you can attach a formula to a list name only if you switched to it from view-names context.

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**View-Names Context**

In view-names context, the entry line displays the list name and the list elements.

To remove a list from the stat list editor, press {. Remaining lists shift to the left one column. The list is not deleted from memory.

To insert a name in the current column, press y 6. Remaining columns shift to the right one column.

**Enter-Name Context**

In enter-name context, the **Name=** prompt is displayed in the entry line, and alpha-lock is on.

At the **Name=** prompt, you can create a new list name, paste a list name from **L1** to **L6** from the keyboard, or paste an existing list name from the **LIST NAMES** menu (Chapter 11). The symbol is not required at the **Name=** prompt.

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To leave enter-name context without entering a list name, press . The stat list editor switches to view-names context.

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STAT EDIT Menu

**STAT EDIT Menu**

To display the **STAT EDIT** menu, press .

**EDIT** ** CALC TESTS**

**1:Edit...** Displays the stat list editor. **2:SortA(** Sorts a list in ascending order. **3:SortD(** Sorts a list in descending order. **4:ClrList** Deletes all elements of a list. **5:SetUpEditor** Stores lists in the stat list editor.

**Note:** Chapter 13: Inferential Statistics describes the **STAT TESTS** menu items.

**SortA(, SortD(**

**SortA(** (sort ascending) sorts list elements from low to high values. **SortD(** (sort descending) sorts list elements from high to low values. Complex lists are sorted based on magnitude (modulus). **SortA(** and **SortD(** each can sort in either of two ways.

With one *listname*, **SortA(** and **SortD(** sort the elements in *listname* and update the list in memory.

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With two or more lists, **SortA(** and **SortD(** sort *keylistname*, and then sort each *dependlist* by placing its elements in the same order as the corresponding elements in *keylistname*. This lets you sort two-variable data on **X** and keep the data pairs together. All lists must have the same dimension.

The sorted lists are updated in memory.

**SortA(***listname***)** **SortD(***listname***)** **SortA(***keylistname***,***dependlist1*[**,***dependlist2***,**...**,***dependlist n*]**)** **SortD(***keylistname***,***dependlist1*[**,***dependlist2***,**...**,***dependlist n*]**)**

**Note:** **SortA(** and **SortD(** are the same as **SortA(** and **SortD(** on the **LIST OPS** menu.

**ClrList**

**ClrList** clears (deletes) from memory the elements of one or more *listnames*. **ClrList** also detaches any formula attached to a *listname*.

**ClrList** *listname1***,***listname2***,**...**,***listname n*

**Note:** To clear from memory all elements of all list names, use** ClrAllLists** (Chapter 18).

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**SetUpEditor**

With **SetUpEditor** you can set up the stat list editor to display one or more *listnames* in the order that you specify. You can specify zero to 20 *listnames*.

Additionally, if you want to use *listnames* which happen to be archived, the SetUp Editor will automatically unarchive the *listnames* and place them in the stat list editor at the same time.

**SetUpEditor **[*listname1***,***listname2***,**...**,***listname n*]

**SetUpEditor** with one to 20 *listnames* removes all list names from the stat list editor and then stores *listnames* in the stat list editor columns in the specified order, beginning in column **1**.

If you enter a *listname* that is not stored in memory already, then *listname* is created and stored in memory; it becomes an item on the **LIST NAMES**

menu.

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**Restoring L1 through L6 to the Stat List Editor**

**SetUpEditor** with no *listnames* removes all list names from the stat list editor and restores list names **L1** through **L6** in the stat list editor columns **1** through **6**.

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Regression Model Features

**Regression Model Features**

**STAT CALC** menu items **3** through **C** are regression models. The automatic residual list and automatic regression equation features apply to all regression models. Diagnostics display mode applies to some regression models.

**Automatic Residual List**

When you execute a regression model, the automatic residual list feature computes and stores the residuals to the list name **RESID**. **RESID** becomes an item on the **LIST NAMES** menu (Chapter 11).

The TI-83 Plus uses the formula below to compute **RESID** list elements. The next section describes the variable **RegEQ**.

**RESID** = *Ylistname* N **RegEQ**(*Xlistname*)

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**Automatic Regression Equation**

Each regression model has an optional argument, *regequ*, for which you can specify a **Y=** variable such as **Y1**. Upon execution, the regression equation is stored automatically to the specified **Y=** variable and the **Y=** function is selected.

Regardless of whether you specify a **Y=** variable for *regequ*, the regression equation always is stored to the TI-83 Plus variable **RegEQ**, which is item **1** on the **VARS Statistics EQ** secondary menu.

**Note:** For the regression equation, you can use the fixed-decimal mode setting to control the number of digits stored after the decimal point (Chapter 1). However, limiting the number of digits to a small number could affect the accuracy of the fit.

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**Diagnostics Display Mode**

When you execute some regression models, the TI-83 Plus computes and stores diagnostics values for **r** (correlation coefficient) and **r2**

(coefficient of determination) or for **R2** (coefficient of determination).

**r** and **r2** are computed and stored for these regression models.

**LinReg(ax+b)** **LnReg** **PwrReg** **LinReg(a+bx)** **ExpReg**

**R2** is computed and stored for these regression models.

**QuadReg** **CubicReg** **QuartReg**

The **r** and **r2** that are computed for** LnReg**, **ExpReg**, and **PwrReg** are based on the linearly transformed data. For example, for **ExpReg** (y=ab^x), **r** and **r2** are computed on ln y=ln a+x(ln b).

By default, these values are not displayed with the results of a regression model when you execute it. However, you can set the diagnostics display mode by executing the **DiagnosticOn** or **DiagnosticOff** instruction. Each instruction is in the **CATALOG** (Chapter 15).

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**Note:** To set **DiagnosticOn** or **DiagnosticOff** from the home screen, press y N, and then select the instruction for the mode you want. The instruction is pasted to the home screen. Press to set the mode.

When **DiagnosticOn** is set, diagnostics are displayed with the results when you execute a regression model.

When **DiagnosticOff** is set, diagnostics are not displayed with the results when you execute a regression model.

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STAT CALC Menu

**STAT CALC Menu**

To display the **STAT CALC** menu, press ~.

**EDIT** **CALC TESTS** **1:1-Var Stats** Calculates 1-variable statistics. **2:2-Var Stats** Calculates 2-variable statistics. **3:Med-Med** Calculates a median-median line. **4:LinReg(ax+b)** Fits a linear model to data. **5:QuadReg** Fits a quadratic model to data. **6:CubicReg** Fits a cubic model to data. **7:QuartReg** Fits a quartic model to data. **8:LinReg(a+bx)** Fits a linear model to data. **9:LnReg** Fits a logarithmic model to data. **0:ExpReg** Fits an exponential model to data. **A:PwrReg** Fits a power model to data. **B:Logistic** Fits a logistic model to data. **C:SinReg** Fits a sinusoidal model to data.

For each **STAT CALC** menu item, if neither *Xlistname* nor *Ylistname* is specified, then the default list names are **L1** and **L2**. If you do not specify *freqlist*, then the default is **1** occurrence of each list element.

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**Frequency of Occurrence for Data Points**

For most **STAT CALC** menu items, you can specify a list of data occurrences, or frequencies (*freqlist*).

Each element in *freqlist* indicates how many times the corresponding data point or data pair occurs in the data set you are analyzing.

For example, if **L1={15,12,9,14}** and **FREQ={1,4,1,3}**, then the TI-83 Plus interprets the instruction **1.Var Stats** **L1**, **FREQ** to mean that **15** occurs once, **12** occurs four times, **9** occurs once, and **14** occurs three times.

Each element in *freqlist* must be 0, and at least one element must be > 0.

Noninteger *freqlist* elements are valid. This is useful when entering frequencies expressed as percentages or parts that add up to 1. However, if *freqlist* contains noninteger frequencies, **Sx** and **Sy** are undefined; values are not displayed for **Sx** and **Sy** in the statistical results.

**1.Var Stats**

**1.Var Stats** (one-variable statistics) analyzes data with one measured variable. Each element in *freqlist* is the frequency of occurrence for each corresponding data point in *Xlistname*. *freqlist* elements must be real numbers > 0.

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**1.Var Stats** [*Xlistname***,***freqlist*]

**2.Var Stats**

**2.Var Stats** (two-variable statistics) analyzes paired data. *Xlistname* is the independent variable. *Ylistname* is the dependent variable. Each element in *freqlist* is the frequency of occurrence for each data pair (*Xlistname,Ylistname*).

**2.Var Stats** [*Xlistname***,***Ylistname***,***freqlist*]

**Med.Med (ax+b)**

**Med.Med** (median-median) fits the model equation y=ax+b to the data using the median-median line (resistant line) technique, calculating the summary points **x1**, **y1**, **x2**, **y2**, **x3**, and **y3**. **Med.Med **displays values for **a** (slope) and **b** (y-intercept).

**Med.Med** [*Xlistname***,***Ylistname***,***freqlist***,***regequ*]

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**LinReg (ax+b)**

**LinReg(ax+b)** (linear regression) fits the model equation y=ax+b to the data using a least-squares fit. It displays values for **a** (slope) and **b** (y-intercept); when **DiagnosticOn** is set, it also displays values for **r2** and **r**.

**LinReg(ax+b)** [*Xlistname***,***Ylistname***,***freqlist***,***regequ*]

**QuadReg (ax2+bx+c)**

**QuadReg** (quadratic regression) fits the second-degree polynomial y=ax2+bx+c to the data. It displays values for **a**, **b**, and **c**; when **DiagnosticOn** is set, it also displays a value for **R2**. For three data points, the equation is a polynomial fit; for four or more, it is a polynomial regression. At least three data points are required.

**QuadReg** [*Xlistname***,***Ylistname***,***freqlist***,***regequ*]

**CubicReg(ax3+bx2+cx+d)**

**CubicReg** (cubic regression) fits the third-degree polynomial y=ax3+bx2+cx+d to the data. It displays values for **a**, **b**, **c**, and **d**; when **DiagnosticOn** is set, it also displays a value for **R2**. For four points, the equation is a polynomial fit; for five or more, it is a polynomial regression. At least four points are required.

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**CubicReg** [*Xlistname***,***Ylistname***,***freqlist***,***regequ*]

**QuartReg(ax4+bx3+cx2+ dx+e)**

**QuartReg** (quartic regression) fits the fourth-degree polynomial y=ax4+bx3+cx2+dx+e to the data. It displays values for **a**, **b**, **c**, **d**, and **e**; when **DiagnosticOn** is set, it also displays a value for **R2**. For five points, the equation is a polynomial fit; for six or more, it is a polynomial regression. At least five points are required.

**QuartReg** [*Xlistname***,***Ylistname***,***freqlist***,***regequ*]

**LinReg(a+bx)**

**LinReg(a+bx)** (linear regression) fits the model equation y=a+bx to the data using a least-squares fit. It displays values for **a** (y-intercept) and **b** (slope); when **DiagnosticOn** is set, it also displays values for **r2** and **r**.

**LinReg(a+bx)** [*Xlistname***,***Ylistname***,***freqlist***,***regequ*]

**LnReg(a+b ln(x))**

**LnReg** (logarithmic regression) fits the model equation y=a+b ln(x) to the data using a least-squares fit and transformed values ln(x) and y. It displays values for **a** and **b**; when **DiagnosticOn** is set, it also displays values for **r2** and **r**.

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**LnReg** [*Xlistname***,***Ylistname***,***freqlist***,***regequ*]

**ExpReg(abx)**

**ExpReg** (exponential regression) fits the model equation y=abx to the data using a least-squares fit and transformed values x and ln(y). It displays values for **a** and **b**; when **DiagnosticOn** is set, it also displays values for **r2**

and **r**.

**ExpReg** [*Xlistname***,***Ylistname***,***freqlist***,***regequ*]

**PwrReg(axb)**

**PwrReg** (power regression) fits the model equation y=axb to the data using a least-squares fit and transformed values ln(x) and ln(y). It displays values for **a** and **b**; when **DiagnosticOn** is set, it also displays values for** r2**

and **r**.

**PwrReg** [*Xlistname***,***Ylistname***,***freqlist***,***regequ*]

**Logisticc/(1+aeLbx)**

**Logistic** fits the model equation y=c/(1+aeLbx) to the data using an iterative least-squares fit. It displays values for **a**, **b**, and **c**.

**Logistic** [*Xlistname***,***Ylistname***,***freqlist***,***regequ*]

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**SinRega sin(bx+c)+d**

**SinReg **(sinusoidal regression) fits the model equation y=a sin(bx+c)+d to the data using an iterative least-squares fit. It displays values for **a**, **b**, **c**, and **d**. At least four data points are required. At least two data points per cycle are required in order to avoid aliased frequency estimates.

**SinReg** [*iterations*,*Xlistname*,*Ylistname*,*period*,*regequ*]

*iterations* is the maximum number of times the algorithm will iterate to find a solution. The value for *iterations* can be an integer 1 and 16; if not specified, the default is 3. The algorithm may find a solution before *iterations* is reached. Typically, larger values for *iterations* result in longer execution times and better accuracy for **SinReg**, and vice versa.

A *period* guess is optional. If you do not specify *period*, the difference between time values in *Xlistname* must be equal and the time values must be ordered in ascending sequential order. If you specify *period*, the algorithm may find a solution more quickly, or it may find a solution when it would not have found one if you had omitted a value for *period*. If you specify *period*, the differences between time values in *Xlistname* can be unequal.

**Note:** The output of **SinReg** is always in radians, regardless of the **Radian/Degree** mode setting.

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**SinReg Example: Daylight Hours in Alaska for One Year**

Compute the regression model for the number of hours of daylight in Alaska during one year.

&

&

With noisy data, you will achieve better convergence results when you specify an accurate estimate for *period*. You can obtain a *period* guess in either of two ways.

Plot the data and trace to determine the x-distance between the beginning and end of one complete period, or cycle. The illustration above and to the right graphically depicts a complete period, or cycle.

1 period

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Plot the data and trace to determine the x-distance between the beginning and end of N complete periods, or cycles. Then divide the total distance by N.

After your first attempt to use **SinReg** and the default value for *iterations* to fit the data, you may find the fit to be approximately correct, but not optimal. For an optimal fit, execute **SinReg 16,***Xlistname***,***Ylistname***,2p / ***b* where *b* is the value obtained from the previous **SinReg** execution.

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Statistical Variables

The statistical variables are calculated and stored as indicated below. To access these variables for use in expressions, press , and select **5:Statistics**. Then select the **VARS** menu shown in the column below under **VARS** menu. If you edit a list or change the type of analysis, all statistical variables are cleared.

**Variables** **1.Var** **Stats**

**2.Var** **Stats** **Other**

**VARS** **menu**

mean of **x** values **v** **v** **XY**

sum of **x** values **Gx** **Gx** **G**

sum of **x2** values **Gx2** **Gx2** **G**

sample standard deviation of **x** **Sx** **Sx** **XY**

population standard deviation of **x** **sx** **sx** **XY**

number of data points **n** **n** **XY**

mean of **y** values **w** **XY**

sum of **y** values **Gy** **G**

sum of **y2** values **Gy2** **G**

sample standard deviation of **y** **Sy** **XY**

population standard deviation of **y** **sy** **XY**

sum of **x** **y** **Gxy** **G**

minimum of **x** values **minX** **minX** **XY**

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**Variables** **1.Var** **Stats**

**2.Var** **Stats** **Other**

**VARS** **menu**

maximum of **x** values **maxX** **maxX** **XY**

minimum of **y** values **minY** **XY**

maximum of **y** values **maxY** **XY**

1st quartile **Q1** **PTS**

median **Med** **PTS**

3rd quartile **Q3** **PTS**

regression/fit coefficients **a**, **b** **EQ**

polynomial, **Logistic**, and **SinReg** coefficients

**a**, **b**, **c**, **d**, **e**

**EQ**

correlation coefficient **r** **EQ**

coefficient of determination **r2**, **R2** **EQ**

regression equation **RegEQ** **EQ**

summary points (**Med.Med** only) **x1**, **y1**, **x2**, **y2**, **x3**, **y3**

**PTS**

**Q1 and Q3**

The first quartile (**Q1**) is the median of points between **minX** and **Med** (median). The third quartile (**Q3**) is the median of points between **Med** and **maxX**.

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Statistical Analysis in a Program

**Entering Stat Data**

You can enter statistical data, calculate statistical results, and fit models to data from a program. You can enter statistical data into lists directly within the program (Chapter 11).

**Statistical Calculations**

To perform a statistical calculation from a program, follow these steps.

1. On a blank line in the program editor, select the type of calculation from the **STAT CALC** menu.

2. Enter the names of the lists to use in the calculation. Separate the list names with a comma.

3. Enter a comma and then the name of a **Y=** variable, if you want to store the regression equation to a **Y=** variable.

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Statistical Plotting

**Steps for Plotting Statistical Data in Lists**

You can plot statistical data that is stored in lists. The six types of plots available are scatter plot, xyLine, histogram, modified box plot, regular box plot, and normal probability plot. You can define up to three plots.

To plot statistical data in lists, follow these steps.

1. Store the stat data in one or more lists.

2. Select or deselect **Y=** functions as appropriate.

3. Define the stat plot.

4. Turn on the plots you want to display.

5. Define the viewing window.

6. Display and explore the graph.

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**" (Scatter)**

**Scatter** plots plot the data points from **Xlist **and **Ylist** as coordinate pairs, showing each point as a box ( ), cross ( **+** ), or dot ( ). **Xlist** and **Ylist** must be the same length. You can use the same list for **Xlist **and **Ylist**.

** (xyLine)**

**xyLine** is a scatter plot in which the data points are plotted and connected in order of appearance in **Xlist **and **Ylist**. You may want to use **SortA(** or **SortD(** to sort the lists before you plot them.

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** (Histogram)**

**Histogram** plots one-variable data. The **Xscl** window variable value determines the width of each bar, beginning at **Xmin**. **ZoomStat** adjusts **Xmin**, **Xmax**, **Ymin**, and **Ymax** to include all values, and also adjusts **Xscl**. The inequality (**Xmax** N **Xmin**) **Xscl** 47 must be true. A value that occurs on the edge of a bar is counted in the bar to the right.

** (ModBoxplot)**

**ModBoxplot** (modified box plot) plots one-variable data, like the regular box plot, except points that are 1.5 Interquartile Range beyond the quartiles. (The Interquartile Range is defined as the difference between the third quartile **Q3** and the first quartile **Q1**.) These points are plotted individually beyond the whisker, using the **Mark** ( or **+ **or ) you select. You can trace these points, which are called outliers.

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The prompt for outlier points is **x=**, except when the outlier is the maximum point (**maxX**) or the minimum point (**minX**). When outliers exist, the end of each whisker will display **x=**. When no outliers exist, **minX** and **maxX** are the prompts for the end of each whisker. **Q1**, **Med** (median), and **Q3** define the box.

Box plots are plotted with respect to **Xmin** and **Xmax**, but ignore **Ymin** and **Ymax**. When two box plots are plotted, the first one plots at the top of the screen and the second plots in the middle. When three are plotted, the first one plots at the top, the second in the middle, and the third at the bottom.

** (Boxplot)**

**Boxplot** (regular box plot) plots one-variable data. The whiskers on the plot extend from the minimum data point in the set (**minX**) to the first quartile (**Q1**) and from the third quartile (**Q3**) to the maximum point (**maxX**). The box is defined by **Q1**, **Med** (median), and **Q3**.

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Box plots are plotted with respect to **Xmin** and **Xmax**, but ignore **Ymin** and **Ymax**. When two box plots are plotted, the first one plots at the top of the screen and the second plots in the middle. When three are plotted, the first one plots at the top, the second in the middle, and the third at the bottom.

** (NormProbPlot)**

**NormProbPlot** (normal probability plot) plots each observation **X** in **Data List** versus the corresponding quantile **z** of the standard normal distribution. If the plotted points lie close to a straight line, then the plot indicates that the data are normal.

Enter a valid list name in the **Data List** field. Select **X** or **Y** for the **Data Axis** setting.

If you select **X**, the TI-83 Plus plots the data on the x-axis and the z-values on the y-axis.

If you select **Y**, the TI-83 Plus plots the data on the y-axis and the z-values on the x-axis.

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**Defining the Plots**

To define a plot, follow these steps.

1. Press y ,. The **STAT PLOTS** menu is displayed with the current plot definitions.

2. Select the plot you want to use. The stat plot editor is displayed for the plot you selected.

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3. Press to select **On** if you want to plot the statistical data immediately. The definition is stored whether you select **On** or **Off**.

4. Select the type of plot. Each type prompts for the options checked in this table.

**Plot Type** **XList** **YList** **Mark** **Freq** **Data List** **Data Axis**

**"** **Scatter**

5. Enter list names or select options for the plot type.

**Xlist** (list name containing independent data)

**Ylist** (list name containing dependent data)

**Mark** ( or **+** or )

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**Freq** (frequency list for **Xlist** elements; default is **1**)

**Data List** (list name for **NormProbPlot**)

**Data Axis** (axis on which to plot** Data List**)

**Displaying Other Stat Plot Editors**

Each stat plot has a unique stat plot editor. The name of the current stat plot (**Plot1**, **Plot2**, or **Plot3**) is highlighted in the top line of the stat plot editor. To display the stat plot editor for a different plot, press }, ~, and | to move the cursor onto the name in the top line, and then press . The stat plot editor for the selected plot is displayed, and the selected name remains highlighted.

**Turning On and Turning Off Stat Plots**

**PlotsOn** and **PlotsOff** allow you to turn on or turn off stat plots from the home screen or a program. With no plot number, **PlotsOn** turns on all plots and **PlotsOff** turns off all plots. With one or more plot numbers (**1**, **2**, and **3**), **PlotsOn** turns on specified plots, and **PlotsOff** turns off specified plots.

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**PlotsOff** [**1,2,3**] **PlotsOn** [**1,2,3**]

**Note:** You also can turn on and turn off stat plots in the top line of the Y= editor (Chapter 3).

**Defining the Viewing Window**

Stat plots are displayed on the current graph. To define the viewing window, press p and enter values for the window variables. **ZoomStat** redefines the viewing window to display all statistical data points.

**Tracing a Stat Plot**

When you trace a scatter plot or xyLine, tracing begins at the first element in the lists.

When you trace a histogram, the cursor moves from the top center of one column to the top center of the next, starting at the first column.

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When you trace a box plot, tracing begins at **Med** (the median). Press | to trace to **Q1** and **minX**. Press ~ to trace to **Q3** and **maxX**.

When you press } or to move to another plot or to another Y= function, tracing moves to the current or beginning point on that plot (not the nearest pixel).

The **ExprOn**/**ExprOff** format setting applies to stat plots (Chapter 3). When **ExprOn **is selected, the plot number and plotted data lists are displayed in the top-left corner.

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Statistical Plotting in a Program

**Defining a Stat Plot in a Program**

To display a stat plot from a program, define the plot, and then display the graph.

To define a stat plot from a program, begin on a blank line in the program editor and enter data into one or more lists; then, follow these steps.

1. Press y , to display the **STAT PLOTS** menu.

2. Select the plot to define, which pastes **Plot1(**, **Plot2(**, or **Plot3(** to the cursor location.

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3. Press y , ~ to display the **STAT TYPE** menu.

4. Select the type of plot, which pastes the name of the plot type to the cursor location.

5. Press . Enter the list names, separated by commas.

6. Press y , | to display the **STAT PLOT MARK** menu. (This step is not necessary if you selected **3:Histogram** or **5:Boxplot** in step 4.)

Select the type of mark ( or **+** or ) for each data point. The selected mark symbol is pasted to the cursor location.

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7. Press to complete the command line.

**Displaying a Stat Plot from a Program**

To display a plot from a program, use the **DispGraph** instruction (Chapter 16) or any of the **ZOOM** instructions (Chapter 3).

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Chapter 13: Inferential Statistics and Distributions

Getting Started: Mean Height of a Population

**Getting Started is a fast-paced introduction. Read the chapter for details.**

**Suppose you want to estimate the mean height of a population of women given** **the random sample below. Because heights among a biological population tend** **to be normally distributed, a t distribution confidence interval can be used when** **estimating the mean. The 10 height values below are the first 10 of 90 values,** **randomly generated from a normally distributed population with an assumed** **mean of 165.1 centimeters and a standard deviation of 6.35 centimeters** **(randNorm(165.1,6.35,90) with a seed of 789).**

**Height (in centimeters) of Each of 10 Women**

169.43 168.33 159.55 169.97 159.79 181.42 171.17 162.04 167.15 159.53

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1. Press to display the stat list editor.

Press } to move the cursor onto **L1**, and then press y 6. The **Name=** prompt is displayed on the bottom line. The cursor indicates that alpha-lock is on. The existing list name columns shift to the right.

**Note:** Your stat editor may not look like the one pictured here, depending on the lists you have already stored.

2. Enter [H] [G] [H] [T] at the **Name=** prompt, and then press . The list to which you will store the womens height data is created.

Press to move the cursor onto the first row of the list. **HGHT(1)=** is displayed on the bottom line.

3. Press **169** **43** to enter the first height value. As you enter it, it is displayed on the bottom line.

Press . The value is displayed in the first row, and the rectangular cursor moves to the next row.

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Enter the other nine height values the same way.

4. Press | to display the **STAT TESTS** menu, and then press until **8:TInterval** is highlighted.

5. Press to select **8:TInterval**. The inferential stat editor for **TInterval** is displayed. If **Data** is not selected for** Inpt:**, press | to select **Data**.

Press and [H] [G] [H] [T] at the **List:** prompt (alpha-lock is on).

Press **99** to enter a 99 percent confidence level at the **C.Level:** prompt.

6. Press to move the cursor onto **Calculate**, and then press . The confidence interval is calculated, and the **TInterval** results are displayed on the home screen.

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Interpret the results.

The first line, **(159.74,173.94)**, shows that the 99 percent confidence interval for the population mean is between about 159.74 centimeters and 173.94 centimeters. This is about a 14.2 centimeters spread.

The .99 confidence level indicates that in a very large number of samples, we expect 99 percent of the intervals calculated to contain the population mean. The actual mean of the population sampled is 165.1 centimeters, which is in the calculated interval.

The second line gives the mean height of the sample used to compute this interval. The third line gives the sample standard deviation **Sx**. The bottom line gives the sample size **n**.

To obtain a more precise bound on the population mean **m** of womens heights, increase the sample size to 90. Use a sample mean of 163.8 and sample standard deviation **Sx** of 7.1 calculated from the larger random sample. This time, use the **Stats** (summary statistics) input option.

7. Press | **8** to display the inferential stat editor for **TInterval**.

Press ~ to select **Inpt:Stats**. The editor changes so that you can enter summary statistics as input.

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8. Press **163** **8** to store 163.8 to .

Press **7** **1** to store 7.1 to **Sx**.

Press **90 ** to store 90 to **n**.

9. Press to move the cursor onto **Calculate**, and then press to calculate the new 99 percent confidence interval. The results are displayed on the home screen.

If the height distribution among a population of women is normally distributed with a mean **m** of 165.1 centimeters and a standard deviation of 6.35 centimeters, what height is exceeded by only 5 percent of the women (the 95th percentile)?

10.Press to clear the home screen.

Press y = to display the **DISTR**

(distributions) menu.

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11. Press **3** to paste **invNorm(** to the home screen.

Press **95** **165 ** **1** **6 ** **35** .

**.95** is the area, **165.1** is , and **6.35** is .

The result is displayed on the home screen; it shows that five percent of the women are taller than 175.5 centimeters.

Now graph and shade the top 5 percent of the population.

12. Press p and set the window variables to these values.

**Xmin=145** **Ymin=L.02** **Xres=1** **Xmax=185** **Ymax=.08** **Xscl=5** **Yscl=0**

13. Press y = ~ to display the **DISTR DRAW**

menu.

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14. Press to paste **ShadeNorm(** to the home screen.

Press y Z **1** y D **99** **165** **1** **6** **35** .

**Ans** (175.5448205 from step 11) is the lower bound. 199 is the upper bound. The normal curve is defined by a mean of 165.1 and a standard deviation of 6.35.

15. Press to plot and shade the normal curve.

**Area** is the area above the 95th percentile. **low** is the lower bound. **up** is the upper bound.

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Inferential Stat Editors

**Displaying the Inferential Stat Editors**

When you select a hypothesis test or confidence interval instruction from the home screen, the appropriate inferential statistics editor is displayed. The editors vary according to each test or intervals input requirements. Below is the inferential stat editor for **T-Test**.

**Note: **When you select the **ANOVA(** instruction, it is pasted to the home screen. **ANOVA(** does not have an editor screen.

**Using an Inferential Stat Editor**

To use an inferential stat editor, follow these steps.

1. Select a hypothesis test or confidence interval from the **STAT TESTS**

menu. The appropriate editor is displayed.

2. Select **Data** or **Stats** input, if the selection is available. The appropriate editor is displayed.

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3. Enter real numbers, list names, or expressions for each argument in the editor.

4. Select the alternative hypothesis (, **<**, or **>**) against which to test, if the selection is available.

5. Select **No** or **Yes** for the **Pooled** option, if the selection is available.

6. Select **Calculate** or **Draw** (when **Draw** is available) to execute the instruction.

When you select **Calculate**, the results are displayed on the home screen.

When you select **Draw**, the results are displayed in a graph.

This chapter describes the selections in the above steps for each hypothesis test and confidence interval instruction.

Enter values for arguments

Select **Data** or **Stats** input

Select an alternative hypothesis

Select **Calculate** or **Draw **output

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**Selecting Data or Stats**

Most inferential stat editors prompt you to select one of two types of input. (**1.PropZInt** and **2.PropZTest**, **1.PropZInt** and **2.PropZInt**, **c2.Test**, and **LinRegTTest** do not.)

Select **Data** to enter the data lists as input.

Select **Stats** to enter summary statistics, such as , **Sx**, and **n**, as input.

To select **Data** or **Stats**, move the cursor to either** Data** or **Stats**, and then press .

**Entering the Values for Arguments**

Inferential stat editors require a value for every argument. If you do not know what a particular argument symbol represents, see the Inferential Statistics Input Descriptions tables.

When you enter values in any inferential stat editor, the TI-83 Plus stores them in memory so that you can run many tests or intervals without having to reenter every value.

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**Selecting an Alternative Hypothesis ( < >)**

Most of the inferential stat editors for the hypothesis tests prompt you to select one of three alternative hypotheses.

The first is a alternative hypothesis, such as mm0 for the **Z.Test**.

The second is a **<** alternative hypothesis, such as m1

The third is a **>** alternative hypothesis, such as p1>p2 for the **2.PropZTest**.

To select an alternative hypothesis, move the cursor to the appropriate alternative, and then press .

**Selecting the Pooled Option**

**Pooled** (**2.SampTTest** and **2.SampTInt** only) specifies whether the variances are to be pooled for the calculation.

Select **No** if you do not want the variances pooled. Population variances can be unequal.

Select **Yes** if you want the variances pooled. Population variances are assumed to be equal.

To select the **Pooled** option, move the cursor to **Yes**, and then press .

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**Selecting Calculate or Draw for a Hypothesis Test**

After you have entered all arguments in an inferential stat editor for a hypothesis test, you must select whether you want to see the calculated results on the home screen (**Calculate**) or on the graph screen (**Draw**).

**Calculate** calculates the test results and displays the outputs on the home screen.

**Draw** draws a graph of the test results and displays the test statistic and p-value with the graph. The window variables are adjusted automatically to fit the graph.

To select **Calculate** or **Draw**, move the cursor to either **Calculate** or **Draw**, and then press . The instruction is immediately executed.

**Selecting Calculate for a Confidence Interval**

After you have entered all arguments in an inferential stat editor for a confidence interval, select **Calculate** to display the results. The **Draw** option is not available.

When you press , **Calculate** calculates the confidence interval results and displays the outputs on the home screen.

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**Bypassing the Inferential Stat Editors**

To paste a hypothesis test or confidence interval instruction to the home screen without displaying the corresponding inferential stat editor, select the instruction you want from the **CATALOG** menu. Appendix A describes the input syntax for each hypothesis test and confidence interval instruction.

**Note:** You can paste a hypothesis test or confidence interval instruction to a command line in a program. From within the program editor, select the instruction from either the **CATALOG** (Chapter 15) or the **STAT TESTS** menu.

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STAT TESTS Menu

**STAT TESTS Menu**

To display the **STAT TESTS** menu, press |. When you select an inferential statistics instruction, the appropriate inferential stat editor is displayed.

Most **STAT TESTS** instructions store some output variables to memory. For a list of these variables, see the Test and Interval Output Variables table.

**EDIT** **CALC** **TESTS** **1:** **Z-Test...** Test for 1 m, known s **2:** **T-Test...** Test for 1 m, unknown s **3:** **2-SampZTest...** Test comparing 2 ms, known ss **4:** **2-SampTTest...** Test comparing 2 ms, unknown ss **5:** **1-PropZTest...** Test for 1 proportion **6:** **2-PropZTest...** Test comparing 2 proportions **7:** **ZInterval...** Confidence interval for 1 m, known s **8:** **TInterval...** Confidence interval for 1 m, unknown s **9:** **2-SampZInt...** Confidence interval for difference of 2 ms, known ss **0:** **2-SampTInt...** Confidence interval for difference of 2 ms, unknown ss **A:** **1-PropZInt...** Confidence interval for 1 proportion **B:** **2-PropZInt...** Confidence interval for difference of 2 proportions **C:** **c2-Test...** Chi-square test for 2-way tables **D:** **2-SampTest...** Test comparing 2 ss

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**EDIT** **CALC** **TESTS** **E:** **LinRegTTest...** *t *test for regression slope and r **F:** **ANOVA(** One-way analysis of variance

**Note:** When a new test or interval is computed, all previous output variables are invalidated.

**Inferential Stat Editors for the STAT TESTS Instructions**

In this chapter, the description of each **STAT TESTS** instruction shows the unique inferential stat editor for that instruction with example arguments.

Descriptions of instructions that offer the **Data**/**Stats** input choice show both types of input screens.

Descriptions of instructions that do not offer the **Data**/**Stats** input choice show only one input screen.

The description then shows the unique output screen for that instruction with the example results.

Descriptions of instructions that offer the **Calculate**/**Draw** output choice show both types of screens: calculated and graphic results.

Descriptions of instructions that offer only the **Calculate** output choice show the calculated results on the home screen.

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**Z.Test**

**Z.Test** (one-sample *z *test; item **1**) performs a hypothesis test for a single unknown population mean **m** when the population standard deviation s is known. It tests the null hypothesis H0: m=m0 against one of the alternatives below.

Ha: mm0 (**m:m0**)

Ha: m

Ha: m>m0 (**m:>m0**)

In the example:

**L1={299.4 297.7 301 298.9 300.2 297}**

**Data** **Stats**

Input:

**,** **,**

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**Data** **Stats**

Calculated results:

**,** **,**

Drawn results:

**Note:** All **STAT TESTS** examples assume a fixed-decimal mode setting of **4** (Chapter 1). If you set the decimal mode to **Float** or a different fixed-decimal setting, your output may differ from the output in the examples.

**T.Test**

**T.Test** (one-sample *t* test; item **2**) performs a hypothesis test for a single unknown population mean **m** when the population standard deviation s is unknown. It tests the null hypothesis H0: m=m0 against one of the alternatives below.

Ha: mm0 (**m:m0**) Ha: m**m:>m0**)

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In the example:

**TEST={91.9 97.8 111.4 122.3 105.4 95}**

**Data** **Stats**

Input:

**,** **,**

Calculated results:

**,** **,**

Drawn results:

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**2.SampZTest**

**2.SampZTest** (two-sample *z* test; item **3**) tests the equality of the means of two populations (m1 and m2) based on independent samples when both population standard deviations (s1 and s2) are known. The null hypothesis H0: m1=m2 is tested against one of the alternatives below.

Ha: m1m2 (**m1:m2**)

Ha: m1

Ha: m1>m2 (**m1:>m2**)

In the example:

**LISTA={154 109 137 115 140}**

**LISTB={108 115 126 92 146}**

**Data** **Stats**

Input:

**,** **,**

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Calculated results:

**,** **,**

Drawn results:

**2.SampTTest**

**2.SampTTest** (two-sample *t* test; item **4**) tests the equality of the means of two populations (m1 and m2) based on independent samples when neither population standard deviation (s1 or s2) is known. The null hypothesis H0: m1=m2 is tested against one of the alternatives below.

Ha: m1m2 (**m1:m2**) Ha: m1**m1:>m2**)

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In the example:

**SAMP1={12.207 16.869 25.05 22.429 8.456 10.589}**

**SAMP2={11.074 9.686 12.064 9.351 8.182 6.642}**

**Data** **Stats**

Input:

**,** **,**

Calculated results:

**,** **,**

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Drawn results:

**1.PropZTest**

**1.PropZTest** (one-proportion *z* test; item **5**) computes a test for an unknown proportion of successes (prop). It takes as input the count of successes in the sample *x* and the count of observations in the sample *n*. **1.PropZTest** tests the null hypothesis H0: prop=p0 against one of the alternatives below.

Ha: propp0 (**prop:p0**)

Ha: prop

Ha: prop>p0 (**prop:>p0**)

Input:

**,**

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Calculated results:

**,**

Drawn results:

**2.PropZTest**

**2.PropZTest** (two-proportion *z* test; item **6**) computes a test to compare the proportion of successes (p1 and p2) from two populations. It takes as input the count of successes in each sample (*x*1 and *x*2) and the count of observations in each sample (*n*1 and *n*2). **2.PropZTest** tests the null hypothesis H0: p1=p2 (using the pooled sample proportion ) against one of the alternatives below.

Ha: p1p2 (**p1:p2**)

Ha: p1

Ha: p1>p2 (**p1:>p2**)

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Input:

**,**

Calculated results:

**,**

Drawn results:

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**ZInterval**

**ZInterval** (one-sample *z* confidence interval; item **7**) computes a confidence interval for an unknown population mean m when the population standard deviation s is known. The computed confidence interval depends on the user-specified confidence level.

In the example:

**L1={299.4 297.7 301 298.9 300.2 297}**

**Data** **Stats**

Input:

**,** **,**

Calculated results:

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**TInterval**

**TInterval** (one-sample *t* confidence interval; item **8**) computes a confidence interval for an unknown population mean m when the population standard deviation s is unknown. The computed confidence interval depends on the user-specified confidence level.

In the example:

**L6={1.6 1.7 1.8 1.9}**

**Data** **Stats**

Input:

**,** **,**

Calculated results:

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**2.SampZInt**

**2.SampZInt** (two-sample *z* confidence interval; item **9**) computes a confidence interval for the difference between two population means (m1Nm2) when both population standard deviations (s1 and s2) are known. The computed confidence interval depends on the user-specified confidence level.

In the example:

**LISTC={154 109 137 115 140}**

**LISTD={108 115 126 92 146}**

**Data** **Stats**

Input:

**,** **,**

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Calculated results:

**2.SampTInt**

**2.SampTInt** (two-sample *t* confidence interval; item **0**) computes a confidence interval for the difference between two population means (m1Nm2) when both population standard deviations (s1 and s2) are unknown. The computed confidence interval depends on the user- specified confidence level.

In the example:

**SAMP1={12.207 16.869 25.05 22.429 8.456 10.589}**

**SAMP2={11.074 9.686 12.064 9.351 8.182 6.642}**

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**Data** **Stats**

Input:

**,** **,**

Calculated results:

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**1.PropZInt**

**1.PropZInt** (one-proportion *z* confidence interval; item **A**) computes a confidence interval for an unknown proportion of successes. It takes as input the count of successes in the sample *x* and the count of observations in the sample* n*. The computed confidence interval depends on the user-specified confidence level.

Input:

**,**

Calculated results:

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**2.PropZInt**

**2.PropZInt** (two-proportion *z* confidence interval; item **B**) computes a confidence interval for the difference between the proportion of successes in two populations (p1Np2). It takes as input the count of successes in each sample (*x*1 and *x*2) and the count of observations in each sample (*n*1 and *n*2). The computed confidence interval depends on the user-specified confidence level.

Input:

**,**

Calculated results:

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**c2.Test**

**c2.Test** (chi-square test; item **C**) computes a chi-square test for association on the two-way table of counts in the specified *Observed* matrix. The null hypothesis H0 for a two-way table is: no association exists between row variables and column variables. The alternative hypothesis is: the variables are related.

Before computing a c2.Test, enter the observed counts in a matrix. Enter that matrix variable name at the **Observed:** prompt in the c2.Test editor; default=**[A]**. At the **Expected:** prompt, enter the matrix variable name to which you want the computed expected counts to be stored; default=**[B]**.

Matrix editor:

**Note:** Press y ~ ~ **1** to select **1:[A]** from the MATRX EDIT menu.

Input:

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**,** **Note:** Press y **[B] ** to display matrix** [B]**.

Calculated results:

**,**

Drawn results:

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**2.SampTest**

**2.SampTest** (two-sample -test; item **D**) computes an -test to compare two normal population standard deviations (s1 and s2). The population means and standard deviations are all unknown. **2.SampTest**, which uses the ratio of sample variances Sx12/Sx22, tests the null hypothesis H0: s1=s2 against one of the alternatives below.

Ha: s1s2 (**s1:s2**)

Ha: s1

Ha: s1>s2 (**s1:>s2**)

In the example:

**SAMP4={** **7** **L4** **18** **17** **L3** **L5** **1** **10** **11L2}** **SAMP5={** **L1** **12** **L1** **L3** **3** **L5** **5** **2L11** **L1L3}**

**Data** **Stats**

Input:

**,** **,**

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TI-83 Plus Inferential Statistics and Distributions 415

Calculated results:

**,** **,**

Drawn results:

**LinRegTTest**

**LinRegTTest** (linear regression *t *test; item **E**) computes a linear regression on the given data and a *t* test on the value of slope b and the correlation coefficient r for the equation *y*=a+bx. It tests the null hypothesis H0: b=0 (equivalently, r=0) against one of the alternatives below.

Ha: b0 and r0 (**b & r:0**)

Ha: b<0 and r<0 (**b & r:<0**)

Ha: b>0 and r>0 (**b & r:>0**)

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The regression equation is automatically stored to **RegEQ** (**VARS Statistics**

**EQ** secondary menu). If you enter a **Y=** variable name at the **RegEQ:** prompt, the calculated regression equation is automatically stored to the specified **Y=** equation. In the example below, the regression equation is stored to **Y1**, which is then selected (turned on).

In the example:

**L3={** **38** **56** **59** **6474}** **L4={** **41** **63** **70** **7284}**

Input:

**,**

Calculated results:

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TI-83 Plus Inferential Statistics and Distributions 417

When **LinRegTTest** is executed, the list of residuals is created and stored to the list name **RESID** automatically. **RESID** is placed on the **LIST NAMES**

menu.

**Note:** For the regression equation, you can use the fix-decimal mode setting to control the number of digits stored after the decimal point (Chapter 1). However, limiting the number of digits to a small number could affect the accuracy of the fit.

**ANOVA(**

**ANOVA(** (one-way analysis of variance; item **F**) computes a one-way analysis of variance for comparing the means of two to 20 populations. The **ANOVA** procedure for comparing these means involves analysis of the variation in the sample data. The null hypothesis H0: m1=m2=...=mk is tested against the alternative Ha: not all m1...mk are equal.

**ANOVA(***list1***,***list2*[**,***...***,***list20*]**)**

In the example:

**L1={7 4 6 6 5}** **L2={6 5 5 8 7}** **L3={4 7 6 7 6}**

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Input:

**,**

Calculated results:

**Note: SS** is sum of squares and **MS** is mean square.

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Inferential Statistics Input Descriptions

The tables in this section describe the inferential statistics inputs discussed in this chapter. You enter values for these inputs in the inferential stat editors. The tables present the inputs in the same order that they appear in this chapter.

**Input** **Description**

**m0** Hypothesized value of the population mean that you are testing.

**s** The known population standard deviation; must be a real number > 0.

**List** The name of the list containing the data you are testing.

**Freq** The name of the list containing the frequency values for the data in **List**. Default=1. All elements must be integers | 0.

**Calculate**/**Draw** Determines the type of output to generate for tests and intervals. **Calculate **displays the output on the home screen. In tests, **Draw** draws a graph of the results.

**v**, **Sx**, **n** Summary statistics (mean, standard deviation, and sample size) for the one-sample tests and intervals.

**s1** The known population standard deviation from the first population for the two-sample tests and intervals. Must be a real number > 0.

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**Input** **Description**

**s2** The known population standard deviation from the second population for the two-sample tests and intervals. Must be a real number > 0.

**List1**, **List2** The names of the lists containing the data you are testing for the two-sample tests and intervals. Defaults are **L1** and **L2**, respectively.

**Freq1**, **Freq2** The names of the lists containing the frequencies for the data in **List1** and **List2** for the two-sample tests and intervals. Defaults=1. All elements must be integers | 0.

**v1**, **Sx1**, **n1**, **v2**, **Sx2**, **n2**

Summary statistics (mean, standard deviation, and sample size) for sample one and sample two in the two- sample tests and intervals.

**Pooled** Specifies whether variances are to be pooled for **2.SampTTest** and **2.SampTInt. No** instructs the TI.83 not to pool the variances. **Yes** instructs the TI.83 to pool the variances.

**p**0 The expected sample proportion for **1.PropZTest**. Must be a real number, such that 0 < p0 < 1.

**x** The count of successes in the sample for the **1.PropZTest** and **1.PropZInt.** Must be an integer 0.

**n** The count of observations in the sample for the **1.PropZTest** and **1.PropZInt**. Must be an integer > 0.

**x1** The count of successes from sample one for the **2.PropZTest** and **2.PropZInt**. Must be an integer 0.

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**Input** **Description**

**x2** The count of successes from sample two for the **2.PropZTest** and **2.PropZInt**. Must be an integer 0.

**n1** The count of observations in sample one for the **2.PropZTest** and **2.PropZInt**. Must be an integer > 0.

**n2** The count of observations in sample two for the **2.PropZTest** and **2.PropZInt**. Must be an integer > 0.

**C.Level** The confidence level for the interval instructions. Must be 0 and <100. If it is 1, it is assumed to be given as a percent and is divided by 100. Default=0.95.

**Observed (Matrix)** The matrix name that represents the columns and rows for the observed values of a two-way table of counts for the c2**.Test**. **Observed** must contain all integers 0. Matrix dimensions must be at least 22.

**Expected (Matrix)** The matrix name that specifies where the expected values should be stored. **Expected **is created upon successful completion of the c2**.Test**.

**Xlist**, **Ylist** The names of the lists containing the data for **LinRegTTest**. Defaults are **L1** and **L2**, respectively. The dimensions of **Xlist** and **Ylist** must be the same.

**RegEQ** The prompt for the name of the **Y=** variable where the calculated regression equation is to be stored. If a **Y=** variable is specified, that equation is automatically selected (turned on). The default is to store the regression equation to the **RegEQ** variable only.

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Test and Interval Output Variables

The inferential statistics variables are calculated as indicated below. To access these variables for use in expressions, press , **5** (**5:Statistics**), and then select the **VARS** menu listed in the last column below.

**Variables** **Tests** **Intervals** **LinRegTTest**

**ANOVA** **VARS** **Menu**

p-value **p** **p** **TEST**

test statistics **z, t, c2, ** **t, ** **TEST**

degrees of freedom **df** **df** **df** **TEST**

sample mean of x values for sample 1 and sample 2

**v1, v2** **v1, v2** **TEST**

sample standard deviation of x for sample 1 and sample 2

**Sx1,** **Sx2**

**Sx1,** **Sx2**

**TEST**

number of data points for sample 1 and sample 2

**n1, n2** **n1, n2** **TEST**

pooled standard deviation **SxP** **SxP** **SxP** **TEST**

estimated sample proportion **TEST**

estimated sample proportion for population 1

**1** **1** **TEST**

estimated sample proportion for population 2

**2** **2** **TEST**

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**Variables** **Tests** **Intervals** **LinRegTTest**

**ANOVA** **VARS** **Menu**

confidence interval pair **lower,** **upper**

**TEST**

mean of x values **v** **v** **XY**

sample standard deviation of x **Sx** **Sx** **XY**

number of data points **n** **n** **XY**

standard error about the line **s** **TEST**

regression/fit coefficients **a, b** **EQ**

correlation coefficient **r** **EQ**

coefficient of determination **r2** **EQ**

regression equation **RegEQ** **EQ**

**Note:** The variables listed above cannot be archived.

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Distribution Functions

**DISTR menu**

To display the **DISTR** menu, press y =.

**DISTR** ** DRAW** **1:normalpdf(** Normal probability density **2:normalcdf(** Normal distribution probability **3:invNorm(** Inverse cumulative normal distribution **4:tpdf(** Student-*t* probability density **5:tcdf(** Student-*t* distribution probability **6:c2pdf(** Chi-square probability density **7:c2cdf** Chi-square distribution probability **8:****pdf(** probability density **9:****cdf(** distribution probability **0:binompdf(** Binomial probability **A:binomcdf(** Binomial cumulative density **B:poissonpdf(** Poisson probability **C:poissoncdf(** Poisson cumulative density **D:geometpdf(** Geometric probability **E:geometcdf(** Geometric cumulative density

**Note:** L199 and 199 specify infinity. If you want to view the area left of *upperbound*, for example, specify *lowerbound*= L199.

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**normalpdf(**

**normalpdf(** computes the probability density function (**pdf**) for the normal distribution at a specified *x* value. The defaults are mean m=0 and standard deviation s=1. To plot the normal distribution, paste **normalpdf(** to the** Y=** editor. The probability density function (pdf) is:

0, 2

1 )( 2

2

2 )(

>=

*x*

*exf*

**normalpdf(***x*[**,**m**,**s]**)** **Note:** For this example, Xmin = 28 Xmax = 42 Ymin = 0 Ymax = .25

**Tip:** For plotting the normal distribution, you can set window variables **Xmin** and **Xmax** so that the mean m falls between them, and then select **0:ZoomFit** from the **ZOOM** menu.

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**normalcdf(**

**normalcdf(** computes the normal distribution probability between *lowerbound* and *upperbound* for the specified mean m and standard deviation s. The defaults are m=0 and s=1.

**normalcdf(***lowerbound***,***upperbound*[**,**m**,**s]**)**

**invNorm(**

**invNorm(** computes the inverse cumulative normal distribution function for a given *area* under the normal distribution curve specified by mean m and standard deviation s. It calculates the *x *value associated with an *area* to the left of the *x* value. 0 *area * 1 must be true. The defaults are m=0 and s=1.

**invNorm(***area*[**,**m**,**s]**)**

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**tpdf(**

**tpdf(** computes the probability density function (pdf) for the Student-*t* distribution at a specified *x* value. *df *(degrees of freedom) must be >0. To plot the Student-*t* distribution, paste **tpdf(** to the **Y=** editor. The probability density function (pdf)is:

*df*

*dfx*

*df*

*df* *xf*

*df*

2/)1(2 )/1(

)2/(

]2/)1[( )(

++

+=

**tpdf(***x***,***df***)**

**Note:** For this example, Xmin = L4.5 Xmax = 4.5 Ymin = 0 Ymax = .4

**tcdf(**

**tcdf(** computes the Student-*t* distribution probability between *lowerbound* and* upperbound* for the specified* df *(degrees of freedom), which must be > 0.

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**tcdf(***lowerbound***,***upperbound***,***df***)**

**c2pdf(**

**c2pdf(** computes the probability density function (pdf) for the c2 (chi-square) distribution at a specified *x* value. *df* (degrees of freedom) must be an integer > 0. To plot the c2 distribution, paste **c2pdf(** to the **Y=** editor. The probability density function (pdf) is:

0,2)/(1 )2/(

1 )( 2/12/2/

= *xex*

*df* *xf* *xdfdf*

**c2pdf(***x***,***df***)**

**Note:** For this example, **Xmin = 0** **Xmax = 30** **Ymin = L.02** **Ymax = .132**

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**c2cdf(**

**c2cdf(** computes the c2 (chi-square) distribution probability between *lowerbound* and* upperbound* for the specified *df *(degrees of freedom), which must be an integer > 0.

**c2cdf(***lowerbound***,***upperbound***,***df***)**

**pdf(**

**pdf(** computes the probability density function (pdf) for the distribution at a specified *x* value. *numerator df* (degrees of freedom) and *denominator df* must be integers > 0. To plot the distribution, paste **pdf(** to the **Y=** editor. The probability density function (pdf) is:

0,)/1( )2/()2/(

]2/)[( )( 2/)(12/2/ +

+= + *xdnxx*

*d*

*n*

*dn*

*dn* *xf* *dnnn*

where *n* = numerator degrees of freedom *d* = denominator degrees of freedom

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**pdf(***x***,***numerator df***,***denominator df***)**

**Note:** For this example, **Xmin = 0** **Xmax = 5** **Ymin = 0** **Ymax = 1**

**cdf(**

**cdf(** computes the distribution probability between *lowerbound *and *upperbound* for the specified *numerator df* (degrees of freedom) and *denominator df*.* numerator df* and *denominator df* must be integers >0.

**cdf(***lowerbound***,***upperbound***,***numerator df***,***denominator df***)**

**binompdf**

**binompdf(** computes a probability at *x* for the discrete binomial distribution with the specified *numtrials* and probability of success (*p*) on each trial. *x* can be an integer or a list of integers. 0*p*1 must be true. *numtrials* must be an integer > 0. If you do not specify *x*, a list of

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probabilities from 0 to *numtrials* is returned. The probability density function (pdf) is:

*nxppx* *nxf* *xnx* ,,1,0,)1()( K=

=

where *n = numtrials*

**binompdf(***numtrials***,***p*[**,***x*]**)**

**binomcdf(**

**binomcdf(** computes a cumulative probability at *x* for the discrete binomial distribution with the specified *numtrials* and probability of success (*p*) on each trial. *x* can be a real number or a list of real numbers. 0*p*1 must be true. *numtrials* must be an integer > 0. If you do not specify *x*, a list of cumulative probabilities is returned.

**binomcdf(***numtrials***,***p*[**,***x*]**)**

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**poissonpdf(**

**poissonpdf(** computes a probability at *x* for the discrete Poisson distribution with the specified mean m, which must be a real number > 0. *x* can be an integer or a list of integers. The probability density function (pdf) is:

,2,1,0,!/)( == *xxexf* *x*

**poissonpdf(**m**,***x***)**

**poissoncdf(**

**poissoncdf(** computes a cumulative probability at *x* for the discrete Poisson distribution with the specified mean m, which must be a real number > 0. *x* can be a real number or a list of real numbers.

**poissoncdf(**m**,***x***)**

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**geometpdf(**

**geometpdf(** computes a probability at *x*, the number of the trial on which the first success occurs, for the discrete geometric distribution with the specified probability of success *p*. 0*p*1 must be true. *x* can be an integer or a list of integers. The probability density function (pdf) is:

,2,1,)1()( 1 == *xppxf* *x*

**geometpdf(***p***,***x***)**

**geometcdf(**

**geometcdf(** computes a cumulative probability at *x*, the number of the trial on which the first success occurs, for the discrete geometric distribution with the specified probability of success *p*. 0*p*1 must be true.* x* can be a real number or a list of real numbers.

**geometcdf(***p***,***x***)**

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Distribution Shading

**DISTR DRAW Menu**

To display the **DISTR DRAW** menu, press y = ~. **DISTR DRAW**

instructions draw various types of density functions, shade the area specified by *lowerbound* and *upperbound*, and display the computed area value.

To clear the drawings, select **1:ClrDraw** from the **DRAW** menu (Chapter 8).

**Note**: Before you execute a **DISTR DRAW** instruction, you must set the window variables so that the desired distribution fits the screen.

**DISTR** **DRAW**

**1:** **ShadeNorm(** Shades normal distribution. **2:** **Shade_t(** Shades Student-*t* distribution. **3:** **Shadec2(** Shades c2 distribution. **4:** **Shade(** Shades distribution.

**Note:** L199 and 199 specify infinity. If you want to view the area left of *upperbound*, for example, specify *lowerbound*=L199.

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**ShadeNorm(**

**ShadeNorm(** draws the normal density function specified by mean m and standard deviation s and shades the area between *lowerbound* and *upperbound*. The defaults are m=0 and s=1.

**ShadeNorm(***lowerbound***,***upperbound*[**,**m**,**s]**)** **Note:** For this example, **Xmin = 55** **Xmax = 72** **Ymin = L.05** **Ymax = .2**

**Shade_t(**

**Shade_t(** draws the density function for the Student-*t* distribution specified by *df* (degrees of freedom) and shades the area between *lowerbound* and *upperbound*.

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**Shade_t(***lowerbound***,***upperbound***,***df***)**

**Note:** For this example, **Xmin = L3** **Xmax = 3** **Ymin = L.15** **Ymax = .5**

**Shadec2(**

**Shadec2(** draws the density function for the c2 (chi-square) distribution specified by *df* (degrees of freedom) and shades the area between *lowerbound* and *upperbound*.

**Shadec2(***lowerbound***,***upperbound***,***df***)**

**Note:** For this example, **Xmin = 0** **Xmax = 35** **Ymin = L.025** **Ymax = .1**

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**Shade(**

**Shade(** draws the density function for the distribution specified by *numerator df* (degrees of freedom)* *and* denominator df* and shades the area between *lowerbound* and *upperbound*.

**Shade(***lowerbound***,***upperbound***,***numerator df***,***denominator df***)**

**Note:** For this example, **Xmin = 0** **Xmax = 5** **Ymin = L.25** **Ymax = .9**

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Chapter 14: Applications

The Applications Menu

The TI-83 Plus comes with **Finance** and **CBLCBR** applications already listed on the **APPLICATIONS** menu. Except for the **Finance** application, you can add and remove applications as space permits. The **Finance** application is built into the TI-83 Plus code and cannot be deleted.

You can buy additional TI-83 Plus software applications that allow you to customize further your calculators functionality. The calculator reserves 1.54 M of space within ROM memory specifically for applications.

Your TI-83 Plus includes Flash applications in addition to the ones mentioned above. Press to see the complete list of applications that came with your calculator.

Documentation for TI Flash applications is on the TI Resource CD. Visit education.ti.com/guides for additional Flash application guidebooks.

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**Steps for Running the Finance Application**

Follow these basic steps when using the **Finance** application.

Select the Finance application.

Press 9 b.

Select from list of functions.

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Getting Started: Financing a Car

**Getting Started is a fast-paced introduction. Read the chapter for details.**

**You have found a car you would like to buy. The car costs 9,000. You can afford** **payments of 250 per month for four years. What annual percentage rate (APR) will** **make it possible for you to afford the car?**

1. Press z ~ ~ ~ to set the fixed- decimal mode setting to **2**. The TI-83 Plus will display all numbers with two decimal places).

2. Press to select **1:Finance** from the **APPLICATIONS** menu.

3. Press to select **1:TVM Solver** from the CALC VARS menu. The **TVM Solver** is displayed.

Press **48** to store 48 months to . Press **9000** to store 9,000 to **PV**. Press **250** to store L250 to **PMT**. (Negation indicates cash outflow.) Press **0** to store 0 to **FV**.

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Press **12** to store 12 payments per year to **P/Y** and 12 compounding periods per year to **C/Y**. Setting **P/Y** to 12 will compute an annual percentage rate (compounded monthly) for . Press to select **PMT:END**, which indicates that payments are due at the end of each period.

4. Press } } } } } } to move the cursor to the prompt. Press \ to solve for . What APR should you look for?

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Getting Started: Computing Compound Interest

**At what annual interest rate, compounded monthly, will 1,250 accumulate to 2,000** **in 7 years?**

**Note: Because there are no payments when you solve compound interest** **problems,** **PMT** **must be set to** **0** **and** **P/Y** **must be** **set to** **1**.

1. Press to select **1:Finance** from the **APPLICATIONS** menu.

2. Press to select **1:TVM Solver** from the **CALC VARS** menu. The **TVM Solver** is displayed. Press **7** to enter the number of periods in years. Press **1250** to enter the present value as a cash outflow (investment). Press **0** to specify no payments. Press **2000** to enter the future value as a cash inflow (return). Press **1** to enter payment periods per year. Press **12** to set compounding periods per year to **12**.

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3. Press } } } } } to place the cursor on the prompt.

4. Press \ to solve for , the annual interest rate.

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Using the TVM Solver

**Using the TVM Solver**

The **TVM Solver** displays the time-value-of-money (**TVM**) variables. Given four variable values, the **TVM Solver** solves for the fifth variable.

The FINANCE VARS menu section describes the five **TVM** variables (, , **PV**, **PMT**, and **FV**) and **P/Y** and **C/Y**.

**PMT: END BEGIN** in the **TVM Solver** corresponds to the **FINANCE CALC** menu items **Pmt_End** (payment at the end of each period) and **Pmt_Bgn** (payment at the beginning of each period).

To solve for an unknown **TVM** variable, follow these steps.

1. Press to display the **TVM Solver**. The screen below shows the default values with the fixed-decimal mode set to two decimal places.

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2. Enter the known values for four **TVM** variables.

**Note:** Enter cash inflows as positive numbers and cash outflows as negative numbers.

3. Enter a value for **P/Y**, which automatically enters the same value for **C/Y**; if **P/Y** **C/Y**, enter a unique value for **C/Y**.

4. Select **END** or **BEGIN** to specify the payment method.

5. Place the cursor on the **TVM** variable for which you want to solve.

6. Press \. The answer is computed, displayed in the **TVM** **Solver**, and stored to the appropriate **TVM** variable. An indicator square in the left column designates the solution variable.

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Using the Financial Functions

**Entering Cash Inflows and Cash Outflows**

When using the TI-83 Plus financial functions, you must enter cash inflows (cash received) as positive numbers and cash outflows (cash paid) as negative numbers. The TI-83 Plus follows this convention when computing and displaying answers.

**FINANCE CALC Menu**

To display the **FINANCE CALC** menu, press .

**CALC** ** VARS** **1:** **TVM Solver...** Displays the **TVM Solver**. **2:** **tvm_Pmt** Computes the amount of each payment. **3:** **tvm_** Computes the interest rate per year. **4:** **tvm_PV** Computes the present value. **5:** **tvm_** Computes the number of payment periods. **6:** **tvm_FV** Computes the future value. **7:** **npv(** Computes the net present value. **8:** **irr(** Computes the internal rate of return. **9:** **bal(** Computes the amortization sched. balance. **0:** **GPrn(** Computes the amort. sched. princ. sum. **A:** **GInt(** Computes the amort. sched. interest sum.

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**CALC** ** VARS** **B:** **4Nom(** Computes the nominal interest rate. **C:** **4Eff(** Computes the effective interest rate. **D:** **dbd(** Calculates the days between two dates. **E:** **Pmt_End** Selects ordinary annuity (end of period). **F:** **Pmt_Bgn** Selects annuity due (beginning of period).

Use these functions to set up and perform financial calculations on the home screen.

**TVM Solver**

**TVM Solver** displays the **TVM Solver**.

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Calculating Time Value of Money (TVM)

**Calculating Time Value of Money**

Use time-value-of-money (**TVM**) functions (menu items **2** through** 6**) to analyze financial instruments such as annuities, loans, mortgages, leases, and savings.

Each **TVM** function takes zero to six arguments, which must be real numbers. The values that you specify as arguments for these functions are not stored to the **TVM** variables.

**Note:** To store a value to a **TVM** variable, use the **TVM Solver** or use and any **TVM** variable on the **FINANCE VARS** menu.

If you enter less than six arguments, the TI-83 Plus substitutes a previously stored **TVM** variable value for each unspecified argument.

If you enter any arguments with a **TVM** function, you must place the argument or arguments in parentheses.

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**tvm_Pmt**

**tvm_Pmt** computes the amount of each payment.

**tvm_Pmt**[**(****,****,***PV***,***FV***,***P/Y***,***C/Y***)**]

**Note:** In the example above, the values are stored to the **TVM** variables in the **TVM Solver**. Then the payment (**tvm_Pmt**) is computed on the home screen using the values in the **TVM Solver**. Next, the interest rate is changed to 9.5 to illustrate the effect on the payment amount.

**tvm_**

**tvm_** computes the annual interest rate.

**tvm_**[**(****,***PV***,***PMT***,***FV***,***P/Y***,***C/Y***)**]

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**tvm_PV**

**tvm_PV** computes the present value.

**tvm_PV**[**(****,****,***PMT***,***FV***,***P/Y***,***C/Y***)**]

**tvm_**

**tvm_** computes the number of payment periods.

**tvm_**[**(****,***PV***,***PMT***,***FV***,***P/Y***,***C/Y***)**]

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**tvm_FV**

**tvm_FV** computes the future value.

**tvm_FV**[**(****,****,***PV***,***PMT***,***P/Y***,***C/Y***)**]

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Calculating Cash Flows

**Calculating a Cash Flow**

Use the cash flow functions (menu items **7** and **8**) to analyze the value of money over equal time periods. You can enter unequal cash flows, which can be cash inflows or outflows. The syntax descriptions for** npv(** and **irr(** use these arguments.

*interest rate* is the rate by which to discount the cash flows (the cost of money) over one period.

*CF0* is the initial cash flow at time 0; it must be a real number.

*CFList* is a list of cash flow amounts after the initial cash flow *CF0*.

*CFFreq* is a list in which each element specifies the frequency of occurrence for a grouped (consecutive) cash flow amount, which is the corresponding element of *CFList*. The default is 1; if you enter values, they must be positive integers < 10,000.

For example, express this uneven cash flow in lists.

2000 40002000 2000

- 3000

4000

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*CF0* = **2000** *CFList *= **{2000,L3000,4000}** *CFFreq *= **{2,1,2}**

**npv(, irr(**

**npv(** (net present value) is the sum of the present values for the cash inflows and outflows. A positive result for **npv** indicates a profitable investment.

**npv(***interest rate***,***CF0***,***CFList*[**,***CFFreq*]**)**

**irr(** (internal rate of return) is the interest rate at which the net present value of the cash flows is equal to zero.

**irr(***CF0***,***CFList*[**,***CFFreq*]**)**

300050001000

- 2000 - 2500

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Calculating Amortization

**Calculating an Amortization Schedule**

Use the amortization functions (menu items **9**, **0**, and **A**) to calculate balance, sum of principal, and sum of interest for an amortization schedule.

**bal(**

**bal(** computes the balance for an amortization schedule using stored values for , **PV**, and **PMT**. *npmt* is the number of the payment at which you want to calculate a balance. It must be a positive integer < 10,000. *roundvalue* specifies the internal precision the calculator uses to calculate the balance; if you do not specify *roundvalue*, then the TI-83 Plus uses the current **Float**/**Fix** decimal-mode setting.

**bal(***npmt*[**,***roundvalue*]**)**

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**GPrn(, GInt(**

**GPrn(** computes the sum of the principal during a specified period for an amortization schedule using stored values for , **PV**, and **PMT**. *pmt1* is the starting payment. *pmt2* is the ending payment in the range. *pmt1* and *pmt2* must be positive integers < 10,000. *roundvalue* specifies the internal precision the calculator uses to calculate the principal; if you do not specify *roundvalue*, the TI-83 Plus uses the current **Float**/**Fix** decimal-mode setting.

**Note:** You must enter values for , **PV**, **PMT**, and before computing the principal.

**GPrn(***pmt1***,***pmt2*[**,***roundvalue*]**)**

**GInt(** computes the sum of the interest during a specified period for an amortization schedule using stored values for , **PV**, and **PMT**. *pmt1* is the starting payment. *pmt2* is the ending payment in the range.* pmt1* and *pmt2* must be positive integers < 10,000. *roundvalue* specifies the internal precision the calculator uses to calculate the interest; if you do not specify *roundvalue*, the TI-83 Plus uses the current **Float**/**Fix** decimal-mode setting.

**GInt(***pmt1***,***pmt2*[**,***roundvalue*]**)**

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**Amortization Example: Calculating an Outstanding Loan Balance**

You want to buy a home with a 30-year mortgage at 8 percent APR. Monthly payments are 800. Calculate the outstanding loan balance after each payment and display the results in a graph and in the table.

1. Press z. Press ~ ~ ~ to set the fixed-decimal mode setting to **2**. Press ~ to select **Par** graphing mode.

2. Press to display the **TVM Solver**.

3. Press **360** to enter number of payments. Press **8** to enter the interest rate. Press **800** to enter the payment amount. Press **0** to enter the future value of the mortgage. Press **12** to enter the payments per year, which also sets the compounding periods per year to **12**. Press to select **PMT:END**.

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4. Press } } } } } to place the cursor on the **PV** prompt. Press \ to solve for the present value.

5. Press o to display the parametric **Y=** editor. Turn off all stat plots. Press to define **X1T**

as **T**. Press **9** to define **Y1T** as **bal(T)**.

6. Press p to display the window variables. Enter the values below. **Tmin=0** **Xmin=0** **Ymin=0** **Tmax=360** **Xmax=360** **Ymax=125000** **Tstep=12** **Xscl=50** **Yscl=10000**

7. Press r to draw the graph and activate the trace cursor. Press ~ and | to explore the graph of the outstanding balance over time. Press a number and then press to view the balance at a specific time **T**.

8. Press y - and enter the values below. **TblStart=0** **@Tbl=12**

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9. Press y 0 to display the table of outstanding balances (**Y1T**).

10.Press z ~ ~ to select **G.T** split-screen mode, in which the graph and table are displayed simultaneously.

Press r to display **X1T** (time) and **Y1T**

(balance) in the table.

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TI-83 Plus Applications 459

Calculating Interest Conversion

**Calculating an Interest Conversion**

Use the interest conversion functions (menu items **B** and **C**) to convert interest rates from an annual effective rate to a nominal rate (**4Nom(** ) or from a nominal rate to an annual effective rate (**4Eff(** ).

**4Nom(**

**4Nom(** computes the nominal interest rate. *effective rate* and *compounding* *periods* must be real numbers.* compounding periods* must be >0.

**4Nom(***effective rate***,***compounding periods***)**

**4Eff(**

**4Eff(** computes the effective interest rate. *nominal rate* and *compounding* *periods* must be real numbers. *compounding periods* must be >0.

**4Eff(***nominal rate***,***compounding periods***)**

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Finding Days between Dates/Defining Payment Method

**dbd(**

Use the date function **dbd(** (menu item **D**) to calculate the number of days between two dates using the actual-day-count method. *date1* and *date2* can be numbers or lists of numbers within the range of the dates on the standard calendar.

**Note:** Dates must be between the years 1950 through 2049.

**dbd(***date1***,***date2***)**

You can enter *date1* and *date2* in either of two formats.

MM.DDYY (United States)

DDMM.YY (Europe)

The decimal placement differentiates the date formats.

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**Defining the Payment Method**

**Pmt_End** and **Pmt_Bgn** (menu items **E** and** F**) specify a transaction as an ordinary annuity or an annuity due. When you execute either command, the **TVM Solver** is updated.

**Pmt_End**

**Pmt_End** (payment end) specifies an ordinary annuity, where payments occur at the end of each payment period. Most loans are in this category. **Pmt_End** is the default.

**Pmt_End**

On the **TVM Solver**s **PMT:END BEGIN** line, select **END** to set **PMT** to ordinary annuity.

**Pmt_Bgn**

**Pmt_Bgn** (payment beginning) specifies an annuity due, where payments occur at the beginning of each payment period. Most leases are in this category.

**Pmt_Bgn**

On the **TVM Solver**s **PMT:END BEGIN** line, select **BEGIN** to set **PMT** to annuity due.

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Using the TVM Variables

**FINANCE VARS Menu**

To display the **FINANCE VARS** menu, press ~. You can use **TVM** variables in **TVM** functions and store values to them on the home screen.

**CALC** **VARS**

**1:** Total number of payment periods **2:** Annual interest rate **3:PV** Present value **4:PMT** Payment amount **5:FV** Future value **6:P/Y** Number of payment periods per year **7:C/Y** Number of compounding periods/year

**, , PV, PMT, FV**

, , **PV**, **PMT**, and **FV** are the five **TVM** variables. They represent the elements of common financial transactions, as described in the table above. ** **is an annual interest rate that is converted to a per-period rate based on the values of **P/Y** and **C/Y**.

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**P/Y and C/Y**

**P/Y** is the number of payment periods per year in a financial transaction.

**C/Y** is the number of compounding periods per year in the same transaction.

When you store a value to **P/Y**, the value for **C/Y** automatically changes to the same value. To store a unique value to **C/Y**, you must store the value to **C/Y** after you have stored a value to **P/Y**.

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The CBL/CBR Application

The **CBL/CBR** application allows you to collect real world data. The TI-83 Plus comes with the **CBLCBR** application already listed on the **APPLICATIONS** menu (9 **2**).

**Steps for Running the CBLCBR Application**

Follow these basic steps when using the **CBLCBR** application. You may not have to do all of them each time.

Select the CBLCBR application.

Press 9 2**.**

Specify the data collection method.

Press 1, 2, or 3**.**

Press b.

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Select options, if applicable.

Collect the data. Follow directions, if

applicable. Select **Go **or **START NOW**.

Stop the data collection, if necessary. Repeat these

steps or exit the APPLICATIONS menu.

Press ^ and or .

Highlight options or enter value and press b.

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**Selecting the CBL/CBR Application**

To use a **CBL/CBR** application, you need a **CBL 2/CBL** or **CBR** (as applicable), a TI-83 Plus, and a unit-to-unit link cable.

1. Press .

2. Select** 2:CBL/CBR **to set up the TI-83 Plus to use either of the applications. An informational screen appears first.

3. Press any key to continue to the next menu.

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Data Collection Methods and Options

**Specifying the Data Collection Method from the CBL/CBR APP** **Menu**

With a **CBL 2/CBL** or **CBR**, you can collect data in one of three ways: **GAUGE**

(bar or meter), **DATA LOGGER** (a Temp-Time, Light-Time, Volt-Time, or Sonic-Time graph), or **RANGER**, which runs the **RANGER** program, the built-in **CBR** data collection program.

The **CBL/CBR APP** menu contains the following data collection methods:

**CBL/CBR APP:** **1:** **GAUGE** Displays results as either a bar or meter. **2:** **DATA LOGGER** Displays results as a Temp-Time, Light-Time, Volt-Time, or

Sonic-Time graph. **3:** **RANGER** Sets up and runs the **RANGER** program. **4:** **QUIT** Quits the CBLCBR application.

**Note:** **CBL 2/CBL** and **CBR** differ in that **CBL 2/CBL** allows you to collect data using one of several different probes including: Temp (Temperature), Light, Volt (Voltage), or Sonic. CBR collects data using only the built-in Sonic probe. You can find more information on CBL 2/CBL and CBR in their user manuals.

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**Specifying Options for Each Data Collection Method**

After you select a data collection method from the **CBL/CBR APP** menu, a screen showing the options for that method is displayed. The method you choose, as well as the data collection options you choose for that method, determine whether you use the **CBR** or the **CBL 2/CBL**. Refer to the charts in the following sections to find the options for the application you are using.

**GAUGE**

The **GAUGE** data collection method lets you choose one of four different probes: temp, Light, Volt, or Sonic.

1. Press **2** .

2. Select **1:GAUGE**.

3. Select options.

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When you select a probe option, all other options change accordingly. Use " and ! to move between the probe options. To select a probe, highlight the one you want with the cursor keys, and then press .

**GAUGE Options (Defaults)**

**Probe:** **Temp** **Light** **Volt** **Sonic**

**Type:** **Bar or Meter**

**Min:** **0** **0** **M10** **0**

**Max:** **100** **1** **10** **6**

**Units:** **C or F** **mWcm2** **Volt** **m or Ft**

**Directions:** **On or Off**

**TYPE**

The **GAUGE** data collection results are represented according to **TYPE**: **Bar** or **Meter**. Highlight the one you want with the cursor keys, and then press .

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**Bar** **Meter**

**MIN and MAX**

**MIN** and **MAX** refer to the minimum and maximum **UNIT **values for the specified probe. Defaults are listed in the Gauge Options table. See the CBL 2/CBL and CBR guidebook for specific **MINMAX** ranges. Enter values using the number keys.

**UNITS**

The results are displayed according to the **UNITS** specified. To specify a unit measurement (**Temp** or **Sonic** probes only), highlight the one you want using the cursor keys, enter a value using the number keys, and then press .

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**DIRECTNS (Directions)**

If **DIRECTNS=On**, the calculator displays step-by-step directions on the screen, which help you set up and run the data collection. To select **On** or **Off**, highlight the one you want with the cursor keys, and then press .

With the **Sonic** data collection probe, if **DIRECTNS=On**, the calculator displays a menu screen before starting the application asking you to select **1:CBL** or **2:CBR.** This ensures that you get the appropriate directions. Press **1** to specify **CBL 2/CBL** or **2** to specify **CBR**.

**Data Collection Comments and Results**

To label a specific data point, press to pause the data collection. You will see a Reference#: prompt. Enter a number using the number keys. The calculator automatically converts the reference numbers and the corresponding results into list elements using the following list names (you cannot rename these lists):

**Probe** **Comment Labels (X) Stored to:** **Data Results (Y) Stored to:**

**Temp** TREF TEMP

**Light** LREF LIGHT

**Volt** VREF VOLT

**Sonic** DREF DIST

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To see all elements in one of these lists, you can insert these lists into the List editor just as you would any other list. Access list names from the - 9 **NAMES** menu.

**Note:** These lists are only temporary placeholders for comment labels and data results for any particular probe. Therefore, every time you collect data and enter comments for one of the four probes, the two lists pertaining to that probe are overwritten with comment labels and data results from the most recently collected data..

If you want to save comment labels and data results from more than one data collection, copy all list elements that you want to save to a list with a different name.

Also, the **DATA LOGGER** data collection method stores data results to the same list names, overwriting previously-collected data results, even those collected using the **GAUGE** data collection method.

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**DATA LOGGER**

1. Press **2 **.

2. Select **2:DATA LOGGER**.

The **DATA LOGGER** data collection method lets you choose one of four different probes: **Temp**, **Light**, **Volt**, or **Sonic**. You can use the **CBL 2/CBL**

with all probes; you can use the **CBR** only with the **Sonic** probe.

When you select a probe option, all other options change accordingly. Use " and ! to move between the probe options. To select a probe, highlight the one you want with the cursor keys, and then press .

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**DATA LOGGER Options (Defaults)**

**Temp** **Light** **Volt** **Sonic**

**#SAMPLES:** **99** **99** **99** **99**

**INTRVL** **(SEC):** **1** **1** **1** **1**

**UNITS:** **C or F** **mW/cm2** **Volt** **Cm or Ft**

**PLOT:** **RealTme or End**

**DIRECTNS:** **On or Off**

**Ymin** **(**'**):** **0** **0** **M10** **0**

**Ymax** **(**'**):** **100** **1** **10** **6**

The **DATA LOGGER** data collection results are represented as a Temp-Time, Light-Time, Volt-Time, or Distance-Time graph.

A Distance-Time graph in meters (**Sonic** probe).

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**#SAMPLES**

**#SAMPLES** refers to how many data samples are collected and then graphed. For example, if **#SAMPLES=99**, data collection stops after the 99th sample is collected. Enter values using the number keys.

**INTRVL (SEC)**

**INTRVL** **(SEC)** specifies the interval in seconds between each data sample that is collected. For example, if you want to collect 99 samples and **INTRVL=1**, it takes 99 seconds to finish data collection. Enter values using the number keys. See the **CBL 2/CBL** or **CBR** guidebook for more information about interval limits.

**UNITS**

The results are displayed according to the **UNITS** specified. To specify a unit measurement (**Temp** or **Sonic** only), highlight the one you want using the cursor keys, and then press .

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**PLOT**

You can specify whether you want the calculator to collect realtime (**RealTme**) samples, which means that the calculator graphs data points immediately as they are being collected, or you can wait and show the graph only after all data points have been collected (**End**). Highlight the option you want with the cursor keys, and then press .

**Ymin and Ymax**

To specify **Ymin** and **Ymax** values for the final graph, press p to view the **PLOT WINDOW** screen. Use $ and # to move between options. Enter **Ymin** and **Ymax** using the number keys. Press - l to return to the **DATA LOGGER** options screen.

**DIRECTNS (Directions)**

If **DIRECTNS=On**, the calculator displays step-by-step directions on the screen, which help you set up and run the data collection. To select **On** or **Off**, highlight the one you want with the cursor keys, and then press b.

With the **Sonic** data collection probe, if **DIRECTNS=On**, the calculator displays a menu screen before starting the application asking you to select **1:CBL** or **2:CBR.** This ensures that you get the appropriate directions. Press 1 to specify **CBL 2/CBL** or **2** to specify **CBR**.

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**Data Collection Results**

The calculator automatically converts all collected data points into list elements using the following list names (you cannot rename the lists):

**Probe** **Time Values (**X**) stored to:** **Data Results (**Y**) Stored to:**

**Temp** TTEMP TEMP

**Light** TLGHT LIGHT

**Volt** TVOLT VOLT

**Sonic** TDIST DIST

To see all elements in one of these lists, you can insert these lists into the List editor just as you would any other list. Access list names from the - 9 **NAMES** menu.

**Note:** These lists are only temporary placeholders for data results for any particular probe. Therefore, every time you collect data for one of the four probes, the list pertaining to that probe is overwritten with data results from the most recently collected data.

If you want to save data results from more than one data collection, copy all list elements that you want to save to a list with a different name.

Also, the **GAUGE** data collection method stores data results to the same list names, overwriting previously-collected data results, even those collected using the **DATA LOGGER** data collection method.

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**RANGER**

Selecting the **RANGER** data collection method runs the CBR **RANGER**

program, a customized program especially for the TI-83 Plus that makes it compatible with the CBR. When the collection process is halted, the **CBR RANGER** is deleted from RAM. To run the CBR **RANGER** program again, press and select the **CBL/CBR** application.

**Note:** The Ranger data collection method only uses the Sonic probe.

1. Press 9 **2 **b.

2. Select **3:RANGER**.

3. Press b.

4. Select options.

For detailed information about the **RANGER** program as well as option explanations, see the Getting Started with CBR guidebook.

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Starting Data Collection

**Collecting the Data**

After you specify all of the options for your data collection method, select the **Go** option from the **GAUGE** or **DATA LOGGER** options screen. If you are using the **RANGER** data collection method, select **1:SETUPSAMPLE **from the **MAIN **menu, and then **START NOW**.

If **DIRECTNS=Off**, **GAUGE **and **DATA LOGGER** data collection begin immediately.

If **DIRECTNS=On**, the calculator displays step-by-step directions.

If **PROBE=Sonic**, the calculator first displays a menu screen asking you to select **1:CBL** or **2:CBR.** This ensures that you get the appropriate directions. Press 1 to specify **CBL 2/CBL** or **2** to specify **CBR**.

If you select **START NOW** from the **MAIN menu** of the **RANGER** data collection method, the calculator displays one directions screen. Press b to begin data collection.

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Stopping Data Collection

To stop the **GAUGE** data collection method, press : on the TI-83 Plus.

The **DATA LOGGER** and **RANGER** data collection methods stop after the specified number of samples have been collected. To stop them before this happens:

1. Press ^ on the TI-83 Plus.

2. Press on the CBR, T on the CBL 2, or P on the CBL.

To exit from the **GAUGE** or **DATA LOGGER** option menus without beginning data collection, press - l.

To exit from the **RANGER** option menu without beginning data collection, select **MAIN** menu. Select **6:QUIT** to return to the **CBLCBR APP** menu.

Press **4:QUIT** from the **CBLCBR APP** menu to return to the TI-83 Plus Home screen.

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Chapter 15: CATALOG, Strings, Hyperbolic Functions

Browsing the TI-83 Plus CATALOG

**What Is the CATALOG?**

The **CATALOG** is an alphabetical list of all functions and instructions on the TI-83 Plus. You also can access each **CATALOG** item from a menu or the keyboard, except:

The six string functions

The six hyperbolic functions

The **solve(** instruction without the equation solver editor (Chapter 2)

The inferential stat functions without the inferential stat editors (Chapter 13)

**Note:** The only **CATALOG** programming commands you can execute from the home screen are **GetCalc(**, **Get(**, and **Send(**.

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**Selecting an Item from the CATALOG**

To select a **CATALOG** item, follow these steps.

1. Press y CATALOG to display the **CATALOG**.

The **4** in the first column is the selection cursor.

2. Press or } to scroll the **CATALOG** until the selection cursor points to the item you want.

To jump to the first item beginning with a particular letter, press that letter; alpha-lock is on.

Items that begin with a number are in alphabetical order according to the first letter after the number. For example, **2.PropZTest(** is among the items that begin with the letter **P**.

Functions that appear as symbols, such as **+**, **L1**, **<**, and **(**, follow the last item that begins with **Z**. To jump to the first symbol, **!**, press [q].

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3. Press to paste the item to the current screen.

**Tip:** From the top of the **CATALOG** menu, press } to move to the bottom. From the bottom, press to move to the top.

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Entering and Using Strings

**What Is a String?**

A string is a sequence of characters that you enclose within quotation marks. On the TI-83 Plus, a string has two primary applications.

It defines text to be displayed in a program.

It accepts input from the keyboard in a program.

Characters are the units that you combine to form a string.

Count each number, letter, and space as one character.

Count each instruction or function name, such as **sin(** or **cos(**, as one character; the TI-83 Plus interprets each instruction or function name as one character.

**Entering a String**

To enter a string on a blank line on the home screen or in a program, follow these steps.

1. Press [] to indicate the beginning of the string.

2. Enter the characters that comprise the string.

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Use any combination of numbers, letters, function names, or instruction names to create the string.

To enter a blank space, press ['].

To enter several alpha characters in a row, press y 7 to activate alpha-lock.

3. Press [] to indicate the end of the string.

**"***string***"**

4. Press . On the home screen, the string is displayed on the next line without quotations. An ellipsis (**...**) indicates that the string continues beyond the screen. To scroll the entire string, press ~ and |.

**Note:** Quotation marks do not count as string characters.

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Storing Strings to String Variables

**String Variables**

The TI-83 Plus has 10 variables to which you can store strings. You can use string variables with string functions and instructions.

To display the **VARS STRING** menu, follow these steps.

1. Press to display the **VARS** menu. Move the cursor to **7:String**.

2. Press to display the **STRING** secondary menu.

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**Storing a String to a String Variable**

To store a string to a string variable, follow these steps.

1. Press [], enter the string, and press [].

2. Press .

3. Press **7** to display the **VARS STRING** menu.

4. Select the string variable (from **Str1** to **Str9**, or** Str0**) to which you want to store the string.

The string variable is pasted to the current cursor location, next to the store symbol (**!**).

5. Press to store the string to the string variable. On the home screen, the stored string is displayed on the next line without quotation marks.

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**Displaying the Contents of a String Variable**

To display the contents of a string variable on the home screen, select the string variable from the **VARS STRING** menu, and then press . The string is displayed.

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String Functions and Instructions in the CATALOG

**Displaying String Functions and Instructions in the CATALOG**

String functions and instructions are available only from the **CATALOG**. The table below lists the string functions and instructions in the order in which they appear among the other **CATALOG** menu items. The ellipses in the table indicate the presence of additional **CATALOG** items.

**CATALOG**

**...**

**Equ4String(** Converts an equation to a string. **expr(** Converts a string to an expression. **...**

**inString(** Returns a characters place number. **...**

**length(** Returns a strings character length. **...**

**String4Equ(** Converts a string to an equation. **sub(** Returns a string subset as a string. **...**

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**+ (Concatenation)**

To concatenate two or more strings, follow these steps.

1. Enter *string1*, which can be a string or string name.

2. Press .

3. Enter *string2*, which can be a string or string name. If necessary, press and enter *string3*, and so on.

*string1***+***string2***+***string3*. . .

4. Press to display the strings as a single string.

**Selecting a String Function from the CATALOG**

To select a string function or instruction and paste it to the current screen, follow the steps for selecting an item from the **CATALOG**.

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**Equ4String(**

**Equ4String(** converts to a string an equation that is stored to any **VARS**

**Y.VARS** variable. **Y**n contains the equation. **Str**n (from **Str1** to **Str9**, or **Str0**) is the string variable to which you want the equation to be stored as a string.

**Equ4String(Y**n**,Str**n**)**

**expr(**

**expr(** converts the character string contained in *string* to an expression and executes it. *string* can be a string or a string variable.

**expr(***string***)**

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**inString(**

**inString(** returns the character position in *string* of the first character of *substring*. *string* can be a string or a string variable. *start* is an optional character position at which to start the search; the default is 1.

**inString(***string***,***substring*[**,***start*]**)**

**Note:** If *string* does not contain *substring*, or *start* is greater than the length of *string*, **inString(** returns **0**.

**length(**

**length(** returns the number of characters in *string*. *string* can be a string or string variable.

**Note:** An instruction or function name, such as **sin(** or **cos(,** counts as one character.

**length(***string***)**

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**String4Equ(**

**String4Equ(** converts *string* into an equation and stores the equation to **Y**n. *string* can be a string or string variable. **String4Equ(** is the inverse of **Equ4String(**.

**String4Equ(***string***,Y**n**)**

**sub(**

**sub(** returns a string that is a subset of an existing *string*. *string* can be a string or a string variable. *begin* is the position number of the first character of the subset. *length* is the number of characters in the subset.

**sub(***string***,***begin***,***length***)**

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**Entering a Function to Graph during Program Execution**

In a program, you can enter a function to graph during program execution using these commands.

**Note:** When you execute this program, enter a function to store to **Y3 **at the **ENTRY=** prompt.

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Hyperbolic Functions in the CATALOG

**Hyperbolic Functions**

The hyperbolic functions are available only from the **CATALOG**. The table below lists the hyperbolic functions in the order in which they appear among the other **CATALOG** menu items. The ellipses in the table indicate the presence of additional **CATALOG** items.

**CATALOG** **...**

**cosh(** Hyperbolic cosine **coshL1(** Hyperbolic arccosine **...**

**sinh(** Hyperbolic sine **sinhL1(** Hyperbolic arcsine **...**

**tanh(** Hyperbolic tangent **tanhL1(** Hyperbolic arctangent **...**

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**sinh(, cosh(, tanh(**

**sinh(**, **cosh(**, and **tanh(** are the hyperbolic functions. Each is valid for real numbers, expressions, and lists.

**sinh(***value***)** **cosh(***value***)** **tanh(***value***)**

**sinhL1(, coshL1(, tanhL1(**

**sinhL1(** is the hyperbolic arcsine function. **coshL1(** is the hyperbolic arccosine function. **tanhL1(** is the hyperbolic arctangent function. Each is valid for real numbers, expressions, and lists.

**sinhL1(***value***)** **coshL1(***value***)** **sinhL1(***value***)**

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Chapter 16: Programming

Getting Started: Volume of a Cylinder

**Getting Started is a fast-paced introduction. Read the chapter for details.**

**A program is a set of commands that the TI-83 Plus executes sequentially, as if** **you had entered them from the keyboard. Create a program that prompts for the** **radius R and the height H of a cylinder and then computes its volume.**

1. Press ~ ~ to display the **PRGM NEW**

menu.

2. Press to select **1:Create New**. The **Name=** prompt is displayed, and alpha-lock is on. Press [C] [Y] [L] [I] [N] [D] [E] [R], and then press to name the program **CYLINDER**.

You are now in the program editor. The colon ( **:** ) in the first column of the second line indicates the beginning of a command line.

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3. Press ~ **2** to select **2:Prompt** from the **PRGM I/O** menu. **Prompt** is copied to the command line. Press [R] [H] to enter the variable names for radius and height. Press .

4. Press y p [R] [H] [V] to enter the expression pR2H and store it to the variable **V**.

5. Press ~ **3** to select **3:Disp** from the **PRGM**

**I/O** menu. **Disp** is pasted to the command line. Press y 7 [V] [O] [L] [U] [M] [E]['] [I] [S] [V] to set up the program to display the text **VOLUME IS** on one line and the calculated value of **V** on the next.

6. Press y 5 to display the home screen.

7. Press to display the **PRGM EXEC** menu. The items on this menu are the names of stored programs.

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8. Press to paste **prgmCYLINDER** to the current cursor location. (If **CYLINDER** is not item **1** on your **PRGM EXEC** menu, move the cursor to **CYLINDER** before you press .)

9. Press to execute the program. Enter **1.5** for the radius, and then press . Enter **3** for the height, and then press . The text **VOLUME IS**, the value of **V**, and **Done** are displayed.

Repeat steps 7 through 9 and enter different values for **R** and **H**.

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Creating and Deleting Programs

**What Is a Program?**

A program is a set of one or more command lines. Each line contains one or more instructions. When you execute a program, the TI-83 Plus performs each instruction on each command line in the same order in which you entered them. The number and size of programs that the TI-83 Plus can store is limited only by available memory.

**Creating a New Program**

To create a new program, follow these steps.

1. Press | to display the **PRGM NEW** menu.

2. Press to select **1:Create New**. The **Name=** prompt is displayed, and alpha-lock is on.

3. Press a letter from A to Z or q to enter the first character of the new program name.

**Note:** A program name can be one to eight characters long. The first character must be a letter from A to Z or q. The second through eighth characters can be letters, numbers, or q.

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4. Enter zero to seven letters, numbers, or q to complete the new program name.

5. Press . The program editor is displayed.

6. Enter one or more program commands.

7. Press y 5 to leave the program editor and return to the home screen.

**Managing Memory and Deleting a Program**

To check whether adequate memory is available for a program you want to enter:

1. Press y L to display the **MEMORY** menu.

2. Select **2:Mem Mgmt/Del** to display the **MEMORY MANAGEMENT/DELETE**

menu (Chapter 18).

3. Select **7:Prgm** to display the PRGM editor.

The TI-83 Plus expresses memory quantities in bytes.

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You can increase available memory in one of two ways. You can delete one or more programs or you can archive some programs.

To increase available memory by deleting a specific program:

1. Press y L and then select **2:Mem Mgmt/Del** from the **MEMORY**

menu.

2. Select **7:Prgm** to display the PRGM editor (Chapter 18).

3. Press } and to move the selection cursor (**4**) next to the program you want to delete, and then press {. The program is deleted from memory. **Note:** You will receive a message asking you to confirm this delete action. Select **2:yes** to continue.

To leave the PRGM editor screen without deleting anything, press y 5, which displays the home screen.

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To increase available memory by archiving a program:

1. Press y L and then select **2:Mem Mgmt/Del** from the **MEMORY**

menu.

2. Select **2:Mem Mgmt/Del** to display the **MEM MGMT/DEL** menu.

3. Select **7:Prgm...** to display the **PRGM** menu.

4. Press to archive the program. An asterisk will appear to the left

of the program to indicate it is an archived program.

To unarchive a program in this screen, put the cursor next to the archived program and press . The asterisk will disappear.

**Note:** Archive programs cannot be edited or executed. In order to edit or execute an archived program, you must first unarchive it.

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Entering Command Lines and Executing Programs

**Entering a Program Command Line**

You can enter on a command line any instruction or expression that you could execute from the home screen. In the program editor, each new command line begins with a colon. To enter more than one instruction or expression on a single command line, separate each with a colon.

**Note:** A command line can be longer than the screen is wide; long command lines wrap to the next screen line.

While in the program editor, you can display and select from menus. You can return to the program editor from a menu in either of two ways.

Select a menu item, which pastes the item to the current command line.

Press .

When you complete a command line, press . The cursor moves to the next command line.

Programs can access variables, lists, matrices, and strings saved in memory. If a program stores a new value to a variable, list, matrix, or string, the program changes the value in memory during execution.

You can call another program as a subroutine.

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**Executing a Program**

To execute a program, begin on a blank line on the home screen and follow these steps.

1. Press to display the **PRGM EXEC** menu.

2. Select a program name from the **PRGM EXEC** menu. **prgm***name* is pasted to the home screen (for example, **prgmCYLINDER**).

3. Press to execute the program. While the program is executing, the busy indicator is on.

Last Answer (**Ans**) is updated during program execution. Last Entry is not updated as each command is executed (Chapter 1).

The TI-83 Plus checks for errors during program execution. It does not check for errors as you enter a program.

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**Breaking a Program**

To stop program execution, press . The **ERR:BREAK** menu is displayed.

To return to the home screen, select **1:Quit**.

To go where the interruption occurred, select **2:Goto**.

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Editing Programs

**Editing a Program**

To edit a stored program, follow these steps.

1. Press ~ to display the **PRGM EDIT** menu.

2. Select a program name from the **PRGM EDIT** menu. Up to the first seven lines of the program are displayed.

**Note:** The program editor does not display a $ to indicate that a program continues beyond the screen.

3. Edit the program command lines.

Move the cursor to the appropriate location, and then delete, overwrite, or insert.

Press to clear all program commands on the command line (the leading colon remains), and then enter a new program command.

**Tip:** To move the cursor to the beginning of a command line, press y |; to move to the end, press y ~. To scroll the cursor down seven command lines, press . To scroll the cursor up seven command lines, press }.

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**Inserting and Deleting Command Lines**

To insert a new command line anywhere in the program, place the cursor where you want the new line, press y 6, and then press . A colon indicates a new line.

To delete a command line, place the cursor on the line, press to clear all instructions and expressions on the line, and then press { to delete the command line, including the colon.

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Copying and Renaming Programs

**Copying and Renaming a Program**

To copy all command lines from one program into a new program, follow steps 1 through 5 for Creating a New Program, and then follow these steps.

1. Press y K. **Rcl** is displayed on the bottom line of the program editor in the new program (Chapter 1).

2. Press | to display the **PRGM EXEC** menu.

3. Select a name from the menu. **prgm***name* is pasted to the bottom line of the program editor.

4. Press . All command lines from the selected program are copied into the new program.

Copying programs has at least two convenient applications.

You can create a template for groups of instructions that you use frequently.

You can rename a program by copying its contents into a new program.

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**Note:** You also can copy all the command lines from one existing program to another existing program using **RCL**.

**Scrolling the PRGM EXEC and PRGM EDIT Menus**

The TI-83 Plus sorts **PRGM EXEC** and **PRGM EDIT** menu items automatically into alphanumerical order. Each menu only labels the first 10 items using **1** through **9**, then **0**.

To jump to the first program name that begins with a particular alpha character or q, press [letter from A to Z or q].

**Tip:** From the top of either the **PRGM EXEC** or **PRGM EDIT** menu, press } to move to the bottom. From the bottom, press to move to the top. To scroll the cursor down the menu seven items, press . To scroll the cursor up the menu seven items, press }.

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PRGM CTL (Control) Instructions

**PRGM CTL Menu**

To display the **PRGM CTL** (program control) menu, press from the program editor only.

**CTL** ** I/O EXEC**

**1:If** Creates a conditional test. **2:Then** Executes commands when **If** is true. **3:Else** Executes commands when **If** is false. **4:For(** Creates an incrementing loop. **5:While** Creates a conditional loop. **6:Repeat** Creates a conditional loop. **7:End** Signifies the end of a block. **8:Pause** Pauses program execution. **9:Lbl** Defines a label. **0:Goto** Goes to a label. **A:IS>(** Increments and skips if greater than. **B:DS<(** Decrements and skips if less than. **C:Menu(** Defines menu items and branches. **D:prgm** Executes a program as a subroutine. **E:Return** Returns from a subroutine. **F:Stop** Stops execution. **G:DelVar** Deletes a variable from within program. **H:GraphStyle(** Designates the graph style to be drawn.

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These menu items direct the flow of an executing program. They make it easy to repeat or skip a group of commands during program execution. When you select an item from the menu, the name is pasted to the cursor location on a command line in the program.

To return to the program editor without selecting an item, press .

**Controlling Program Flow**

Program control instructions tell the TI-83 Plus which command to execute next in a program. **If**, **While**, and **Repeat** check a defined condition to determine which command to execute next. Conditions frequently use relational or Boolean tests (Chapter 2), as in:

**If A<7:A+1!A**

or

**If N=1 and M=1:Goto Z**

**If**

Use **If** for testing and branching. If *condition* is false (zero), then the *command* immediately following **If** is skipped. If *condition* is true (nonzero), then the next *command* is executed. **If** instructions can be nested.

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**:If ***condition* **:***command* (if true) **:***command*

**Program** **Output**

**If.Then**

**Then** following an **If** executes a group of *commands* if *condition* is true (nonzero). **End** identifies the end of the group of *commands*.

**:If ***condition* **:Then** **:***command* (if true) **:***command* (if true) **:End** **:***command*

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**Program** **Output**

**If.Then.Else**

**Else** following **If.Then** executes a group of *commands* if *condition* is false (zero). **End** identifies the end of the group of *commands*.

**:If ***condition* **:Then** **:***command* (if true) **:***command* (if true) **:Else** **:***command* (if false) **:***command* (if false) **:End** **:***command*

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**Program** **Output**

**For(**

**For(** loops and increments. It increments *variable* from *begin* to *end* by *increment*. *increment* is optional (default is 1) and can be negative (*end*<*begin*). *end* is a maximum or minimum value not to be exceeded. **End** identifies the end of the loop. **For(** loops can be nested.

**:For(***variable***,***begin***,***end*[**,***increment*]**)** **:***command* (while *end* not exceeded) **:***command* (while *end* not exceeded) **:End** **:***command*

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**Program** **Output**

**While**

**While** performs a group of *commands* while *condition* is true. *condition* is frequently a relational test (Chapter 2). *condition* is tested when **While** is encountered. If *condition* is true (nonzero), the program executes a group of *commands*. **End** signifies the end of the group. When *condition* is false (zero), the program executes each *command* following **End**. **While** instructions can be nested.

**:While** *condition* **:***command* (while *condition* is true) **:***command* (while *condition* is true) **:End** **:***command*

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**Program** **Output**

**Repeat**

**Repeat** repeats a group of *commands* until *condition* is true (nonzero). It is similar to **While**, but *condition* is tested when **End** is encountered; therefore, the group of *commands* is always executed at least once. **Repeat** instructions can be nested.

**:Repeat** *condition* **:***command* (until *condition* is true) **:***command* (until *condition* is true) **:End** **:**c*ommand*

**Program** **Output**

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**End**

**End** identifies the end of a group of *commands*. You must include an **End** instruction at the end of each **For(**, **While**, or **Repeat** loop. Also, you must paste an **End** instruction at the end of each **If.Then** group and each **If.Then.Else** group.

**Pause**

**Pause** suspends execution of the program so that you can see answers or graphs. During the pause, the pause indicator is on in the top-right corner. Press to resume execution.

**Pause** without a *value* temporarily pauses the program. If the **DispGraph** or **Disp** instruction has been executed, the appropriate screen is displayed.

**Pause** with *value* displays *value* on the current home screen. *value* can be scrolled.

**Pause **[*value*]

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**Program** **Output**

**Lbl, Goto**

**Lbl** (label) and **Goto** (go to) are used together for branching.

**Lbl** specifies the *label* for a command. *label* can be one or two characters (**A** through **Z**, **0** through **99**, or **q**).

**Lbl** *label*

**Goto** causes the program to branch to *label* when **Goto** is encountered.

**Goto** *label*

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TI-83 Plus Programming 520

**Program** **Output**

**IS>(**

**IS>(** (increment and skip) adds 1 to *variable. *If the answer is > *value* (which can be an expression), the next *command* is skipped; if the answer is { *value*, the next *command* is executed. *variable* cannot be a system variable.

**:IS>(***variable***,***value***)** **:***command *(if answer *value*) **:***command *(if answer >* value*)

**Program** **Output**

**Note:** **IS>( **is not a looping instruction.

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TI-83 Plus Programming 521

**DS<(**

**DS<(** (decrement and skip) subtracts 1 from *variable*. If the answer is < *value* (which can be an expression), the next *command* is skipped; if the answer is | *value*, the next *command* is executed. *variable* cannot be a system variable.

**:DS<(**variable**,**value**)** **:***command *(if answer *value*) **:***command *(if answer <* value*)

**Program** **Output**

**Note:** **DS<( **is not a looping instruction.

**Menu(**

**Menu(** sets up branching within a program. If **Menu(** is encountered during program execution, the menu screen is displayed with the specified menu items, the pause indicator is on, and execution pauses until you select a menu item.

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TI-83 Plus Programming 522

The menu *title* is enclosed in quotation marks ( **"** ). Up to seven pairs of menu items follow. Each pair comprises a *text* item (also enclosed in quotation marks) to be displayed as a menu selection, and a *label* item to which to branch if you select the corresponding menu selection.

**Menu("***title***","***text1***",***label1***,"***text2***",***label2***,** . . .**)**

**Program** **Output**

The program above pauses until you select **1** or **2**. If you select **2**, for example, the menu disappears and the program continues execution at **Lbl B**.

**prgm**

Use **prgm** to execute other programs as subroutines. When you select **prgm**, it is pasted to the cursor location. Enter characters to spell a program *name*. Using **prgm** is equivalent to selecting existing programs from the **PRGM EXEC** menu; however, it allows you to enter the name of a program that you have not yet created.

**prgm***name*

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TI-83 Plus Programming 523

**Note:** You cannot directly enter the subroutine name when using **RCL**. You must paste the name from the **PRGM EXEC** menu.

**Return**

**Return** quits the subroutine and returns execution to the calling program, even if encountered within nested loops. Any loops are ended. An implied **Return** exists at the end of any program that is called as a subroutine. Within the main program, **Return** stops execution and returns to the home screen.

**Stop**

**Stop** stops execution of a program and returns to the home screen. **Stop** is optional at the end of a program.

**DelVar**

**DelVar** deletes from memory the contents of *variable*.

**DelVar ***variable*

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**GraphStyle(**

**GraphStyle(** designates the style of the graph to be drawn. *function#* is the number of the **Y=** function name in the current graphing mode. *graphstyle* is a number from **1** to **7** that corresponds to the graph style, as shown below.

**1** = (line) **5** = (path) **2** = (thick) **6** = (animate) **3** = (shade above) **7** = (dot) **4** = (shade below)

**GraphStyle(***function#***,***graphstyle***)**

For example, **GraphStyle(1,5)** in **Func** mode sets the graph style for **Y1** to (path; **5**).

Not all graph styles are available in all graphing modes. For a detailed description of each graph style, see the Graph Styles table in Chapter 3.

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PRGM I/O (Input/Output) Instructions

**PRGM I/O Menu**

To display the **PRGM I/O** (program input/output) menu, press ~ from within the program editor only.

**CTL** **I/O EXEC** **1:Input** Enters a value or uses the cursor. **2:Prompt** Prompts for entry of variable values. **3:Disp** Displays text, value, or the home screen. **4:DispGraph** Displays the current graph. **5:DispTable** Displays the current table. **6:Output(** Displays text at a specified position. **7:getKey** Checks the keyboard for a keystroke. **8:ClrHome** Clears the display. **9:ClrTable** Clears the current table. **0:GetCalc(** Gets a variable from another TI-83 Plus. **A:Get(** Gets a variable from CBL 2/CBL or CBR. **B:Send(** Sends a variable to CBL 2/CBL or CBR.

These instructions control input to and output from a program during execution. They allow you to enter values and display answers during program execution.

To return to the program editor without selecting an item, press .

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TI-83 Plus Programming 526

**Displaying a Graph with Input**

**Input** without a variable displays the current graph. You can move the free-moving cursor, which updates **X** and **Y** (and **R** and **q** for **PolarGC** format). The pause indicator is on. Press to resume program execution.

**Input**

**Program** **Output**

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**Storing a Variable Value with Input**

**Input** with *variable* displays a **?** (question mark) prompt during execution. *variable* may be a real number, complex number, list, matrix, string, or **Y=** function. During program execution, enter a value, which can be an expression, and then press . The value is evaluated and stored to *variable*, and the program resumes execution.

**Input** [*variable*]

You can display *text* or the contents of **Str***n* (a string variable) of up to 16 characters as a prompt. During program execution, enter a value after the prompt and then press . The value is stored to *variable*, and the program resumes execution.

**Input **[**"***text***",***variable*] **Input **[**Str***n***,***variable*]

**Program** **Output**

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TI-83 Plus Programming 528

**Note:** When a program prompts for input of lists and **Yn** functions during execution, you must include the braces ( **{ }** ) around the list elements and quotation marks ( **"** ) around the expressions.

**Prompt**

During program execution, **Prompt** displays each *variable*, one at a time, followed by **=?**. At each prompt, enter a value or expression for each *variable*, and then press . The values are stored, and the program resumes execution.

**Prompt** *variableA*[**,***variableB***,**...**,***variable n*]

**Program** **Output**

**Note: **Y= functions are not valid with **Prompt**.

**Displaying the Home Screen**

**Disp** (display) without a value displays the home screen. To view the home screen during program execution, follow the **Disp** instruction with a **Pause** instruction.

**Disp**

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TI-83 Plus Programming 529

**Displaying Values and Messages**

**Disp** with one or more *values* displays the value of each.

**Disp **[*valueA***,***valueB***,***valueC***,**...**,***value n*]

If *value* is a variable, the current value is displayed.

If *value* is an expression, it is evaluated and the result is displayed on the right side of the next line.

If *value* is text within quotation marks, it is displayed on the left side of the current display line. **!** is not valid as text.

**Program** **Output**

If **Pause** is encountered after **Disp**, the program halts temporarily so you can examine the screen. To resume execution, press .

**Note:** If a matrix or list is too large to display in its entirety, ellipses (**...**) are displayed in the last column, but the matrix or list cannot be scrolled. To scroll, use **Pause ***value*.

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TI-83 Plus Programming 530

**DispGraph**

**DispGraph** (display graph) displays the current graph. If **Pause** is encountered after **DispGraph**, the program halts temporarily so you can examine the screen. Press to resume execution.

**DispTable**

**DispTable** (display table) displays the current table. The program halts temporarily so you can examine the screen. Press to resume execution.

**Output(**

**Output(** displays *text* or *value* on the current home screen beginning at *row* (**1** through **8**) and *column* (**1** through **16**), overwriting any existing characters.

**Tip:** You may want to precede **Output(** with **ClrHome**.

Expressions are evaluated and values are displayed according to the current mode settings. Matrices are displayed in entry format and wrap to the next line. **!** is not valid as text.

**Output(***row***,***column***,"***text***")** **Output(***row***,***column***,***value***)**

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TI-83 Plus Programming 531

**Program** **Output**

For **Output(** on a **Horiz** split screen, the maximum value for *row* is 4.

**getKey**

**getKey** returns a number corresponding to the last key pressed, according to the key code diagram below. If no key has been pressed, **getKey** returns 0. Use **getKey** inside loops to transfer control, for example, when creating video games.

**Program** **Output**

**Note:** , , , and were pressed during program execution.

**Note:** You can press at any time during execution to break the program.

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TI-83 Plus Programming 532

** TI-83 Plus Key Code Diagram**

**ClrHome, ClrTable**

**ClrHome** (clear home screen) clears the home screen during program execution.

**ClrTable** (clear table) clears the values in the table during program execution.

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TI-83 Plus Programming 533

**GetCalc(**

**GetCalc(** gets the contents of *variable* on another TI-83 Plus and stores it to *variable* on the receiving TI-83 Plus. *variable* can be a real or complex number, list element, list name, matrix element, matrix name, string, **Y=** variable, graph database, or picture.

**GetCalc(***variable***)**

**Note: GetCalc(** does not work between TI.82 and TI-83 Plus calculators.

**Get(, Send(**

**Get(** gets data from the CBL 2/CBL or CBR and stores it to *variable *on the receiving TI-83 Plus. *variable *can be a real number, list element, list name, matrix element, matrix name, string, **Y=** variable, graph database, or picture.

**Get(***variable***)**

**Note:** If you transfer a program that references the **Get(** command to the TI-83 Plus from a TI.82, the TI-83 Plus will interpret it as the **Get(** described above. Use **GetCalc( **to get data from another TI-83 Plus.

**Send(** sends the contents of *variable *to the CBL 2/CBL or CBR. You cannot use it to send to another TI-83 Plus. *variable *can be a real number, list element, list name, matrix element, matrix name, string, **Y=** variable, graph database, or picture. *variable *can be a list of elements.

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TI-83 Plus Programming 534

**Send(***variable***)**

**Note:** This program gets sound data and time in seconds from CBL 2/CBL.

**Note:** You can access **Get(**, **Send(**, and **GetCalc(** from the **CATALOG** to execute them from the home screen (Chapter 15).

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TI-83 Plus Programming 535

Calling Other Programs as Subroutines

**Calling a Program from Another Program**

On the TI-83 Plus, any stored program can be called from another program as a subroutine. Enter the name of the program to use as a subroutine on a line by itself.

You can enter a program name on a command line in either of two ways.

Press | to display the **PRGM EXEC** menu and select the name of the program **prgm***name* is pasted to the current cursor location on a command line.

Select **prgm** from the **PRGM CTL** menu, and then enter the program name.

**prgm***name*

When **prgm***name* is encountered during execution, the next command that the program executes is the first command in the second program. It returns to the subsequent command in the first program when it encounters either **Return** or the implied **Return** at the end of the second program.

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TI-83 Plus Programming 536

**Program** **Output**

**&**

**Subroutine ( '**

**Notes about Calling Programs**

Variables are global.

*label* used with **Goto** and **Lbl** is local to the program where it is located. *label* in one program is not recognized by another program. You cannot use **Goto** to branch to a *label* in another program.

**Return** exits a subroutine and returns to the calling program, even if it is encountered within nested loops.

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TI-83 Plus Programming 537

Running an Assembly Language Program

You can run programs written for the TI-83 Plus in assembly language. Typically, assembly language programs run much faster and provide greater control than than the keystroke programs that you write with the built-in program editor.

**Note:** Because an assembly langauge program has greater control over the calculator, if your assembly language program has error(s), it may cause your calculator to reset and lose all data, programs, and applications stored in memory.

When you download an assembly language program, it is stored among the other programs as a **PRGM** menu item. You can:

Transmit it using the TI-83 Plus communication link (Chapter 19).

Delete it using the **MEM MGMT** **DEL** screen (Chapter 18).

To run an assembly Program, the syntax is: **Asm(***assemblyprgmname***)**

If you write an assembly language program, use the two instructions below from the **CATALOG** to identify and compile the program.

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TI-83 Plus Programming 538

**Instructions** **Comments**

**AsmComp(***prgmASM1,* *prgmASM2***)**

Compiles an assembly language program written in ASCII and stores the hex version

**AsmPrgm** Identifies an assembly language program; must be entered as the first line of an assembly language program

To compile an assembly program that you have written:

1. Follow the steps for writing a program (16-4) but be sure to include **AsmPrgm** as the first line of your program.

2. From the home screen, press y N and then select **AsmComp(** to paste it to the screen

3. Press to display the **PRGM EXEC** menu.

4. Select the program you want to compile. It will be pasted to the home screen.

5. Press and then select **prgm** from the **CATALOG**

6. Key in the name you have chosen for the output program.

**Note:** This name must be unique not a copy of an existing program name.

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TI-83 Plus Programming 539

7. Press to complete the sequence.

The sequence of the arguments should be as follows:

**AsmComp(***prgmASM1,**prgmASM2*)

8. Press to compile your program and generate the output program.

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TI-83 Plus Activities 540

Chapter 17: Activities

The Quadratic Formula

**Entering a Calculation**

**Use the quadratic formula to solve the quadratic equations 3X2 + 5X + 2 = 0 and** **2X2 N X + 3 = 0. Begin with the equation 3X2 + 5X + 2 = 0.**

1. Press **3** [A] (above ) to store the coefficient of the X2 term.

2. Press [ : ] (above ). The colon allows you to enter more than one instruction on a line.

3. Press **5** [B] (above ) to store the coefficient of the X term. Press [ : ] to enter a new instruction on the same line. Press **2** [C] (above ) to store the constant.

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TI-83 Plus Activities 541

4. Press to store the values to the variables A, B, and C.

The last value you stored is shown on the right side of the display. The cursor moves to the next line, ready for your next entry.

5. Press [B] y C [B] **4** [A] [C] **2** [A] to enter the expression for one of the solutions for the quadratic formula,

*a*

*acbb*

2

42

6. Press to find one solution for the equation 3X2 + 5X + 2 = 0.

The answer is shown on the right side of the display. The cursor moves to the next line, ready for you to enter the next expression.

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TI-83 Plus Activities 542

The Quadratic Formula

**Converting to a Fraction**

You can show the solution as a fraction.

1. Press to display the** MATH** menu.

2. Press **1 **to select **1:4Frac** from the** MATH **menu.

When you press **1**, **Ans4Frac** is displayed on the home screen. **Ans** is a variable that contains the last calculated answer.

3. Press to convert the result to a fraction.

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TI-83 Plus Activities 543

To save keystrokes, you can recall the last expression you entered, and then edit it for a new calculation.

4. Press y [ (above ) to recall the fraction conversion entry, and then press y [ again to recall the quadratic-formula expression,

*a*

*acbb*

2 42+

5. Press } to move the cursor onto the **+** sign in the formula. Press to edit the quadratic- formula expression to become:

*a*

*acbb*

2

42

6. Press to find the other solution for the quadratic equation 3X2 + 5X + 2 = 0.

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TI-83 Plus Activities 544

The Quadratic Formula

**Displaying Complex Results**

Now solve the equation 2X2 N X + 3 = 0. When you set **a+b i** complex number mode, the TI-83 Plus displays complex results.

1. Press z (6 times), and then press ~ to position the cursor over **a+b i**. Press to select

**a+b**complex-number mode.

*i*2. Press y 5 (above z) to return to the home screen, and then press to clear it.

3. Press **2** [A] [ : ] **1** [B] [ : ] **3** [C] .

The coefficient of the X2 term, the coefficient of the X term, and the constant for the new equation are stored to A, B, and C, respectively.

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TI-83 Plus Activities 545

4. Press y [ to recall the store instruction, and then press y [ again to recall the quadratic-formula expression,

*a*

*acbb*

2

42

5. Press to find one solution for the equation 2X2 N X + 3 = 0.

6. Press y [ repeatedly until this quadratic- formula expression is displayed:

*a*

*acbb*

2 42+

7. Press to find the other solution for the quadratic equation: 2X2 N X + 3 = 0.

**Note:** An alternative for solving equations for real numbers is to use the built-in Equation Solver (Chapter 2).

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TI-83 Plus Activities 546

Box with Lid

**Defining a Function**

Take a 20 cm 25 cm. sheet of paper and cut X X squares from two corners. Cut X 12.5 cm rectangles from the other two corners as shown in the diagram below. Fold the paper into a box with a lid. What value of X would give your box the maximum volume V? Use the table and graphs to determine the solution.

Begin by defining a function that describes the volume of the box.

From the diagram: 2X + A = 20 2X + 2B = 25 V = A*B*X

Substituting: V = (20 N 2X) (25 2 N X) X

1. Press o to display the **Y=** editor, which is where you define functions for tables and graphing.

A20

X

X B X B

25

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TI-83 Plus Activities 547

2. Press **20** **2** **25** 2 to define the volume function as **Y1** in terms of **X**.

lets you enter **X** quickly, without having to press . The highlighted **=** sign indicates that **Y1** is selected.

Box with Lid

**Defining a Table of Values**

The table feature of the TI-83 Plus displays numeric information about a function. You can use a table of values from the function you just defined to estimate an answer to the problem.

1. Press y - (above p) to display the **TABLE SETUP** menu.

2. Press to accept **TblStart=0**.

3. Press **1** to define the table increment **@Tbl=1**. Leave **Indpnt: Auto** and **Depend: Auto** so that the table will be generated automatically.

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TI-83 Plus Activities 548

4. Press y 0 (above s) to display the table.

Notice that the maximum value for **Y1** (boxs volume) occurs when **X** is about **4**, between **3** and **5**.

5. Press and hold to scroll the table until a negative result for **Y1** is displayed.

Notice that the maximum length of **X** for this problem occurs where the sign of **Y1** (boxs volume) changes from positive to negative, between **10** and **11**.

6. Press y -.

Notice that **TblStart** has changed to **6** to reflect the first line of the table as it was last displayed. (In step 5, the first value of **X** displayed in the table is **6**.)

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TI-83 Plus Activities 549

Box with Lid

**Zooming In on the Table**

You can adjust the way a table is displayed to get more information about a defined function. With smaller values for **@Tbl**, you can zoom in on the table.

1. Press **3** to set **TblStart**. Press **1** to set **@Tbl**.

This adjusts the table setup to get a more accurate estimate of **X** for maximum volume **Y1**.

2. Press y 0.

3. Press and } to scroll the table.

Notice that the maximum value for **Y1** is **410.26**, which occurs at **X**=**3.7**. Therefore, the maximum occurs where **3.6**<**X**<**3.8**.

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TI-83 Plus Activities 550

4. Press y -. Press **3 ** **6** to set **TblStart**. Press **01** to set **@Tbl**.

5. Press y 0, and then press and } to scroll the table.

Four equivalent maximum values are shown, **410.26** at **X**=**3.67**, **3.68**, **3.69**, and **3.70**.

6. Press or } to move the cursor to **3.67**. Press ~ to move the cursor into the **Y1** column.

The value of **Y1** at **X**=**3.67** is displayed on the bottom line in full precision as **410.261226**.

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TI-83 Plus Activities 551

7. Press to display the other maximum.

The value of **Y1** at **X**=**3.68** in full precision is **410.264064**, at **X**=**3.69** is **410.262318** and at **X**=**3.7** is **410.256**.

The maximum volume of the box would occur at **3.68** if you could measure and cut the paper at .01-centimeter increments.

Box with Lid

**Setting the Viewing Window**

You also can use the graphing features of the TI-83 Plus to find the maximum value of a previously defined function. When the graph is activated, the viewing window defines the displayed portion of the coordinate plane. The values of the window variables determine the size of the viewing window.

1. Press p to display the window editor, where you can view and edit the values of the window variables.

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TI-83 Plus Activities 552

The standard window variables define the viewing window as shown. **Xmin**, **Xmax**, **Ymin**, and **Ymax** define the boundaries of the display. **Xscl** and **Yscl** define the distance between tick marks on the **X** and **Y** axes. **Xres** controls resolution.

Xmax

Ymin

Ymax

Xscl

Yscl

Xmin

2. Press **0** to define **Xmin**.

3. Press **20 ** **2** to define **Xmax** using an expression.

4. Press . The expression is evaluated, and **10** is stored in **Xmax**. Press to accept **Xscl** as **1**.

5. Press **0** **500** **100** **1 ** to define the remaining window variables.

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TI-83 Plus Activities 553

Box with Lid

**Displaying and Tracing the Graph**

Now that you have defined the function to be graphed and the window in which to graph it, you can display and explore the graph. You can trace along a function using the **TRACE** feature.

1. Press to graph the selected function in the viewing window.

The graph of **Y1=(20N2X)(252NX)X** is displayed.

2. Press ~ to activate the free-moving graph cursor.

The **X** and **Y** coordinate values for the position of the graph cursor are displayed on the bottom line.

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TI-83 Plus Activities 554

3. Press |, ~, }, and to move the free- moving cursor to the apparent maximum of the function.

As you move the cursor, the **X** and **Y** coordinate values are updated continually.

4. Press r. The trace cursor is displayed on the **Y1** function.

The function that you are tracing is displayed in the top-left corner.

5. Press | and ~ to trace along **Y1**, one **X** dot at a time, evaluating **Y1** at each **X**.

You also can enter your estimate for the maximum value of **X**.

6. Press **3** **8**. When you press a number key while in **TRACE**, the **X=** prompt is displayed in the bottom-left corner.

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TI-83 Plus Activities 555

7. Press .

The trace cursor jumps to the point on the **Y1**

function evaluated at **X=3.8**.

8. Press | and ~ until you are on the maximum **Y** value.

This is the maximum of **Y1(X)** for the **X** pixel values. The actual, precise maximum may lie between pixel values.

Box with Lid

**Zooming In on the Graph**

To help identify maximums, minimums, roots, and intersections of functions, you can magnify the viewing window at a specific location using the **ZOOM** instructions.

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TI-83 Plus Activities 556

1. Press q to display the **ZOOM** menu.

This menu is a typical TI-83 Plus menu. To select an item, you can either press the number or letter next to the item, or you can press until the item number or letter is highlighted, and then press .

2. Press **2 **to select **2:Zoom In**.

The graph is displayed again. The cursor has changed to indicate that you are using a **ZOOM**

instruction.

3. With the cursor near the maximum value of the function, press .

The new viewing window is displayed. Both **Xmax**N**Xmin** and **Ymax**N**Ymin** have been adjusted by factors of 4, the default values for the zoom factors.

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TI-83 Plus Activities 557

4. Press p to display the new window settings.

Box with Lid

**Finding the Calculated Maximum**

You can use a **CALCULATE** menu operation to calculate a local maximum of a function.

1. Press y / (above r) to display the **CALCULATE** menu. Press **4** to select **4:maximum**.

The graph is displayed again with a **Left Bound?** prompt.

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TI-83 Plus Activities 558

2. Press | to trace along the curve to a point to the left of the maximum, and then press .

A **4** at the top of the screen indicates the selected bound.

A **Right Bound?** prompt is displayed.

3. Press ~ to trace along the curve to a point to the right of the maximum, and then press .

A **3** at the top of the screen indicates the selected bound.

A **Guess?** prompt is displayed.

4. Press | to trace to a point near the maximum, and then press .

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TI-83 Plus Activities 559

Or, press **3** **8**, and then press to enter a guess for the maximum.

When you press a number key in **TRACE**, the **X=** prompt is displayed in the bottom-left corner.

Notice how the values for the calculated maximum compare with the maximums found with the free-moving cursor, the trace cursor, and the table.

**Note:** In steps 2 and 3 above, you can enter values directly for Left Bound and Right Bound, in the same way as described in step 4.

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TI-83 Plus Activities 560

Comparing Test Results Using Box Plots

**Problem**

An experiment found a significant difference between boys and girls pertaining to their ability to identify objects held in their left hands, which are controlled by the right side of their brains, versus their right hands, which are controlled by the left side of their brains. The TI Graphics team conducted a similar test for adult men and women.

The test involved 30 small objects, which participants were not allowed to see. First, they held 15 of the objects one by one in their left hands and guessed what they were. Then they held the other 15 objects one by one in their right hands and guessed what they were. Use box plots to compare visually the correct-guess data from this table.

**Correct Guesses**

**Women** **Left**

**Women** **Right**

**Men** **Left**

**Men** **Right**

8 4 7 12 9 1 8 6

12 8 7 12 11 12 5 12 10 11 7 7 8 11 8 11

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TI-83 Plus Activities 561

**Women** **Left**

**Women** **Right**

**Men** **Left**

**Men** **Right**

12 13 11 12 7 12 4 8 9 11 10 12

11 12 14 11 13 9 5 9

**Procedure**

1. Press **5** to select **5:SetUpEditor**. Enter list names **WLEFT**, **WRGHT**, **MLEFT**, and **MRGHT**, separated by commas. Press . The stat list editor now contains only these four lists.

2. Press **1** to select **1:Edit**.

3. Enter into **WLEFT** the number of correct guesses each woman made using her left hand (Women Left). Press ~ to move to **WRGHT** and enter the number of correct guesses each woman made using her right hand (Women Right).

4. Likewise, enter each mans correct guesses in **MLEFT** (**Men Left**) and **MRGHT** (**Men Right**).

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TI-83 Plus Activities 562

5. Press y ,. Select **1:Plot1**. Turn on plot 1; define it as a modified box plot that uses **WLEFT**. Move the cursor to the top line and select **Plot2**. Turn on plot 2; define it as a modified box plot that uses **WRGHT**.

6. Press o. Turn off all functions.

7. Press p. Set **Xscl=1** and **Yscl=0**. Press q **9** to select **9:ZoomStat**. This adjusts the viewing window and displays the box plots for the womens results.

8. Press r.

% Womens left-hand data

% Womens right-hand data

Use | and ~ to examine **minX**, **Q1**, **Med**, **Q3**, and **maxX** for each plot. Notice the outlier to the womens right-hand data. What is the median for the left hand? For the right hand? With which hand were the women more accurate guessers, according to the box plots?

9. Examine the mens results. Redefine plot 1 to use **MLEFT**, redefine plot 2 to use **MRGHT**. Press r.

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TI-83 Plus Activities 563

% Mens left-hand data

% Mens right-hand data

Press | and ~ to examine **minX**, **Q1**, **Med**, **Q3**, and **maxX** for each plot. What difference do you see between the plots?

10.Compare the left-hand results. Redefine plot 1 to use **WLEFT**, redefine plot 2 to use **MLEFT**, and then press r to examine **minX**, **Q1**, **Med**, **Q3**, and **maxX** for each plot. Who were the better left-hand guessers, men or women?

11.Compare the right-hand results. Define plot 1 to use **WRGHT**, define plot 2 to use **MRGHT**, and then press r to examine **minX**, **Q1**, **Med**, **Q3**, and **maxX** for each plot. Who were the better right-hand guessers?

In the original experiment boys did not guess as well with right hands, while girls guessed equally well with either hand. This is not what our box plots show for adults. Do you think that this is because adults have learned to adapt or because our sample was not large enough?

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TI-83 Plus Activities 564

Graphing Piecewise Functions

**Problem**

The fine for speeding on a road with a speed limit of 45 kilometers per hour (kph) is 50; plus 5 for each kph from 46 to 55 kph; plus 10 for each kph from 56 to 65 kph; plus 20 for each kph from 66 kph and above. Graph the piecewise function that describes the cost of the ticket.

The fine (Y) as a function of kilometers per hour (X) is:

Y = 0 0 < X 45 Y = 50 + 5 (X N 45) 45 < X 55 Y = 50 + 5 10 + 10 (X N 55) 55 < X 65 Y = 50 + 5 10 + 10 10 + 20 (X N 65) 65 < X

**Procedure**

1. Press z. Select **Func** and the default settings.

2. Press o. Turn off all functions and stat plots. Enter the **Y=** function to describe the fine. Use the **TEST** menu operations to define the piecewise function. Set the graph style for **Y1** to (dot).

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TI-83 Plus Activities 565

3. Press p and set **Xmin=L2**, **Xscl=10**, **Ymin=L5**, and **Yscl=10**. Ignore **Xmax** and **Ymax**; they are set by **@X** and **@Y** in step 4.

4. Press y 5 to return to the home screen. Store **1** to **@X**, and then store **5** to **@Y**. **@X** and **@Y **are on the **VARS Window X/Y** secondary menu. **@X** and **@Y** specify the horizontal and vertical distance between the centers of adjacent pixels. Integer values for **@X** and **@Y** produce nice values for tracing.

5. Press r to plot the function. At what speed does the ticket exceed 250?

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TI-83 Plus Activities 566

Graphing Inequalities

**Problem**

Graph the inequality 0.4X3 N 3X + 5 < 0.2X + 4. Use the **TEST** menu operations to explore the values of X where the inequality is true and where it is false.

**Procedure**

1. Press z. Select **Dot**, **Simul**, and the default settings. Setting **Dot** mode changes all graph style icons to (dot) in the **Y=** editor.

2. Press o. Turn off all functions and stat plots. Enter the left side of the inequality as **Y4** and the right side as **Y5**.

3. Enter the statement of the inequality as **Y6**. This function evaluates to **1** if true or **0** if false.

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TI-83 Plus Activities 567

4. Press q **6** to graph the inequality in the standard window.

5. Press r to move to **Y6**. Then press | and ~ to trace the inequality, observing the value of **Y**.

6. Press o. Turn off **Y4**, **Y5**, and **Y6**. Enter equations to graph only the inequality.

7. Press r. Notice that the values of **Y7** and **Y8** are zero where the inequality is false.

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TI-83 Plus Activities 568

Solving a System of Nonlinear Equations

**Problem**

Using a graph, solve the equation X3 N 2X = 2cos(X). Stated another way, solve the system of two equations and two unknowns: Y = X3N2X and Y = 2cos(X). Use **ZOOM** factors to control the decimal places displayed on the graph.

**Procedure**

1. Press z. Select the default mode settings. Press o. Turn off all functions and stat plots. Enter the functions.

2. Press q **4** to select **4:ZDecimal**. The display shows that two solutions may exist (points where the two functions appear to intersect).

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TI-83 Plus Activities 569

3. Press q ~ **4** to select **4:SetFactors** from the **ZOOM MEMORY** menu. Set **XFact=10** and **YFact=10**.

4. Press q **2** to select **2:Zoom In**. Use |, ~, }, and to move the free-moving cursor onto the apparent intersection of the functions on the right side of the display. As you move the cursor, notice that the **X** and **Y** values have one decimal place.

5. Press to zoom in. Move the cursor over the intersection. As you move the cursor, notice that now the **X** and **Y** values have two decimal places.

6. Press to zoom in again. Move the free-moving cursor onto a point exactly on the intersection. Notice the number of decimal places.

7. Press y / **5** to select **5:intersect**. Press to select the first curve and to select the second curve. To guess, move the trace cursor near the intersection. Press . What are the coordinates of the intersection point?

8. Press q **4** to select **4:ZDecimal** to redisplay the original graph.

9. Press q. Select **2:Zoom In** and repeat steps 4 through 8 to explore the apparent function intersection on the left side of the display.

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TI-83 Plus Activities 570

Using a Program to Create the Sierpinski Triangle

**Setting up the Program**

This program creates a drawing of a famous fractal, the Sierpinski Triangle, and stores the drawing to a picture. To begin, press ~ ~ **1**. Name the program **SIERPINS**, and then press . The program editor is displayed.

**Program**

**PROGRAM:SIERPINS** **:FnOff :ClrDraw** **:PlotsOff** **:AxesOff** **:0!Xmin:1!Xmax** **:0!Ymin:1!Ymax**

Set viewing window.

**:rand!X:rand!Y**

**:For(K,1,3000)** **:rand!N**

Beginning of **For** group.

**:If N13** **:Then** **:.5X!X** **:.5Y!Y** **:End**

**If**/**Then** group

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TI-83 Plus Activities 571

**:If 13 **

**:Then**

**:.5(.5+X)!X**

**:.5(1+Y)!Y**

**:End**

**If**/**Then** group.

**:If 23 **

**:Then**

**:.5(1+X)!X**

**:.5Y!Y**

**:End**

**If**/**Then** group.

**:Pt-On(X,Y)** Draw point. **:End** End of **For** group. **:StorePic 6** Store picture.

**After you execute the program above, you can recall and display the picture with the instruction RecallPic 6.**

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**TI-83 Plus Activities 572 **

**Graphing Cobweb Attractors **

**Problem**

**Using Web format, you can identify points with attracting and repelling behavior in sequence graphing. **

**Procedure**

**1. Press z. Select Seq and the default mode settings. Press y .. Select Web format and the default format settings. **

**2. Press o. Clear all functions and turn off all stat plots. Enter the sequence that corresponds to the expression Y = K X(1NX). **

**u(n)=Ku(nN1)(1Nu(nN1))** **u(nMin)=.01**

**3. Press y 5 to return to the home screen, and then store 2.9 to K. **

**4. Press p. Set the window variables. nMin=0 Xmin=0 Ymin=M.26 nMax=10 Xmax=1 Ymax=1.1 PlotStart=1 Xscl=1 Yscl=1 PlotStep=1**

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**TI-83 Plus Activities 573 **

**5. Press r to display the graph, and then press ~ to trace the cobweb. This is a cobweb with one attractor. **

**6. Change K to 3.44 and trace the graph to show a cobweb with two attractors. **

**7. Change K to 3.54 and trace the graph to show a cobweb with four attractors.**

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**TI-83 Plus Activities 574 **

**Using a Program to Guess the Coefficients **

**Setting Up the Program**

**This program graphs the function A sin(BX) with random integer coefficients between 1 and 10. Try to guess the coefficients and graph your guess as C sin(DX). The program continues until your guess is correct. **

**Program**

**PROGRAM:GUESS** **:PlotsOff :Func** **:FnOff :Radian** **:ClrHome** **:"Asin(BX)"!Y1** **:"Csin(DX)"!Y2** Define equations.

**:GraphStyle(1,1)** **:GraphStyle(2,5)** Set line and path graph styles.

**:FnOff 2**

**:randInt(1,10)!A** **:randInt(1,10)!B** **:0!C:0!D**

**Initialize coefficients. **

**:L2p!Xmin** **:2p!Xmax** **:p2!Xscl** **:L10!Ymin** **:10!Ymax**

**Set viewing window.**

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**TI-83 Plus Activities 575 **

**:1!Yscl** **:DispGraph** **:Pause**

**Display graph. **

**:FnOn 2** **:Lbl Z** **:Prompt C,D** Prompt for guess. **:DispGraph** **:Pause**

**Display graph. **

**:If C=A** **:Text(1,1,"C IS OK")** **:If CA** **:Text(1,1,"C IS WRONG")** **:If D=B** **:Text(1,50,"D IS OK")** **:If DB** **:Text(1,50,"D IS WRONG")**

**Display results. **

**:DispGraph** **:Pause** Display graph.

**:If C=A and D=B** **:Stop** **:Goto Z**

**Quit if guesses are correct.**

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**TI-83 Plus Activities 576 **

**Graphing the Unit Circle and Trigonometric Curves **

**Problem**

**Using parametric graphing mode, graph the unit circle and the sine curve to show the relationship between them. **

**Any function that can be plotted in Func mode can be plotted in Par mode by defining the X component as T and the Y component as F(T). **

**Procedure**

**1. Press z. Select Par, Simul, and the default settings. **

**2. Press p. Set the viewing window. Tmin=0 Xmin=L2 Ymin=L3 Tmax=2p Xmax=7.4 Ymax=3 Tstep=.1 Xscl=p2 Yscl=1 **

**3. Press o. Turn off all functions and stat plots. Enter the expressions to define the unit circle centered on (0,0).**

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**TI-83 Plus Activities 577 **

**4. Enter the expressions to define the sine curve. **

**5. Press r. As the graph is plotting, you may press to pause and again to resume graphing as you watch the sine function unwrap from the unit circle. **

**Note:** You can generalize the unwrapping. Replace **sin(T)** in **Y2T** with any other trig function to unwrap that function.

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**TI-83 Plus Activities 578 **

**Finding the Area between Curves **

**Problem**

**Find the area of the region bounded by **

**f(x) = 300x / (x2 + 625) g(x) = 3cos(.1x) x = 75 **

**Procedure**

**1. Press z. Select the default mode settings. **

**2. Press p. Set the viewing window. Xmin=0 Ymin=L5 Xmax=100 Ymax=10 Xscl=10 Yscl=1 **

**Xres=1**

**3. Press o. Turn off all functions and stat plots. Enter the upper and lower functions. Y1=300X(X2+625) Y2=3cos(.1X)**

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**TI-83 Plus Activities 579 **

**4. Press y / 5 to select 5:Intersect. The graph is displayed. Select a first curve, second curve, and guess for the intersection toward the left side of the display. The solution is displayed, and the value of X at the intersection, which is the lower limit of the integral, is stored in Ans and X. **

**5. Press y 5 to go to the home screen. Press y < 7 and use Shade( to see the area graphically. **

**Shade(Y2,Y1,Ans,75)**

**6. Press y 5 to return to the home screen. Enter the expression to evaluate the integral for the shaded region. **

**fnInt(Y1Y2,X,Ans,75)**

**The area is 325.839962.**

Page 583

**TI-83 Plus Activities 580 **

**Using Parametric Equations: Ferris Wheel Problem **

**Problem**

**Using two pairs of parametric equations, determine when two objects in motion are closest to each other in the same plane. **

**A ferris wheel has a diameter (d) of 20 meters and is rotating counterclockwise at a rate (s) of one revolution every 12 seconds. The parametric equations below describe the location of a ferris wheel passenger at time T, where a is the angle of rotation, (0,0) is the bottom center of the ferris wheel, and (10,10) is the passengers location at the rightmost point, when T=0. **

**X(T) = r cos a where a = 2pTs and r = d2 Y(T) = r + r sin a **

**A person standing on the ground throws a ball to the ferris wheel passenger. The throwers arm is at the same height as the bottom of the ferris wheel, but 25 meters (b) to the right of the ferris wheels lowest point (25,0). The person throws the ball with velocity (v0) of 22 meters per second at an angle (q) of 66 from the horizontal. The parametric equations below describe the location of the ball at time T. **

**X(T) = b N Tv0 cosq Y(T) = Tv0 sinq N (g2) T2 where g = 9.8 m/sec2**

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**TI-83 Plus Activities 581 **

**Procedure**

**1. Press z. Select Par, Simul, and the default settings. Simul (simultaneous) mode simulates the two objects in motion over time. **

**2. Press p. Set the viewing window. Tmin=0 Xmin=L13 Ymin=0 Tmax=12 Xmax=34 Ymax=31 Tstep=.1 Xscl=10 Yscl=10 **

**3. Press o. Turn off all functions and stat plots. Enter the expressions to define the path of the ferris wheel and the path of the ball. Set the graph style for X2T to (path). **

**Tip:** Try setting the graph styles to ** X1T** and ** X2T**, which simulates a chair on the ferris wheel and the ball flying through the air when you press .

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**TI-83 Plus Activities 582 **

**4. Press to graph the equations. Watch closely as they are plotted. Notice that the ball and the ferris wheel passenger appear to be closest where the paths cross in the top-right quadrant of the ferris wheel. **

**5. Press p. Change the viewing window to concentrate on this portion of the graph. Tmin=1 Xmin=0 Ymin=10 Tmax=3 Xmax=23.5 Ymax=25.5 Tstep=.03 Xscl=10 Yscl=10 **

**6. Press r. After the graph is plotted, press ~ to move near the point on the ferris wheel where the paths cross. Notice the values of X, Y, and T.**

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**TI-83 Plus Activities 583 **

**7. Press to move to the path of the ball. Notice the values of X and Y (T is unchanged). Notice where the cursor is located. This is the position of the ball when the ferris wheel passenger passes the intersection. Did the ball or the passenger reach the intersection first? **

**You can use r to, in effect, take snapshots in time and explore the relative behavior of two objects in motion.**

Page 587

**TI-83 Plus Activities 584 **

**Demonstrating the Fundamental Theorem of Calculus **

**Problem 1**

**Using the functions fnInt( and nDeriv( from the MATH menu to graph functions defined by integrals and derivatives demonstrates graphically that: **

** >== x **

*xxdtxF* 1

**0),(ln)( and that **

*x* *dt*

*t* *Dx*

*x* 1

**1 **

**1 = **

**Procedure 1**

**1. Press z. Select the default settings. **

**2. Press p. Set the viewing window. Xmin=.01 Ymin=M1.5 Xres=3 Xmax=10 Ymax=2.5 Xscl=1 Yscl=1**

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**TI-83 Plus Activities 585 **

**3. Press o. Turn off all functions and stat plots. Enter the numerical integral of 1T from 1 to X and the function ln(X). Set the graph style for Y1 to (line) and Y2 to (path). **

**4. Press r. Press |, }, ~, and to compare the values of Y1 **

**and Y2. **

**5. Press o. Turn off Y1 and Y2, and then enter the numerical derivative of the integral of 1X and the function 1X. Set the graph style for Y3 **

**to (line) and Y4 to (thick). **

**6. Press r. Again, use the cursor keys to compare the values of the two graphed functions, Y3 and Y4.**

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**TI-83 Plus Activities 586 **

**Problem 2**

**Explore the functions defined by **

**= xxx **

*dttdttdtty* 2

**2 0 **

**2 2 **

**2 ,and,, **

**Procedure 2**

**1. Press o. Turn off all functions and stat plots. Use a list to define these three functions simultaneously. Store the function in Y5. **

**2. Press q 6 to select 6:ZStandard. **

**3. Press r. Notice that the functions appear identical, only shifted vertically by a constant.**

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**TI-83 Plus Activities 587 **

**4. Press o. Enter the numerical derivative of Y5 in Y6. **

**5. Press r. Notice that although the three graphs defined by Y5 are different, they share the same derivative.**

Page 591

**TI-83 Plus Activities 588 **

**Computing Areas of Regular N-Sided Polygons **

**Problem**

**Use the equation solver to store a formula for the area of a regular N-sided polygon, and then solve for each variable, given the other variables. Explore the fact that the limiting case is the area of a circle, pr2. **

**Consider the formula A = NB2 sin(pN) cos(pN) for the area of a regular polygon with N sides of equal length and B distance from the center to a vertex. **

**N = 4 sides N = 8 sides N = 12 sides **

**Procedure**

**1. Press 0 to select 0:Solver from the MATH menu. Either the equation editor or the interactive solver editor is displayed. If the**

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**TI-83 Plus Activities 589 **

**interactive solver editor is displayed, press } to display the equation editor. **

**2. Enter the formula as 0=ANNB2sin(p / N)cos(p / N), and then press . The interactive solver editor is displayed. **

**3. Enter N=4 and B=6 to find the area (A) of a square with a distance (B) from center to vertex of 6 centimeters. **

**4. Press } } to move the cursor onto A, and then press \. The solution for A is displayed on the interactive solver editor. **

**5. Now solve for B for a given area with various number of sides. Enter A=200 and N=6. To find the distance B, move the cursor onto B, and then press \.**

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**TI-83 Plus Activities 590 **

**6. Enter N=8. To find the distance B, move the cursor onto B, and then press \. Find B for N=9, and then for N=10. **

**Find the area given B=6, and N=10, 100, 150, 1000, and 10000. Compare your results with p62 (the area of a circle with radius 6), which is approximately 113.097. **

**7. Enter B=6. To find the area A, move the cursor onto A, and then press \. Find A for N=10, then N=100, then N=150, then N=1000, and finally N=10000. Notice that as N gets large, the area A approaches pB2. **

**Now graph the equation to see visually how the area changes as the number of sides gets large. **

**8. Press z. Select the default mode settings. **

**9. Press p. Set the viewing window. Xmin=0 Ymin=0 Xres=1 Xmax=200 Ymax=150 Xscl=10 Yscl=10 **

**10.Press o. Turn off all functions and stat plots. Enter the equation for the area. Use X in place of N. Set the graph styles as shown.**

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**TI-83 Plus Activities 591 **

**11.Press r. After the graph is plotted, press 100 to trace to X=100. Press 150 . Press 188 . Notice that as X increases, the value of Y converges to p62, which is approximately 113.097. Y2=pB2 (the area of the circle) is a horizontal asymptote to Y1. The area of an N-sided regular polygon, with r as the distance from the center to a vertex, approaches the area of a circle with radius r (pr2) as N gets large.**

Page 595

**TI-83 Plus Activities 592 **

**Computing and Graphing Mortgage Payments **

** Problem**

**You are a loan officer at a mortgage company, and you recently closed on a 30-year home mortgage at 8 percent interest with monthly payments of 800. The new home owners want to know how much will be applied to the interest and how much will be applied to the principal when they make the 240th payment 20 years from now. **

**Procedure**

**1. Press z and set the fixed-decimal mode to 2 decimal places. Set the other mode settings to the defaults. **

**2. Press to display the TVM Solver. Enter these values. **

**Note:** Enter a positive number (**800**) to show **PMT** as a cash inflow. Payment values will be displayed as positive numbers on the graph. Enter **0** for **FV**,

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**TI-83 Plus Activities 593 **

**since the future value of a loan is 0 once it is paid in full. Enter PMT: END, since payment is due at the end of a period. **

**3. Move the cursor onto the PV= prompt, and then press \. The present value, or mortgage amount, of the house is displayed at the PV= prompt. **

**Now compare the graph of the amount of interest with the graph of the amount of principal for each payment. **

**4. Press z. Set Par and Simul. **

**5. Press o. Turn off all functions and stat plots. Enter these equations and set the graph styles as shown. **

**Note:** **GPrn(** and **GInt(** are located on the **FINANCE menu** (**APPS 1:FINANCE**).

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**TI-83 Plus Activities 594 **

**6. Press p. Set these window variables. Tmin=1 Xmin=0 Ymin=0 Tmax=360 Xmax=360 Ymax=1000 Tstep=12 Xscl=10 Yscl=100 **

**Tip:** To increase the graph speed, change **Tstep** to **24**.

**7. Press r. After the graph is drawn, press 240 to move the trace cursor to T=240, which is equivalent to 20 years of payments. **

**The graph shows that for the 240th payment ( X=240), 358.03 of the 800 payment is applied to principal (Y=358.03). **

**Note:** The sum of the payments (**Y3T=Y1T+Y2T**) is always 800.

**8. Press to move the cursor onto the function for interest defined by X2T and Y2T. Enter 240.**

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**TI-83 Plus Activities 595 **

**The graph shows that for the 240th payment ( X=240), 441.97 of the 800 payment is interest (Y=441.97). **

**9. Press y 5 9 to paste 9:bal( to the home screen. Check the figures from the graph. **

**At which monthly payment will the principal allocation surpass the interest allocation?**

Page 599

**TI-83 Plus Memory and Variable Management 596 **

**Chapter 18: Memory and Variable Management **

**Checking Available Memory **

**MEMORY Menu**

**At any time you can check available memory or manage existing memory by selecting items from the MEMORY menu. To access this menu, press y L. **

**MEMORY** **1:About...** Displays information about the calculator. **2:Mem Mgmt/Del...** Reports memory availability and variable usage. **3:Clear Entries** Clears **ENTRY** (last-entry storage). **4:ClrAllLists** Clears all lists in memory. **5:Archive...** Archives a selected variable. **6:UnArchive...** UnArchives a selected variable. **7:Reset...** Displays the **RAM**, **ARCHIVE**, and **ALL** menus **8:Group...** Displays **GROUP** and **UNGROUP** menus.

**To check memory usage, first press y L and then press 2:Mem Mgmt/Del.**

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**TI-83 Plus Memory and Variable Management 597 **

**Displaying the** **MEMORY MANAGEMENT/DELETE Menu**

**Mem Mgmt/Del** displays the **MEMORY MANAGEMENT/DELETE **menu. The two lines at the top report the total amount of available **RAM** and **ARCHIVE**

**memory. By selecting menu items on this screen, you can see the amount of memory each variable type is using. This information can help you determine if some variables need to be deleted from memory to make room for new data, such as programs or applications. **

**To check memory usage, follow these steps. **

**1. Press y L to display the MEMORY menu. **

**Note:** The # and $ in the top or bottom of the left column indicate that you can scroll up or down to view more variable types.

**2. Select 2:Mem Mgmt/Del to display the MEMORY MANAGEMENT/DELETE **

**menu. The TI-83 Plus expresses memory quantities in bytes.**

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**TI-83 Plus Memory and Variable Management 598 **

**3. Select variable types from the list to display memory usage. **

**Note:** **Real**, **List**, **Y.Vars**, and **Prgm** variable types never reset to zero, even after memory is cleared.

**Apps** are independent applications which are stored in Flash ROM. **AppVars** is a variable holder used to store variables created by independent applications. You cannot edit or change variables in **AppVars** unless you do so through the application which created them.

**To leave the MEMORY MANAGEMENT/DELETE menu, press either y 5 or . Both options display the home screen.**

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**TI-83 Plus Memory and Variable Management 599 **

**Deleting Items from Memory **

**Deleting an Item**

**To increase available memory by deleting the contents of any variable (real or complex number, list, matrix, Y= variable, program, Apps, AppVars, picture, graph database, or string), follow these steps. **

**1. Press y L to display the MEMORY menu. **

**2. Select 2:Mem Mgmt/Del to display the MEMORY MANAGEMENT/DELETE **

**menu. **

**3. Select the type of data you want to delete, or select 1:All for a list of all variables of all types. A screen is displayed listing each variable of the type you selected and the number of bytes each variable is using. **

**For example, if you select 4:List, the LIST editor screen is displayed.**

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**TI-83 Plus Memory and Variable Management 600 **

**4. Press } and to move the selection cursor ( 4) next to the item you want to delete, and then press {. The variable is deleted from memory. You can delete individual variables one by one from this screen. **

**Note:** If you are deleting programs or Apps, you will receive a message asking you to confirm this delete action. Select **2:Yes** to continue.

**To leave any variable screen without deleting anything, press y 5, which displays the home screen. **

**Note:** You cannot delete some system variables, such as the last-answer variable **Ans** and the statistical variable **RegEQ**.

Page 604

**TI-83 Plus Memory and Variable Management 601 **

**Clearing Entries and List Elements **

**Clear Entries**

**Clear Entries** clears the contents of the **ENTRY** (last entry) storage area (Chapter 1). To clear the **ENTRY** storage area, follow these steps.

**1. Press y L to display the MEMORY menu. **

**2. Select 3:Clear Entries to paste the instruction to the home screen. **

**3. Press to clear the ENTRY storage area. **

**To cancel Clear Entries, press . **

**Note:** If you select **3:Clear Entries** from within a program, the **Clear Entries** instruction is pasted to the program editor, and the **Entry** (last entry) is cleared when the program is executed.

Page 605

**TI-83 Plus Memory and Variable Management 602 **

**ClrAllLists**

**ClrAllLists** sets the dimension of each list in RAM only to **0**.

**To clear all elements from all lists, follow these steps. **

**1. Press y L to display the MEMORY menu. **

**2. Select 4:ClrAllLists to paste the instruction to the home screen. **

**3. Press to set to 0 the dimension of each list in memory. **

**To cancel ClrAllLists, press . **

**ClrAllLists** does not delete list names from memory, from the **LIST NAMES**

**menu, or from the stat list editor. **

**Note:** If you select **4:ClrAllLists** from within a program, the **ClrAllLists** instruction is pasted to the program editor. The lists are cleared when the program is executed.

Page 606

**TI-83 Plus Memory and Variable Management 603 **

**Resetting the TI-83 Plus **

**RAM ARCHIVE ALL Menu**

**The RAM ARCHIVE ALL menu gives you the option of resetting all memory (including default settings) or resetting selected portions of memory while preserving other data stored in memory, such as programs and Y= functions. For instance, you can choose to reset all of RAM or just restore the default settings. Be aware that if you choose to reset RAM, all data and programs in RAM will be erased. For archive memory, you can reset variables (Vars), applications (Apps), or both of these. Be aware that if you choose to reset Vars, all data and programs in archive memory will be erased. If you choose to reset Apps, all applications in archive memory will be erased. **

**When you reset defaults on the TI-83 Plus, all defaults in RAM are restored to the factory settings. Stored data and programs are not changed. **

**These are some examples of TI-83 Plus defaults that are restored by resetting the defaults. **

** Mode settings such as Normal (notation); Func (graphing); Real (numbers); and Full (screen) **

** Y= functions off**

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**TI-83 Plus Memory and Variable Management 604 **

** Window variable values such as Xmin=L10; Xmax=10; Xscl=1; Yscl=1; and Xres=1 **

** Stat plots off **

** Format settings such as CoordOn (graphing coordinates on); AxesOn; and ExprOn (expression on) **

** rand seed value to 0 **

**Displaying the RAM ARCHIVE ALL Menu**

**To display the RAM ARCHIVE ALL menu on the TI-83 Plus, follow these steps. **

**1. Press y L to display the MEMORY menu. **

**2. Select 7:Reset to display the RAM ARCHIVE ALL menu. **

**Resetting RAM Memory**

**Resetting RAM restores RAM system variables to factory settings and deletes all nonsystem variables and all programs. Resetting defaults restores all system variables to default settings without deleting variables**

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**TI-83 Plus Memory and Variable Management 605 **

**and programs in RAM. Resetting RAM or resetting defaults does not affect variables and applications in user data archive. **

**Tip:** Before you reset all RAM memory, consider restoring sufficient available memory by deleting only selected data.

**To reset all RAM memory or RAM defaults on the TI-83 Plus, follow these steps. **

**1. From the RAM ARCHIVE ALL menu, select 1:ALL RAM to display the RESET RAM menu or 2:Defaults to display the RESET DEFAULTS menu. **

**2. If you are resetting RAM, read the message below the RESET RAM **

**menu. **

** To cancel the reset and return to the home screen, press . **

** To erase RAM memory or reset defaults, select 2:Reset. Depending on your choice, the message RAM cleared or Defaults set is displayed on the home screen.**

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**TI-83 Plus Memory and Variable Management 606 **

**Resetting Archive Memory**

**When resetting archive memory on the TI-83 Plus, you can choose to delete from user data archive all variables, all applications, or both variables and applications. **

**To reset all or part of user data archive memory, follow these steps. **

**1. From the RAM ARCHIVE ALL menu, press ~ to display the ARCHIVE **

**menu. **

**2. Select one of the following: **

**1:Vars** to display the **RESET ARC VAR** menu

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**TI-83 Plus Memory and Variable Management 607 **

**2:Apps** to display the **RESET ARC APPS **menu.

**3:Both** to display the **RESET ARC BOTH **menu.

**3. Read the message below the menu. **

** To cancel the reset and return to the home screen, press . **

** To continue with the reset, select 2:Reset. A message indicating the type of archive memory cleared will be displayed on the home screen.**

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**TI-83 Plus Memory and Variable Management 608 **

**Resetting All Memory**

**When resetting all memory on the TI-83 Plus, RAM and user data archive memory is restored to factory settings. All nonsystem variables, applications, and programs are deleted. All system variables are reset to default settings. **

**Tip:** Before you reset all memory, consider restoring sufficient available memory by deleting only selected data.

**To reset all memory on the TI-83 Plus, follow these steps. **

**1. From the RAM ARCHIVE ALL menu, press ~ ~ to display the ALL menu. **

**2. Select 1:All Memory to display the RESET MEMORY menu.**

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**TI-83 Plus Memory and Variable Management 609 **

**3. Read the message below the RESET MEMORY menu. **

** To cancel the reset and return to the home screen, press . **

** To continue with the reset, select 2:Reset. The message MEM cleared is displayed on the home screen. **

**Note:** When you clear memory, the contrast sometimes changes. If the screen is faded or blank, adjust the contrast by pressing y } or .

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**TI-83 Plus Memory and Variable Management 610 **

**Archiving and UnArchiving Variables **

**Archiving and UnArchiving Variables**

**Archiving allows you to store data, programs, or other variables to the user data archive where they cannot be edited or deleted inadvertently. Archiving also allows you to free up RAM for variables that may require additional memory. **

**Archived variables cannot be edited or executed. They can only be seen and unarchived. For example, if you archive list L1, you will see that L1 exists in memory but if you select it and paste the name L1 to the home screen, you wont be able to see its contents or edit it. **

**Note:** Not all variables may be archived. Not all archived variables may be unarchived. For example, system variables including r, t, x, y, and **q** cannot be archived. Apps and Groups always exist in Flash ROM so there is no need to archive them. Groups cannot be unarchived. However, you can ungroup or delete them.

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**TI-83 Plus Memory and Variable Management 611 **

**Variable Type** **Names** **Archive?** **(yes/no)**

**UnArchive?** **(yes/no)**

**Real numbers A, B, ... , Z yes yes **

**Complex numbers A, B, ... , Z yes yes **

**Matrices A, B, C, ... , J yes yes **

**Lists L1, L2, L3, L4, L5, L6, and user-defined names **

**yes yes **

**Programs yes yes **

**Functions Y1, Y2, . . . , Y9, Y0 no not applicable **

**Parametric equations X1T and Y1T, ... , X6T and Y6T **

**no not applicable **

**Polar functions r1, r2, r3, r4, r5, r6 no not applicable **

**Sequence functions u, v, w no not applicable **

**Stat plots Plot1, Plot2, Plot3 no not applicable **

**Graph databases GDB1, GDB2,... yes yes **

**Graph pictures Pic1, Pic2, ... , Pic9, Pic0 **

**yes yes **

**Strings Str1, Str2, . . . Str9, Str0 yes yes**

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**TI-83 Plus Memory and Variable Management 612 **

**Variable Type** **Names** **Archive?** **(yes/no)**

**UnArchive?** **(yes/no)**

**Tables TblStart, Tb1, TblInput **

**no not applicable **

**Apps Applications see Note above **

**no **

**AppVars Application variables yes yes **

**Groups see Note above **

**no **

**Variables with reserved names **

**minX**, **maxX**, **RegEQ,** and others

**no not applicable **

**System variables Xmin, Xmax, and others **

**no not applicable **

**Archiving and unarchiving can be done in two ways: **

** Use the 5:Archive or 6:UnArchive commands from the MEMORY menu or CATALOG. **

** Use a Memory Management editor screen. **

**Before archiving or unarchiving variables, particularly those with a large byte size (such as large programs) use the MEMORY menu to: **

** Find the size of the variable. **

** See if there is enough free space.**

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**TI-83 Plus Memory and Variable Management 613 **

**For:** **Sizes must be such that:**

**Archive Archive free size > variable size **

**UnArchive RAM free size > variable size **

**Note:** If there is not enough space, unarchive or delete variables as necessary. Be aware that when you unarchive a variable, not all the memory associated with that variable in user data archive will be released since the system keeps track of where the variable has been and where it is now in RAM.

**Even if there appears to be enough free space, you may see a Garbage Collection message when you attempt to archive a variable. Depending on the usability of empty blocks in the user data archive, you may need to unarchive existing variables to create more free space. **

**To archive or unarchive a list variable (L1) using the Archive/UnArchive options from the MEMORY menu: **

**1. Press y L to display the MEMORY menu. **

**2. Select 5:Archive or 6:UnArchive to place the command in the edit screen.**

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**TI-83 Plus Memory and Variable Management 614 **

**3. Press y d to place the L1 variable in the edit screen. **

**4. Press to complete the archive process. **

**Note:** An asterisk will be displayed to the left of the Archived variable name to indicate it is archived.

**To archive or unarchive a list variable (L1) using a Memory Management editor: **

**1. Press y L to display the MEMORY menu. **

**2. Select 2:Mem Mgmt/Del... to display the MEMORY MANAGEMENT/DELETE **

**menu.**

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**TI-83 Plus Memory and Variable Management 615 **

**3. Select 4:List... to display the LIST menu. **

**4. Press to archive L1. An asterisk will appear to the left of L1 to indicate it is an archived variable. To unarchive a variable in this screen, put the cursor next to the archived variable and press . The asterisk will disappear. **

**5. Press y 5 to leave the LIST menu. **

**Note:** You can access an archived variable for the purpose of linking, deleting, or unarchiving it, but you cannot edit it.

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**TI-83 Plus Memory and Variable Management 616 **

**Grouping and Ungrouping Variables **

**Grouping Variables**

**Grouping allows you to make a copy of two or more variables residing in RAM and then store them as a group in user data archive. The variables in RAM are not erased. The variables must exist in RAM before they can be grouped. In other words, archived data cannot be included in a group. **

**To create a group of variables: **

**1. Press y L to display the MEMORY menu. **

**2. Select 8:Group... to display GROUP UNGROUP menu.**

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**TI-83 Plus Memory and Variable Management 617 **

**3. Press to display the GROUP menu. **

**4. Enter a name for the new group and press . **

**Note:** A group name can be one to eight characters long. The first character must be a letter from A to Z or q. The second through eighth characters can be letters, numbers, or q.

**5. Select the type of data you want to group. You can select 1:All+ which shows all variables of all types available and selected. You can also select 1:All- which shows all variables of all types available but not selected. A screen is displayed listing each variable of the type you selected. **

**For example, suppose some variables have been created in RAM, and selecting 1:All- displays the following screen.**

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**TI-83 Plus Memory and Variable Management 618 **

**6. Press } and to move the selection cursor ( 4) next to the first item you want to copy into a group, and then press . A small square will remain to the left of all variables selected for grouping. **

**Repeat the selection process until all variables for the new group are selected and then press ~ to display the DONE menu. **

**7. Press to complete the grouping process.**

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**TI-83 Plus Memory and Variable Management 619 **

**Note:** You can only group variables in RAM. You cannot group some system variables, such as the last-answer variable **Ans** and the statistical variable **RegEQ**.

**Ungrouping Variables**

**Ungrouping allows you to make a copy of variables in a group stored in user data archive and place them ungrouped in RAM. **

**DuplicateName Menu**

**During the ungrouping action, if a duplicate variable name is detected in RAM, the DUPLICATE NAME menu is displayed. **

**DuplicateName**

**1:Rename** Prompts to rename receiving variable. **2:Overwrite** Overwrites data in receiving duplicate variable. **3:Overwrite All** Overwrites data in all receiving duplicate variables. **4:Omit** Skips transmission of sending variable. **5:Quit** Stops transmission at duplicate variable.

**Notes about Menu Items: **

** When you select 1:Rename, the Name= prompt is displayed, and alpha-lock is on. Enter a new variable name, and then press . Ungrouping resumes.**

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**TI-83 Plus Memory and Variable Management 620 **

** When you select 2:Overwrite, the unit overwrites the data of the duplicate variable name found in RAM. Ungrouping resumes. **

** When you select 3: Overwrite All, the unit overwrites the data of all duplicate variable names found in RAM. Ungrouping resumes. **

** When you select 4:Omit, the unit does not ungroup the variable in conflict with the duplicated variable name found in RAM. Ungrouping resumes with the next item. **

** When you select 5:Quit, ungrouping stops, and no further changes are made. **

**To ungroup a group of variables: **

**1. Press y L to display the MEMORY menu. **

**2. Select 8:Group... to display the GROUP UNGROUP menu. **

**3. Press ~ to display the UNGROUP menu.**

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**TI-83 Plus Memory and Variable Management 621 **

**4. Press } and to move the selection cursor ( 4) next to the group variable you want to ungroup, and then press . **

**The ungroup action is completed. **

**Note:** Ungrouping does not remove the group from user data archive. You must delete the group in user data archive to remove it.

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**TI-83 Plus Memory and Variable Management 622 **

**Garbage Collection **

**Garbage Collection Message**

**If you use the user data archive extensively, you may see a Garbage Collect? message. This occurs if you try to archive a variable when there is not enough free contiguous archive memory. The TI-83 Plus will attempt to rearrange the archived variables to make additional room. **

**Responding to the Garbage Collection Message**

** To cancel, select 1:No. **

** If you choose 1:No, the message ERR:ARCHIVE FULL will be displayed. **

** To continue archiving, select 2:Yes. **

**If you select 2:Yes, the process message Garbage Collecting... or Defragmenting... will be displayed. **

**Note:** The process message **Defragmenting...** is displayed whenever an application marked for deletion is encountered.

**Garbage collection may take up to 20 minutes, depending on how much of archive memory has been used to store variables.**

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**TI-83 Plus Memory and Variable Management 623 **

**After garbage collection, depending on how much additional space is freed, the variable may or may not be archived. If not, you can unarchive some variables and try again. **

**Why Not Perform Garbage Collection Automatically Without a** **Message?**

**The message: **

** Lets you know an archive will take longer than usual. It also alerts you that the archive will fail if there is not enough memory. **

** Can alert you when a program is caught in a loop that repetitively fills the user data archive. Cancel the archive and determine the reason. **

**Why Is Garbage Collection Necessary?**

**The user data archive is divided into sectors. When you first begin archiving, variables are stored consecutively in sector 1. This continues to the end of the sector. **

**An archived variable is stored in a continuous block within a single sector. Unlike an application stored in user data archive, an archived variable cannot cross a sector boundary. If there is not enough space left in the sector, the next variable is stored at the beginning of the next sector. Typically, this leaves an empty block at the end of the previous sector.**

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**TI-83 Plus Memory and Variable Management 624 **

**Each variable that you archive is stored in the first empty block large enough to hold it. **

**This process continues to the end of the last sector. Depending on the size of individual variables, the empty blocks may account for a significant amount of space. Garbage collection occurs when the variable you are archiving is larger than any empty block. **

**Sector 1 **

**Sector 2 **

**Sector 3 **

**variable A **

**variable B **

**variable C **

**Empty block **

**variable D **

**Depending on its size, variable D is stored in one of these locations.**

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**TI-83 Plus Memory and Variable Management 625 **

**How Unarchiving a Variable Affects the Process**

**When you unarchive a variable, it is copied to RAM but it is not actually deleted from user data archive memory. **

**Unarchived variables are marked for deletion, meaning they will be deleted during the next garbage collection. **

**Sector 1 **

**Sector 2 **

**Sector 3 **

**variable A **

**variable D **

**After you unarchive variables B and C, they continue to take up space.**

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**TI-83 Plus Memory and Variable Management 626 **

**If the MEMORY Screen Shows Enough Free Space**

**Even if the MEMORY screen shows enough free space to archive a variable or store an application, you may still get a Garbage Collect? message or an ERR: ARCHIVE FULL message. **

**When you unarchive a variable, the Archive free amount increases immediately, but the space is not actually available until after the next garbage collection. **

**If the Archive free amount shows enough available space for your variable, there probably will be enough space to archive it after garbage collection (depending on the usability of any empty blocks). **

**The Garbage Collection Process**

**The garbage collection process: **

** Deletes unarchived variables from the user data archive. **

** Rearranges the remaining variables into consecutive blocks. **

**Note:** Power loss during garbage collection may cause all memory (RAM and Archive) to be deleted.

**Sector 1 **

**Sector 2 **

**variable A **

**variable D**

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**TI-83 Plus Memory and Variable Management 627 **

**Using the GarbageCollect Command**

**You can reduce the number of automatic garbage collections by periodically optimizing memory. This is done by using the GarbageCollect command. **

**To use the GarbageCollect command, follow these steps. **

**1. Press y CATALOG to display the CATALOG. **

**2. Press or } to scroll the CATALOG until the selection cursor points to the GarbageCollect command. **

**3. Press to paste the command to the current screen. **

**4. Press to display the Garbage Collect? message. **

**5. Select 2:Yes to begin garbage collection.**

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**TI-83 Plus Memory and Variable Management 628 **

**ERR:ARCHIVE FULL Message **

**Even if the MEMORY screen shows enough free space to archive a variable or store an application, you may still get an ERR: ARCHIVE FULL message. **

**An ERR:ARCHIVE FULL message may be displayed: **

** When there is insufficient space to archive a variable within a continuous block and within a single sector. **

** When there is insufficient space to store an application within a continuous block of memory. **

**When the message is displayed, it will indicate the largest single space of memory available for storing a variable and an application. **

**To resolve the problem, use the GarbageCollect command to optimize memory. If memory is still insufficient, you must delete variables or applications to increase space.**

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**TI-83 Plus Communication Link 629 **

**Chapter 19: Communication Link **

**Getting Started: Sending Variables **

**Getting Started is a fast-paced introduction. Read the chapter for details.**

**Create and store a variable and a matrix, and then transfer them to another** **TI-83 Plus.**

**1. On the home screen of the sending unit, press 5 5 Q. Press to store 5.5 to Q. **

**2. Press y H y H 1 2 y I y H 3 4 y I y I y > 1. Press to store the matrix to [A]. **

**3. On the sending unit, press y L to display the MEMORY menu.**

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**TI-83 Plus Communication Link 630 **

**4. On the sending unit, press 2 to select 2:Mem Mgmt/Del. The MEMORY MANAGEMENT menu is displayed. **

**5. On the sending unit, press 5 to select 5:Matrix. The MATRIX editor screen is displayed. **

**6. On the sending unit, press to archive [A]. An asterisk (*) will appear, signifying that [A] is now archived. **

**7. Connect the calculators with the link cable. Push both ends in firmly. **

**8. On the receiving unit, press y 8 ~ to display the RECEIVE menu. Press 1 to select 1:Receive. The message Waiting... is displayed and the busy indicator is on. **

**9. On the sending unit, press y 8 to display the SEND menu. **

**10.Press 2 to select 2:AllN. The AllN SELECT screen is displayed.**

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**TI-83 Plus Communication Link 631 **

**11.Press until the selection cursor ( 4 ) is next to [A] MATRX. Press . **

**12.Press until the selection cursor is next to Q REAL. Press . A square dot next to [A] and Q indicates that each is selected to send. **

**13.On the sending unit, press ~ to display the TRANSMIT menu. **

**14.On the sending unit, press 1 to select 1:Transmit and begin transmission. The receiving unit displays the message Receiving....When the items are transmitted, both units display the name and type of each transmitted variable.**

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**TI-83 Plus Communication Link 632 **

**TI-83 Plus Silver Edition LINK **

**This chapter describes how to communicate with compatible TI units. A unit-to-unit link cable is included with the TI-83 Plus Silver Edition for this purpose. **

**The TI-83 Plus Silver Edition has a port to connect and communicate with: **

** Another TI-83 Plus Silver Edition **

** A TI-83 Plus **

** A TI-83 **

** A TI-82 **

** A TI-73 **

** A CBL 2/CBL, or a CBR **

**With the TI Connect or TI-GRAPH LINK software and a TI-GRAPH LINK cable, you can link the TI-83 Plus Silver Edition to a personal computer.**

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**TI-83 Plus Communication Link 633 **

**Connecting Two Calculators with a Unit-to-Unit Cable**

**The TI-83 Plus link port is located at the center of the bottom edge of the calculator. **

**1. Firmly insert either end of the unit-to-unit cable into the port. **

**2. Insert the other end of the cable into the other calculators port. **

**Linking to the CBL/CBR System**

**The CBL 2/CBL and the CBR are optional accessories that also connect to a TI-83 Plus with the unit-to-unit link cable. With a CBL 2/CBL or CBR and a TI-83 Plus, you can collect and analyze real-world data. The software that enables this communication is built into the TI-83 Plus. (Chapter 14). **

**Linking to a Computer**

**TI-GRAPH LINK** is an accessory that links a TI-83 Plus to enable communication with a computer. A Macintosh-compatible **TI-GRAPH LINK** is available separately.

**You can access TI-GRAPH LINK guidebooks through education.ti.com/guides.**

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**TI-83 Plus Communication Link 634 **

**Selecting Items to Send **

**LINK SEND Menu**

**To display the LINK SEND menu, press y 8. **

**SEND** ** RECEIVE**

**1:All+...** Displays all items as selected, including RAM and Flash applications.

**2:AllN...** Displays all items as deselected. **3:Prgm...** Displays all program names. **4:List...** Displays all list names. **5:Lists to TI82...** Displays list names **L1** through **L6**. **6:GDB...** Displays all graph databases. **7:Pic...** Displays all picture data types. **8:Matrix...** Displays all matrix data types. **9:Real...** Displays all real variables. **0:Complex...** Displays all complex variables. **A:Y-Vars...** Displays all **Y=** variables. **B:String...** Displays all string variables. **C:Apps...** Displays all software applications. **D:AppVars...** Displays all software application variables. **E:Group...** Displays all grouped variables. **F:SendId** Sends the Calculator ID number immediately. (You do not

**need to select SEND.)**

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**TI-83 Plus Communication Link 635 **

**SEND** ** RECEIVE**

**G:SendOS** Sends operating system updates to another TI-83 Plus Silver Edition or TI-83 Plus.

**H:Back Up...** Selects all RAM and mode settings (no Flash applications or archived items) for backup to another TI-83 Plus Silver Edition or to a TI-83 Plus.

**When you select an item on the LINK SEND menu, the corresponding SELECT screen is displayed. Note: Each SELECT screen, except All+, is initially displayed with nothing pre- selected. All+ is displayed with everything pre-selected. **

**To select items to send: **

**1. Press y 8 on the sending unit to display the LINK SEND menu. **

**2. Select the menu item that describes the data type to send. The corresponding SELECT screen is displayed. **

**3. Press } and to move the selection cursor ( 4 ) to an item you want to select or deselect.**

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**TI-83 Plus Communication Link 636 **

**4. Press to select or deselect the item. Selected names are marked with a 0. **

**Note:** An asterisk (*****) to the left of an item indicates the item is archived (Chapter 18).

**5. Repeat steps 3 and 4 to select or deselect additional items. **

**Sending the Selected Items**

**After you have selected items to send on the sending unit and set the receiving unit to receive, follow these steps to transmit the items. To set the receiving unit, see Receiving Items. **

**1. Press ~ on the sending unit to display the TRANSMIT menu. **

**2. Confirm that Waiting... is displayed on the receiving unit, which indicates it is set to receive.**

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**TI-83 Plus Communication Link 637 **

**3. Press to select 1:Transmit. The name and type of each item are displayed line-by-line on the sending unit as the item is queued for transmission, and then on the receiving unit as each item is accepted. **

**Note:** Items sent from the RAM of the sending unit are transmitted to the RAM of the receiving unit. Items sent from user data archive of the sending unit are transmitted to user data archive of the receiving unit.

**After all selected items have been transmitted, the message Done is displayed on both calculators. Press } and to scroll through the names. **

**Stopping a Transmission**

**To stop a link transmission, press . The Error in Xmit menu is displayed on both units. To leave the error menu, select 1:Quit.**

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**TI-83 Plus Communication Link 638 **

**Sending to a TI-83 Plus Silver Edition or TI-83 Plus**

**You can transfer variables (all types), programs, and Flash applications to another TI-83 Plus Silver Edition or TI-83 Plus. You can also backup the RAM memory of one unit to another. **

**Note: **Keep in mind that the TI.83 Plus has less Flash memory than the TI-83 Plus Silver Edition.

** Variables stored in RAM on the sending TI-83 Plus Silver Edition will be sent to the RAM of the receiving TI-83 Plus Silver Edition or TI-83 Plus. **

** Variables and applications stored in the user data archive of the sending TI-83 Plus Silver Edition will be sent to the user data archive of the receiving TI-83 Plus Silver Edition or TI-83 Plus. **

**After sending or receiving data, you can repeat the same transmission to additional TI-83 Plus Silver Edition or TI-83 Plus unitsfrom either the sending unit or the receiving unitwithout having to reselect data to send. The current items remain selected. However, you cannot repeat transmission if you selected All+ or All..**

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**TI-83 Plus Communication Link 639 **

**To send data to an additional TI-83 Plus Silver Edition or a TI-83 Plus: **

**1. Use a unit-to-unit cable to link two units together. **

**2. On the sending unit press y 8 and select a data type and items to SEND. **

**3. Press ~ on the sending unit to display the TRANSMIT menu. **

**4. On the other unit, press y 8 ~ to display the RECEIVE menu. **

**5. Press on the receiving unit. **

**6. Press on the sending unit. A copy of the selected item(s) is sent to the receiving unit. **

**7. Disconnect the link cable only from the receiving unit and connect it to another unit. **

**8. Press y 8 on the sending unit. **

**9. Select only the data type. For example, if the unit just sent a list, select 4:LIST. **

**Note:** The item(s) you want to send are pre-selected from the last transmission. Do not select or deselect any items. If you select or deselect

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**TI-83 Plus Communication Link 640 **

**an item, all selections or deselections from the last transmission are cleared. **

**10.Press ~ on the sending unit to display the TRANSMIT menu. **

**11.On the new receiving unit, press y 8 ~ to display the RECEIVE **

**menu. **

**12.Press on the receiving unit. **

**13.Press on the sending unit. A copy of the selected item(s) is sent to the receiving unit. **

**14.Repeat steps 7 through 13 until the items are sent to all additional units. **

**Sending to a TI-83**

**You can send all variables from a TI-83 Plus to a TI-83 except Flash applications, application variables, grouped variables, new variable types, or programs with new features in them (such as Archive, UnArchive, Asm(, AsmComp, and AsmPrgm). **

**If archived variables on the TI-83 Plus are variable types recognized and used on the TI-83, you can send these variables to the TI-83. They will be automatically sent to the RAM of the TI-83 during the transfer process.**

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**TI-83 Plus Communication Link 641 **

**Note:** You cannot perform a RAM memory backup from a TI-83 Plus to a TI-83 or from a TI-83 to a TI-83 Plus.

**To send data to a TI-83: **

**1. Use a unit-to-unit cable to link the two units together. **

**2. Set the TI-83 to receive. **

**3. Press y 8 on the sending TI-83 Plus to display the LINK SEND **

**menu. **

**4. Select the menu of the items you want to transmit. **

**5. Press ~ on the sending TI-83 Plus to display the LINK TRANSMIT menu. **

**6. Confirm that the receiving unit is set to receive. **

**7. Press on the sending TI-83 Plus to select 1:Transmit and begin transmitting. **

**Sending Lists to a TI-82**

**The only data type you can transmit from a TI-83 Plus to a TI-82 is real list data stored in L1 through L6 (with up to 99 elements for each list). If dimension is greater than 99 for a TI-83 Plus list that is selected to be sent, the receiving TI-82 will truncate the list at the ninety-ninth element during transmission.**

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**TI-83 Plus Communication Link 642 **

**Note:** You cannot perform a memory backup from a TI-83 Plus to a TI-82 or from a TI-82 to a TI-83 Plus.

**To send lists to a TI-82: **

**1. Use a unit-to-unit cable to link the two units together. **

**2. Set the TI-82 to receive. **

**3. Press y 8 5 on the sending TI-83 Plus to select 5:Lists to TI82. The SELECT screen is displayed. **

**4. Select each list to transmit. **

**5. Press ~ to display the LINK TRANSMIT menu. **

**6. Confirm that the receiving unit is set to receive. **

**7. Press to select 1:Transmit and begin transmitting. **

**Sending to a TI-73**

**You can send real numbers, pics, real lists L1 through L6, and named lists from a TI-73 to a TI-83 Plus or from a TI-83 Plus to a TI-73. **

**Since the Theta symbol (q) is not recognized by the TI-73, you cannot include this symbol in any list names sent to the TI-73.**

Page 646

**TI-83 Plus Communication Link 643 **

**Note:** You cannot perform a RAM memory backup from a TI-83 Plus to a TI-73 or from a to a TI-73 to a TI-83 Plus.

**To transmit data to a TI-73: **

**1. Use a unit-to-unit cable to link two units together. **

**2. Set the TI-73 to receive. **

**3. Press y 8 2 on the sending TI-83 Plus to select 2:All-.... The SELECT screen is displayed. **

**4. Select items you want to send. **

**5. Press ~ on the sending TI-83 Plus to display the LINK TRANSMIT menu. **

**6. Confirm that the receiving unit is set to receive. **

**7. Press on the sending TI-83 Plus to select 1:Transmit and begin transmitting.**

Page 647

**TI-83 Plus Communication Link 644 **

**Receiving Items **

**LINK RECEIVE Menu**

**To display the LINK RECEIVE menu, press y 8 ~. **

**SEND** **RECEIVE**

**1:Receive** Sets unit to receive data transmission.

**Receiving Unit**

**When you select 1:Receive from the LINK RECEIVE menu on the receiving unit, the message Waiting... and the busy indicator are displayed. The receiving unit is ready to receive transmitted items. To exit the receive mode without receiving items, press , and then select 1:Quit from the Error in Xmit menu. **

**When transmission is complete, the unit exits the receive mode. You can select 1:Receive again to receive more items. The receiving unit then displays a list of items received. Press y 5 to exit the receive mode. **

**DuplicateName Menu**

**During transmission, if a variable name is duplicated, the DuplicateName **

**menu is displayed on the receiving unit.**

Page 648

**TI-83 Plus Communication Link 645 **

**DuplicateName**

**1:Rename** Prompts to rename receiving variable. **2:Overwrite** Overwrites data in receiving variable. **3:Omit** Skips transmission of sending variable. **4:Quit** Stops transmission at duplicate variable.

**When you select 1:Rename, the Name= prompt is displayed, and alpha- lock is on. Enter a new variable name, and then press . Transmission resumes. **

**When you select 2:Overwrite, the sending units data overwrites the existing data stored on the receiving unit. Transmission resumes. **

**When you select 3:Omit, the sending unit does not send the data in the duplicated variable name. Transmission resumes with the next item. **

**When you select 4:Quit, transmission stops, and the receiving unit exits receive mode. **

**Receiving from a TI-83 Plus Silver Edition or TI-83 Plus**

**The TI-83 Plus Silver Edition and the TI-83 Plus are totally compatible. Keep in mind, however, that the TI-83 Plus has less Flash memory than a TI-83 Plus Silver Edition.**

Page 649

**TI-83 Plus Communication Link 646 **

**Receiving from a TI-83**

**You can transfer all variables and programs from a TI-83 to a TI-83 Plus if they fit in the RAM of the TI-83 Plus. The RAM of the TI-83 Plus is slightly less than the RAM of the TI-83. **

**Receiving from a TI-82 Resolved Differences**

**Generally, you can transmit items to a TI-83 Plus from a TI-82, but differences between the two products may affect some transmitted data. This table shows differences for which the software built into the TI-83 Plus automatically adjusts when a TI-83 Plus receives TI-82 data. **

**TI.82** **TI-83 Plus**

**nMin** **PlotStart** **nStart** **nMin** **Un** **u** **Vn** **v** **UnStart** **u(nMin)** **VnStart** **v(nMin)** **TblMin** **TblStart**

**For example, if you transmit a program that contains nStart on a command line from a TI-82 to a TI-83 Plus, you will see that nMin has automatically replaced nStart on the command line of the TI-83 Plus.**

Page 650

**TI-83 Plus Communication Link 647 **

**Note:** You can transfer all real variables, pics, and programs from a TI-82 to a TI-83 Plus if they fit in the RAM of the TI-83 Plus. The RAM of the TI-83 Plus is slightly less than the RAM of the TI-82.

**Receiving from a TI-82 Unresolved Differences**

**The software built into the TI-83 Plus cannot resolve some differences between the TI-82 and TI-83 Plus. These differences are described below. **

**You must edit the transmitted data on the receiving TI-83 Plus to account for these differences. If you do not edit these differences, the TI-83 Plus will misinterpret the data. **

** The TI-83 Plus reinterprets TI-82 prefix functions to include open parentheses, which may add extraneous parentheses to transmitted expressions. **

**For example, if you transmit sin X+5 from a TI-82 to a TI-83 Plus, the TI-83 Plus reinterprets it as sin(X+5. Without a closing parenthesis after X, the TI-83 Plus interprets this as sin(X+5), not the sum of 5 and sin(X). **

** If a TI-82 transmits an instruction that the TI-83 Plus cannot translate, the ERR:INVALID menu displays when the TI-83 Plus attempts to execute the instruction.**

Page 651

**TI-83 Plus Communication Link 648 **

**For example, on the TI-82, the character group Un-1 is pasted to the cursor location when you press y [UnN1]. The TI-83 Plus cannot directly translate Un-1 to the TI-83 Plus syntax u(nN1), so the ERR:INVALID menu is displayed. **

**Note:** TI-83 Plus implied multiplication rules differ from those of the TI-82. For example, the TI-83 Plus evaluates **12X** as **(12)X**, while the TI-82 evaluates **12X** as **1(2X)** (Chapter 2).

**Receiving from a TI-73**

**The TI-83 Plus can receive real numbers, pics, real lists L1 through L6, and named lists from a TI-73. **

**Categorical lists (lists containing alpha characters as list elements) cannot be sent from a TI-73 to a TI-83 Plus. **

**To transmit data to a TI-83 Plus from a TI-73: **

**1. Set the TI-83 Plus to receive. **

**2. Press on the sending TI-73 to display the APPLICATIONS menu. **

**3. Press on the sending TI-73 to select 1:Link and display the LINK **

**SEND** menu.

**4. Choose 0:Vars to TI83. and then select the items you want to send.**

Page 652

**TI-83 Plus Communication Link 649 **

**5. Press ~ on the sending TI-73 to display the LINK TRANSMIT menu. **

**6. Confirm that the receiving unit is set to receive. **

**7. Press on the sending TI-73 to select 1:Transmit and begin transmitting.**

Page 653

**TI-83 Plus Communication Link 650 **

**Backing Up RAM Memory **

**Warning:** **H:Back Up** overwrites the RAM memory and mode settings in the receiving unit. All information in the RAM memory of the receiving unit is lost.

**Note: **Archived items on the receiving unit are not overwritten.

**You can backup the contents of RAM memory and mode settings (no Flash applications or archived items) to another TI-83 Plus Silver Edition. You can also backup RAM memory and mode settings to a TI-83 Plus. **

**To perform a RAM memory backup: **

**1. Use a unit-to-unit cable to link two TI-83 Plus Silver Edition units, or a TI-83 Plus Silver Edition and a TI-83 Plus together. **

**2. On the sending unit press y 8 and select H:Back Up. The MEMORYBACKUP screen displays. **

**3. On the receiving unit, press y 8 ~ to display the RECEIVE menu. **

**4. Press on the receiving unit.**

Page 654

**TI-83 Plus Communication Link 651 **

**5. Press on the sending unit. A WARNING Backup message displays on the receiving unit. **

**6. Press on the receiving unit to continue the backup. or Press 2:Quit on the receiving unit to cancel the backup and return to the LINK SEND menu **

**Note:** If a transmission error is returned during a backup, the receiving unit is reset.

**Memory Backup Complete**

**When the backup is complete, both the sending calculator and receiving calculator display a confirmation screen.**

Page 655

**TI-83 Plus Communication Link 652 **

**Error Conditions A transmission error occurs after one or two seconds if: **

** A cable is not attached to the sending unit. **

** A cable is not attached to the receiving unit. Note: If the cable is attached, push it in firmly and try again. **

** The receiving unit is not set to receive transmission. **

** You attempt a backup between a TI-73, a TI-82, or a TI-83 and a TI-83 Plus. **

** You attempt a data transfer from a TI-83 Plus to a TI-83, TI-82, or TI-73 with variables or features not recognized by the TI-83, TI-82, or TI-73. **

** New variable types and features not recognized by the TI-83, TI-82, or TI-73 include applications, application variables, grouped variables, new variable types, or programs with new features in them such as Archive, UnArchive, SendID, SendOS, Asm(, AsmComp(, and AsmPrgm. **

** You attempt a data transfer from a TI-83 Plus to a TI-82 with data other than real lists L1 through L6 or without using menu item 5:Lists to TI82.**

Page 656

**TI-83 Plus Communication Link 653 **

** You attempt a data transfer from a TI-83 Plus to a TI-73 with data other than real numbers, pics, real lists L1 through L6 or named lists with q as part of the name. **

**Although a transmission error does not occur, these two conditions may prevent successful transmission. **

** You try to use Get( with a calculator instead of a CBL 2/CBL or CBR. **

** You try to use GetCalc( with a TI-83 instead of a TI-83 Plus Silver Edition or TI-83 Plus. **

**Insufficient Memory in Receiving Unit**

**During transmission, if the receiving unit does not have sufficient memory to receive an item, the Memory Full menu is displayed on the receiving unit. **

** To skip this item for the current transmission, select 1:Omit. Transmission resumes with the next item. **

** To cancel the transmission and exit receive mode, select 2:Quit.**

Page 657

**TI-83 Plus Tables and Reference Information 654 **

**Appendix A: Tables and Reference Information **

**Table of Functions and Instructions **

**Functions return a value, list, or matrix. You can use functions in an expression. Instructions initiate an action. Some functions and instructions have arguments. Optional arguments and accompanying commas are enclosed in brackets ( [ ] ). For details about an item, including argument descriptions and restrictions, turn to the page listed on the right side of the table. **

**From the CATALOG, you can paste any function or instruction to the home screen or to a command line in the program editor. However, some functions and instructions are not valid on the home screen. The items in this table appear in the same order as they appear in the CATALOG. **

** indicates either keystrokes that are valid in the program editor only or ones that paste certain instructions when you are in the program editor. Some keystrokes display menus that are available only in the program editor. Others paste mode, format, or table-set instructions only when you are in the program editor.**

Page 658

**TI-83 Plus Tables and Reference Information 655 **

**Function or Instruction/** **Arguments** **Result**

**Key or Keys/** **Menu or Screen/Item**

**abs(***value***)** Returns the absolute value of a real number, expression, list, or matrix.

** NUM 1:abs( **

**abs(***complex value***)** Returns the magnitude of a complex number or list.

** CPX 5:abs( **

*valueA* **and** *valueB* Returns 1 if both *valueA* and *valueB* are 0*.* *valueA* and *valueB* can be real numbers, expressions, or lists.

**y : LOGIC 1:and **

**angle(***value***)** Returns the polar angle of a complex number or list of complex numbers.

** CPX 4:angle( **

**ANOVA(***list1***,***list2* [**,***list3***,***...***,***list20*]**)**

**Performs a one-way analysis of variance for comparing the means of two to 20 populations. **

** TESTS F:ANOVA( **

**Ans** Returns the last answer. y Z **Archive** Moves the specified variables from

**RAM to the user data archive memory. **

**y L 5:Archive **

**Asm(***assemblyprgmname***)** Executes an assembly language program.

**y N Asm( **

**AsmComp(***prgmASM1,* *prgmASM2***)**

**Compiles an assembly language program written in ASCII and stores the hex version. **

**y N AsmComp( **

**AsmPrgm** Must be used as the first line of an assembly language program.

**y N AsmPrgm**

Page 659

**TI-83 Plus Tables and Reference Information 656 **

**Function or Instruction/** **Arguments** **Result**

**Key or Keys/** **Menu or Screen/Item**

**augment(***matrixA***,** *matrixB***)**

**Returns a matrix, which is matrixB appended to matrixA as new columns. **

**y > MATH 7:augment( **

**augment(***listA***,***listB***)** Returns a list, which is *listB* concatenated to the end of *listA*.

**y 9 OPS 9:augment( **

**AxesOff** Turns off the graph axes. y . **AxesOff**

**AxesOn** Turns on the graph axes. y . **AxesOn**

**a+b i** Sets the mode to rectangular complex number mode (a+b

*i*).

** z a+bi **

**bal(***npmt*[**,***roundvalue*]**)** Computes the balance at *npmt *for an amortization schedule using stored values for **PV**, , and **PMT** and rounds the computation to *roundvalue.*

** 1:Finance CALC 9:bal( **

**binomcdf(***numtria***)** Computes a cumulative probability at *x* for the discrete binomial distribution with the specified *numtrials* and probability *p* of success on each trial.

**y = DISTR A:binomcdf( **

**binompdf(***numtrials***,***p*[**,***x*]**)** Computes a probability at *x* for the discrete binomial distribution with the specified *numtrials* and probability *p* of success on each trial.

**y = DISTR 0:binompdf(**

Page 660

**TI-83 Plus Tables and Reference Information 657 **

**Function or Instruction/** **Arguments** **Result**

**Key or Keys/** **Menu or Screen/Item**

**c2cdf(***lowerbound***,** *upperbound***,***df***)**

**Computes the c2 distribution probability between lowerbound and upperbound for the specified degrees of freedom df. **

**y = DISTR 7:c2cdf( **

**c2pdf(***x***,***df***)** Computes the probability density function (pdf) for the c2 distribution at a specified *x* value for the specified degrees of freedom *df*.

**y = DISTR 6:c2pdf( **

**c2.Test(***observedmatrix***,** *expectedmatrix* [**,***drawflag*]**)**

**Performs a chi-square test. drawflag=1 draws results; drawflag=0 calculates results. **

** TESTS C:c2-Test( **

**Circle(***X***,***Y***,***radius***)** Draws a circle with center (*X*,*Y*) and *radius*.

**y < DRAW 9:Circle( **

**Clear Entries** Clears the contents of the Last Entry storage area.

**y L MEMORY 3:Clear Entries **

**ClrAllLists** Sets to **0** the dimension of all lists in memory.

**y L MEMORY 4:ClrAllLists **

**ClrDraw** Clears all drawn elements from a graph or drawing.

**y < DRAW 1:ClrDraw **

**ClrHome** Clears the home screen. **I/O** **8:ClrHome**

Page 661

**TI-83 Plus Tables and Reference Information 658 **

**Function or Instruction/** **Arguments** **Result**

**Key or Keys/** **Menu or Screen/Item**

**ClrList** *listname1* [**,***listname2***, ...,** *listname n*]

**Sets to 0 the dimension of one or more listnames. **

** EDIT 4:ClrList **

**ClrTable** Clears all values from the table. **I/O** **9:ClrTable**

**conj(***value***)** Returns the complex conjugate of a complex number or list of complex numbers.

** CPX 1:conj( **

**Connected** Sets connected plotting mode; resets all **Y=** editor graph-style settings to .

** z Connected **

**CoordOff** Turns off cursor coordinate value display.

** y . CoordOff **

**CoordOn** Turns on cursor coordinate value display.

** y . CoordOn **

**cos(***value***)** Returns cosine of a real number, expression, or list.

**cosL1(***value***)** Returns arccosine of a real number, expression, or list.

**y @ **

**cosh(***value***)** Returns hyperbolic cosine of a real number, expression, or list.

**y N cosh( **

**coshL1(***value***)** Returns hyperbolic arccosine of a real number, expression, or list.

**y N coshL1( **

**CubicReg** [*Xlistname***,** *Ylistname***,***freqlist***,** *regequ*]

**Fits a cubic regression model to Xlistname and Ylistname with frequency freqlist, and stores the regression equation to regequ. **

** CALC 6:CubicReg**

Page 662

**TI-83 Plus Tables and Reference Information 659 **

**Function or Instruction/** **Arguments** **Result**

**Key or Keys/** **Menu or Screen/Item**

**c*msum(***list***)** Returns a list of the cumulative sums of the elements in *list*, starting with the first element.

**y 9 OPS 6:c*msum( **

**c*msum(***matrix***)** Returns a matrix of the cumulative sums of *matrix* elements. Each element in the returned matrix is a cumulative sum of a *matrix* column from top to bottom.

**y > MATH 0:c*msum( **

**dbd(***date1***,***date2***)** Calculates the number of days between *date1* and *date2* using the actual-day-count method.

** 1:Finance CALC D:dbd( **

*value***4Dec** Displays a real or complex number, expression, list, or matrix in decimal format.

** MATH 2:4Dec **

**Degree** Sets degree angle mode. z **Degree**

**DelVar ***variable* Deletes from memory the contents of *variable*.

** CTL G:DelVar **

**DependAsk** Sets table to ask for dependent- variable values.

** y - Depend: Ask **

**DependAuto** Sets table to generate dependent- variable values automatically.

** y - Depend: Auto **

**det(***matrix***)** Returns determinant of *matrix*. y > **MATH** **1:det(**

Page 663

**TI-83 Plus Tables and Reference Information 660 **

**Function or Instruction/** **Arguments** **Result**

**Key or Keys/** **Menu or Screen/Item**

**DiagnosticOff** Sets diagnostics-off mode; **r**, **r2**, and **R2** are not displayed as regression model results.

**y N DiagnosticOff **

**DiagnosticOn** Sets diagnostics-on mode; **r**, **r2**, and **R2** are displayed as regression model results.

**y N DiagnosticOn **

**dim(***listname***)** Returns the dimension of *listname*. y 9 **OPS** **3:dim(**

**dim(***matrixname***)** Returns the dimension of *matrixname* as a list.

**y > MATH 3:dim( **

*length***!dim(***listname***)** Assigns a new dimension (*length*) to a new or existing *listname*.

**y 9 OPS 3:dim( **

**{***rows***,***columns***}!** **dim(***matrixname***)**

**Assigns new dimensions to a new or existing matrixname. **

**y > MATH 3:dim( **

**Disp** Displays the home screen. **I/O** **3:Disp**

**Disp **[*valueA***,***valueB***,** *valueC***,**...**,***value n*]

**Displays each value. I/O 3:Disp **

**DispGraph** Displays the graph. **I/O** **4:DispGraph**

Page 664

**TI-83 Plus Tables and Reference Information 661 **

**Function or Instruction/** **Arguments** **Result**

**Key or Keys/** **Menu or Screen/Item**

**DispTable** Displays the table. **I/O** **5:DispTable**

*value***4DMS** Displays *value* in DMS format. y ; **ANGLE** **4:4DMS**

**Dot** Sets dot plotting mode; resets all **Y=** editor graph-style settings to .

** z Dot **

**DrawF** *expression* Draws *expression* (in terms of **X**) on the graph.

**y < DRAW 6:DrawF **

**DrawInv** *expression* Draws the inverse of *expression* by plotting **X** values on the y-axis and **Y** values on the x-axis.

**y < DRAW 8:DrawInv **

**:DS<(***variable***,***value***)** **:***commandA* **:***commands*

**Decrements variable by 1; skips commandA if variable < value. **

** CTL B:DS<( **

**e^(***power***)** Returns **e** raised to *power*. y J **e^(***list***)** Returns a list of **e** raised to a *list* of

**powers. y J **

**Exponent: valueEexponent **

**Returns value times 10 to the exponent. **

**y D **

**Exponent: listEexponent **

**Returns list elements times 10 to the exponent. **

**y D **

**Exponent: matrixEexponent **

**Returns matrix elements times 10 to the exponent. **

**y D**

Page 665

**TI-83 Plus Tables and Reference Information 662 **

**Function or Instruction/** **Arguments** **Result**

**Key or Keys/** **Menu or Screen/Item**

**4Eff(***nominal rate***,** *compounding periods***)**

**Computes the effective interest rate. 1:Finance CALC C:4Eff( **

**Else** *See* **If:Then:Else** **End** Identifies end of** For(**, **If**-**Then**-**Else**,

**Repeat**, or **While** loop. **CTL** **7:End**

**Eng** Sets engineering display mode. z **Eng**

**Equ4String(Y=*** var***,Str***n***)** Converts the contents of a **Y=*** var* to a string and stores it in **Str***n*.

**y N Equ4String( **

**expr(***string***)** Converts *string* to an expression and executes it.

**y N expr( **

**ExpReg** [*Xlistname***,** *Ylistname***,***freqlist***,***regequ*]

**Fits an exponential regression model to Xlistname and Ylistname with frequency freqlist, and stores the regression equation to regequ. **

** CALC 0:ExpReg **

**ExprOff** Turns off the expression display during **TRACE**.

** y . ExprOff **

**ExprOn** Turns on the expression display during **TRACE**.

** y . ExprOn **

**cdf(***lowerbound***,** *upperbound***,** *numerator df***,** *denominator df***)**

**Computes the distribution probability between lowerbound and upperbound for the specified numerator df (degrees of freedom) and denominator df. **

**y = DISTR 9:cdf(**

Page 666

**TI-83 Plus Tables and Reference Information 663 **

**Function or Instruction/** **Arguments** **Result**

**Key or Keys/** **Menu or Screen/Item**

**Fill(***value***,***matrixname***)** Stores *value* to each element in *matrixname*.

**y > MATH 4:Fill( **

**Fill(***value***,***listname***)** Stores *value* to each element in *listname*.

**y 9 OPS 4:Fill( **

**Fix** # Sets fixed-decimal mode for # of decimal places.

** z 0123456789 (select one) **

**Float** Sets floating decimal mode. z **Float**

**fMax(***expression***,***variable***,** *lower***,***upper*[**,***tolerance*]**)**

**Returns the value of variable where the local maximum of expression occurs, between lower and upper, with specified tolerance. **

** MATH 7:fMax( **

**fMin(***expression***,***variable***,** *lower***,***upper*[**,***tolerance*]**)**

**Returns the value of variable where the local minimum of expression occurs, between lower and upper, with specified tolerance. **

** MATH 6:fMin( **

**fnInt(***expression***,***variable***,** *lower***,***upper*[**,***tolerance*]**)**

**Returns the function integral of expression with respect to variable, between lower and upper, with specified tolerance. **

** MATH 9:fnInt( **

**FnOff** [*function#***,** *function#***,...,***function n*]

**Deselects all Y= functions or specified Y= functions. **

** Y-VARS On/Off 2:FnOff**

Page 667

**TI-83 Plus Tables and Reference Information 664 **

**Function or Instruction/** **Arguments** **Result**

**Key or Keys/** **Menu or Screen/Item**

**FnOn** [*function#***,** *function#***,...,***function n*]

**Selects all Y= functions or specified Y= functions. **

** Y-VARS On/Off 1:FnOn **

**:For(***variable***,***begin***,***end* [**,***increment*]**)** **:***commands* **:End** **:***commands*

**Executes commands through End, incrementing variable from begin by increment until variable>end. **

** CTL 4:For( **

**fPart(***value***)** Returns the fractional part or parts of a real or complex number, expression, list, or matrix.

** NUM 4:fPart( **

**pdf(***x***,***numerator df***,** *denominator df***)**

**Computes the distribution probability between lowerbound and upperbound for the specified numerator df (degrees of freedom) and denominator df. **

**y = DISTR 8:pdf( **

*value***4Frac** Displays a real or complex number, expression, list, or matrix as a fraction simplified to its simplest terms.

** MATH 1:4Frac **

**Full** Sets full screen mode. z **Full**

**Func** Sets function graphing mode. z **Func**

**GarbageCollect** Displays the garbage collection menu to allow cleanup of unused archive memory.

**y N GarbageCollect**

Page 668

**TI-83 Plus Tables and Reference Information 665 **

**Function or Instruction/** **Arguments** **Result**

**Key or Keys/** **Menu or Screen/Item**

**gcd(***valueA,valueB***)** Returns the greatest common divisor of *valueA* and *valueB*, which can be real numbers or lists.

** NUM 9:gcd( **

**geometcdf(***p***,***x***)** Computes a cumulative probability at *x*, the number of the trial on which the first success occurs, for the discrete geometric distribution with the specified probability of success *p.*

**y = DISTR E:geometcdf( **

**geometpdf(***p***,***x***)** Computes a probability at *x*, the number of the trial on which the first success occurs, for the discrete geometric distribution with the specified probability of success *p.*

**y = DISTR D:geometpdf( **

**Get(***variable***)** Gets data from the CBL 2/CBL or CBR System and stores it in *variable*.

** I/O A:Get( **

**GetCalc(***variable***)** Gets contents of *variable* on another TI-83 Plus and stores it to *variable* on the receiving TI-83 Plus.

** I/O 0:GetCalc( **

**getKey** Returns the key code for the current keystroke, or **0**, if no key is pressed.

** I/O 7:getKey **

**Goto** *label* Transfers control to *label*. **CTL** **0:Goto**

**GraphStyle(***function#***,** *graphstyle#***)**

**Sets a graphstyle for function#. CTL H:GraphStyle(**

Page 669

**TI-83 Plus Tables and Reference Information 666 **

**Function or Instruction/** **Arguments** **Result**

**Key or Keys/** **Menu or Screen/Item**

**GridOff** Turns off grid format. y . **GridOff**

**GridOn** Turns on grid format. y . **GridOn**

**G-T** Sets graph-table vertical split-screen mode.

** z G-T **

**Horiz** Sets horizontal split-screen mode. z **Horiz**

**Horizontal*** y* Draws a horizontal line at *y*. y < **DRAW** **3:Horizontal**

**identity(***dimension***)** Returns the identity matrix of *dimension* rows *dimension* columns.

**y > MATH 5:identity( **

**:If ***condition* **:***commandA* **:***commands*

**If condition = 0 (false), skips commandA. **

** CTL 1:If **

**:If** *condition* **:Then** **:***commands* **:End** **:***commands*

**Executes commands from Then to End if condition = 1 (true). **

** CTL 2:Then**

Page 670

**TI-83 Plus Tables and Reference Information 667 **

**Function or Instruction/** **Arguments** **Result**

**Key or Keys/** **Menu or Screen/Item**

**:If ***condition* **:Then** **:***commands* **:Else** **:***commands* **:End** **:***commands*

**Executes commands from Then to Else if condition = 1 (true); from Else to End if condition = 0 (false). **

** CTL 3:Else **

**imag(***value***)** Returns the imaginary (nonreal) part of a complex number or list of complex numbers.

** CPX 3:imag( **

**IndpntAsk** Sets table to ask for independent- variable values.

** y - Indpnt: Ask **

**IndpntAuto** Sets table to generate independent- variable values automatically.

** y - Indpnt: Auto **

**Input** Displays graph. **I/O** **1:Input**

**Input** [*variable*] **Input** [**"***text***",***variable*]

**Prompts for value to store to variable. **

** I/O 1:Input **

**Input **[**Str***n***,***variable*] Displays **Str***n* and stores entered value to *variable*.

** I/O 1:Input **

**inString(***string***,***substring* * *[**,***start*]**)**

**Returns the character position in string of the first character of substring beginning at start. **

**y N inString(**

Page 671

**TI-83 Plus Tables and Reference Information 668 **

**Function or Instruction/** **Arguments** **Result**

**Key or Keys/** **Menu or Screen/Item**

**int(***value***)** Returns the largest integer a real or complex number, expression, list, or matrix.

** NUM 5:int( **

**GInt(***pmt1***,***pmt2* * *[**,***roundvalue*]**)**

**Computes the sum, rounded to roundvalue, of the interest amount between pmt1 and pmt2 for an amortization schedule. **

** 1:Finance CALC A:GInt( **

**invNorm(***area*[**,**m**,**s]**)** Computes the inverse cumulative normal distribution function for a given *area* under the normal distribution curve specified by m and s.

**y = DISTR 3:invNorm( **

**iPart(***value***)** Returns the integer part of a real or complex number, expression, list, or matrix.

** NUM 3:iPart( **

**irr(***CF0***,***CFList*[**,***CFFreq*]**)** Returns the interest rate at which the net present value of the cash flow is equal to zero.

** 1:Finance CALC 8:irr( **

**:IS>(***variable***,***value***)** **:***commandA* **:***commands*

**Increments variable by 1; skips commandA if variable>value. **

** CTL A:IS>( **

*listname* Identifies the next one to five characters as a user-created list name.

**y 9 OPS B:( **

**LabelOff** Turns off axes labels. y . **LabelOff**

**LabelOn** Turns on axes labels. y . **LabelOn**

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**TI-83 Plus Tables and Reference Information 669 **

**Function or Instruction/** **Arguments** **Result**

**Key or Keys/** **Menu or Screen/Item**

**Lbl** *label* Creates a *label* of one or two characters.

** CTL 9:Lbl **

**lcm(***valueA,valueB***)** Returns the least common multiple of *valueA* and *valueB*, which can be real numbers or lists.

** NUM 8:lcm( **

**length(***string***)** Returns the number of characters in *string*.

**y N length( **

**Line(***X1***,***Y1***,***X2***,***Y2***)** Draws a line from (*X1*,*Y1*) to (*X2*,*Y2*). y < **DRAW** **2:Line(**

**Line(***X1***,***Y1***,***X2***,***Y2***,0)** Erases a line from (*X1*,*Y1*) to (*X2*,*Y2*).

**y < DRAW 2:Line( **

**LinReg(a+bx)** [*Xlistname***,** *Ylistname***,***freqlist***,** *regequ*]

**Fits a linear regression model to Xlistname and Ylistname with frequency freqlist, and stores the regression equation to regequ. **

** CALC 8:LinReg(a+bx) **

**LinReg(ax+b)** [*Xlistname***,** *Ylistname***,***freqlist***,** *regequ*]

**Fits a linear regression model to Xlistname and Ylistname with frequency freqlist, and stores the regression equation to regequ. **

** CALC 4:LinReg(ax+b) **

**LinRegTTest*** *[*Xlistname***,** *Ylistname***,***freqlist***,** *alternative***,***regequ*]

**Performs a linear regression and a t-test. alternative=L1 is <; alternative=0 is ; alternative=1 is >. **

** TESTS E:LinRegTTest **

**@List(***list***)** Returns a list containing the differences between consecutive elements in *list*.

**y 9 OPS 7:@List(**

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**TI-83 Plus Tables and Reference Information 670 **

**Function or Instruction/** **Arguments** **Result**

**Key or Keys/** **Menu or Screen/Item**

**List 4 matr(***listname1***,**...**,** *listname n***,***matrixname***)**

**Fills matrixname column by column with the elements from each specified listname. **

**y 9 OPS 0:List 4 matr( **

**ln(***value***)** Returns the natural logarithm of a real or complex number, expression, or list.

**LnReg** [*Xlistname***,** *Ylistname***,***freqlist***,** *regequ*]

**Fits a logarithmic regression model to Xlistname and Ylistname with frequency freqlist, and stores the regression equation to regequ. **

** CALC 9:LnReg **

**log(***value***)** Returns logarithm of a real or complex number, expression, or list.

**Logistic **[*Xlistname***,** *Ylistname***,***freqlist***,** *regequ*]

**Fits a logistic regression model to Xlistname and Ylistname with frequency freqlist, and stores the regression equation to regequ. **

** CALC B:Logistic **

**Matr 4 list(***matrix***,** *listnameA***,***...***,***listname n***)**

**Fills each listname with elements from each column in matrix. **

**y 9 OPSA:Matr 4 list( **

**Matr 4 list(***matrix***,** *column#***,***listname***)**

**Fills a listname with elements from a specified column# in matrix. **

**y 9 OPSA:Matr 4 list( **

**max(***valueA***,***valueB***)** Returns the larger of *valueA* and *valueB*.

** NUM 7:max( **

**max(***list***)** Returns largest real or complex element in *list*.

**y 9 MATH 2:max(**

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**TI-83 Plus Tables and Reference Information 671 **

**Function or Instruction/** **Arguments** **Result**

**Key or Keys/** **Menu or Screen/Item**

**max(***listA***,***listB***)** Returns a real or complex list of the larger of each pair of elements in *listA* and *listB*.

**y 9 MATH 2:max( **

**max(***value,list***)** Returns a real or complex list of the larger of *value* or each *list* element.

**y 9 MATH 2:max( **

**mean(***list*[**,***freqlist*]**)** Returns the mean of *list* with frequency *freqlist*.

**y 9 MATH 3:mean( **

**median(***list*[**,***freqlist*]**)** Returns the median of *list* with frequency *freqlist*.

**y 9 MATH 4:median( **

**Med-Med** [*Xlistname***,** *Ylistname***,***freqlist***,** *regequ*]

**Fits a median-median model to Xlistname and Ylistname with frequency freqlist, and stores the regression equation to regequ. **

** CALC 3:Med-Med **

**Menu("***title***","***text1***",***label1* [**,***...***,"***text7***",***label7*]**)**

**Generates a menu of up to seven items during program execution. **

** CTL C:Menu( **

**min(***valueA***,***valueB***)** Returns smaller of *valueA* and *valueB*.

** NUM 6:min( **

**min(***list***)** Returns smallest real or complex element in *list*.

**y 9 MATH 1:min( **

**min(***listA***,***listB***)** Returns real or complex list of the smaller of each pair of elements in *listA* and *listB*.

**y 9 MATH 1:min(**

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**TI-83 Plus Tables and Reference Information 672 **

**Function or Instruction/** **Arguments** **Result**

**Key or Keys/** **Menu or Screen/Item**

**min(***value,list***)** Returns a real or complex list of the smaller of *value* or each *list* element.

**y 9 MATH 1:min( **

*valueA* **nCr** *valueB* Returns the number of combinations of *valueA* taken *valueB* at a time.

** PRB 3:nCr **

*value* **nCr** *list* Returns a list of the combinations of *value* taken each element in *list* at a time.

** PRB 3:nCr **

*list* **nCr** *value* Returns a list of the combinations of each element in *list* taken *value* at a time.

** PRB 3:nCr **

*listA* **nCr** *listB* Returns a list of the combinations of each element in *listA* taken each element in *listB* at a time.

** PRB 3:nCr **

**nDeriv(***expression***,***variable***,** *value*[**,**H]**)**

**Returns approximate numerical derivative of expression with respect to variable at value, with specified H. **

** MATH 8:nDeriv( **

**4Nom(***effective rate***,** *compounding periods***)**

**Computes the nominal interest rate. 1:Finance CALC B:4Nom( **

**Normal** Sets normal display mode. z **Normal**

**normalcdf(***lowerbound***,** *upperbound*[**,**m**,**s]**)**

**Computes the normal distribution probability between lowerbound and upperbound for the specified m and s. **

**y = DISTR 2:normalcdf(**

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**TI-83 Plus Tables and Reference Information 673 **

**Function or Instruction/** **Arguments** **Result**

**Key or Keys/** **Menu or Screen/Item**

**normalpdf(***x*[**,**m**,**s]**)** Computes the probability density function for the normal distribution at a specified *x* value for the specified m and s.

**y = DISTR 1:normalpdf( **

**not(***value***)** Returns **0** if *value* is 0. *value* can be a real number, expression, or list.

**y : LOGIC 4:not( **

*valueA* **nPr** *valueB* Returns the number of permutations of *valueA* taken *valueB* at a time.

** PRB 2:nPr **

*value* **nPr** *list* Returns a list of the permutations of *value* taken each element in *list* at a time.

** PRB 2:nPr **

*list* **nPr** *value* Returns a list of the permutations of each element in *list* taken *value* at a time.

** PRB 2:nPr **

*listA* **nPr** *listB* Returns a list of the permutations of each element in *listA* taken each element in *listB* at a time.

** PRB 2:nPr **

**npv(***interest rate***,***CF0***,** *CFList*[**,***CFFreq*]**)**

**Computes the sum of the present values for cash inflows and outflows. **

** 1:Finance CALC 7:npv( **

*valueA* **or** *valueB* Returns 1 if *valueA* or *valueB* is 0. *valueA* and *valueB* can be real numbers, expressions, or lists.

**y : LOGIC 2:or **

**Output(***row***,***column***,** ** "***text***")**

**Displays text beginning at specified row and column. **

** I/O 6:Output(**

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**TI-83 Plus Tables and Reference Information 674 **

**Function or Instruction/** **Arguments** **Result**

**Key or Keys/** **Menu or Screen/Item**

**Output(***row***,***column***,** *value***)**

**Displays value beginning at specified row and column. **

** I/O 6:Output( **

**Param** Sets parametric graphing mode. z **Par**

**Pause** Suspends program execution until you press .

** CTL 8:Pause **

**Pause **[*value*] Displays *value*; suspends program execution until you press .

** CTL 8:Pause **

**Plot***#***(***type***,***Xlistname***,** *Ylistname***,***mark***)**

**Defines Plot# (1, 2, or 3) of type Scatter or xyLine for Xlistname and Ylistname using mark. **

** y , PLOTS 1:Plot1- 2:Plot2- 3:Plot3- **

**Plot***#***(***type***,***Xlistname***,** *freqlist***)**

**Defines Plot# (1, 2, or 3) of type Histogram or Boxplot for Xlistname with frequency freqlist. **

** y , PLOTS 1:Plot1- 2:Plot2- 3:Plot3- **

**Plot***#***(***type***,***Xlistname***,** *freqlist***,***mark***)**

**Defines Plot# (1, 2, or 3) of type ModBoxplot for Xlistname with frequency freqlist using mark. **

** y , PLOTS 1:Plot1- 2:Plot2- 3:Plot3-**

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**TI-83 Plus Tables and Reference Information 675 **

**Function or Instruction/** **Arguments** **Result**

**Key or Keys/** **Menu or Screen/Item**

**Plot***#***(***type***,***datalistname***,** *data axis***,***mark***)**

**Defines Plot# (1, 2, or 3) of type NormProbPlot for datalistname on data axis using mark. data axis can be X or Y. **

** y , PLOTS 1:Plot1- 2:Plot2- 3:Plot3- **

**PlotsOff** [**1,2,3**] Deselects all stat plots or one or more specified stat plots (**1**, **2**, or **3**).

**y , STAT PLOTS 4:PlotsOff **

**PlotsOn** [**1,2,3**] Selects all stat plots or one or more specified stat plots (**1**, **2**, or **3**).

**y , STAT PLOTS 5:PlotsOn **

**Pmt_Bgn** Specifies an annuity due, where payments occur at the beginning of each payment period.

** 1:Finance CALC F:Pmt_Bgn **

**Pmt_End** Specifies an ordinary annuity, where payments occur at the end of each payment period.

** 1:Finance CALC E:Pmt_End **

**poissoncdf(**m**,***x***)** Computes a cumulative probability at *x* for the discrete Poisson distribution with specified mean m.

**y = DISTR C:poissoncdf( **

**poissonpdf(**m**,***x***)** Computes a probability at *x* for the discrete Poisson distribution with the specified mean m.

**y = DISTR B:poissonpdf( **

**Polar** Sets polar graphing mode. z **Pol**

*complex value ***4Polar** Displays *complex value* in polar format.

** CPX 7:4Polar**

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**TI-83 Plus Tables and Reference Information 676 **

**Function or Instruction/** **Arguments** **Result**

**Key or Keys/** **Menu or Screen/Item**

**PolarGC** Sets polar graphing coordinates format.

** y . PolarGC **

**prgm***name* Executes the program *name*. **CTRL** **D:prgm**

**GPrn(***pmt1***,***pmt2* * *[**,***roundvalue*]**)**

**Computes the sum, rounded to roundvalue, of the principal amount between pmt1 and pmt2 for an amortization schedule. **

** 1:Finance CALC 0:GPrn( **

**prod(***list*[**,***start***,***end*]**)** Returns product of *list* elements between *start* and *end*.

**y 9 MATH 6:prod( **

**Prompt** *variableA* * *[**,***variableB***,**...**,***variable n***]**

**Prompts for value for variableA, then variableB, and so on. **

** I/O 2:Prompt **

**1.PropZInt(***x***,***n* [**,***confidence level*]**)**

**Computes a one-proportion z confidence interval. **

** TESTS A:1-PropZInt( **

**2.PropZInt(***x1***,***n1***,***x2***,***n2* [**,***confidence level*]**)**

**Computes a two-proportion z confidence interval. **

** TESTS B:2-PropZInt( **

**1.PropZTest(***p0***,***x***,***n* [**,***alternative***,***drawflag*]**)**

**Computes a one-proportion z test. alternative=L1 is <; alternative=0 is ; alternative=1 is >. drawflag=1 draws results; drawflag=0 calculates results. **

** TESTS 5:1-PropZTest(**

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**TI-83 Plus Tables and Reference Information 677 **

**Function or Instruction/** **Arguments** **Result**

**Key or Keys/** **Menu or Screen/Item**

**2.PropZTest(***x1***,***n1***,***x2***,***n2* [**,***alternative***,***drawflag*]**)**

**Computes a two-proportion z test. alternative=L1 is <; alternative=0 is ; alternative=1 is >. drawflag=1 draws results; drawflag=0 calculates results. **

** TESTS 6:2-PropZTest( **

**Pt.Change(***x***,***y***)** Reverses a point at (*x*,*y*). y < **POINTS** **3:Pt.Change(**

**Pt.Off(***x***,***y*[**,***mark*]**)** Erases a point at (*x*,*y*) using *mark*. y < **POINTS** **2:Pt.Off(**

**Pt.On(***x***,***y*[**,***mark*]**)** Draws a point at (*x*,*y*) using *mark*. y < **POINTS** **1:Pt.On(**

**PwrReg** [*Xlistname***,** *Ylistname***,***freqlist***,** *regequ*]

**Fits a power regression model to Xlistname and Ylistname with frequency freqlist, and stores the regression equation to regequ. **

** CALC A:PwrReg **

**Pxl.Change(***row***,***column***)** Reverses pixel at (*row*,*column*); 0 *row* 62 and 0 *column* 94.

**y < POINTS 6:Pxl.Change( **

**Pxl.Off(***row***,***column***)** Erases pixel at (*row*,*column*); 0 *row* 62 and 0 *column* 94.

**y < POINTS 5:Pxl.Off( **

**Pxl.On(***row***,***column***)** Draws pixel at (*row*,*column*); 0 *row* 62 and 0 *column* 94.

**y < POINTS 4:Pxl.On(**

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**TI-83 Plus Tables and Reference Information 678 **

**Function or Instruction/** **Arguments** **Result**

**Key or Keys/** **Menu or Screen/Item**

**pxl.Test(***row***,***column***)** Returns 1 if pixel (*row*, *column*) is on, 0 if it is off; 0 *row* 62 and 0 *column* 94.

**y < POINTS 7:pxl.Test( **

**P4Rx(***r***,**q**)** Returns **X**, given polar coordinates *r* and q or a list of polar coordinates.

**y ; ANGLE 7:P4Rx( **

**P4Ry(***r***,**q**)** Returns **Y**, given polar coordinates *r* and q or a list of polar coordinates.

**y ; ANGLE 8:P4Ry( **

**QuadReg** [*Xlistname***,** *Ylistname***,***freqlist***,** *regequ*]

**Fits a quadratic regression model to Xlistname and Ylistname with frequency freqlist, and stores the regression equation to regequ. **

** CALC 5:QuadReg **

**QuartReg** [*Xlistname***,** *Ylistname***,***freqlist***,** *regequ*]

**Fits a quartic regression model to Xlistname and Ylistname with frequency freqlist, and stores the regression equation to regequ. **

** CALC 7:QuartReg **

**Radian** Sets radian angle mode. z **Radian**

**rand**[**(***numtrials***)**] Returns a random number between 0 and 1 for a specified number of trials *numtrials*.

** PRB 1:rand **

**randBin(***numtrials***,***prob* [**,***numsimulations*]**)**

**Generates and displays a random real number from a specified Binomial distribution. **

** PRB 7:randBin(**

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**TI-83 Plus Tables and Reference Information 679 **

**Function or Instruction/** **Arguments** **Result**

**Key or Keys/** **Menu or Screen/Item**

**randInt( ***lower,upper* [*,numtrials*]**)**

**Generates and displays a random integer within a range specified by lower and upper integer bounds for a specified number of trials numtrials. **

** PRB 5:randInt( **

**randM(***rows***,***columns***)** Returns a random matrix of *rows* (**1** **99**) *columns* (**1****99**).

**y > MATH 6:randM( **

**randNorm(**m**,**s[**,***numtrials*]**)** Generates and displays a random real number from a specified Normal distribution specified by m and s for a specified number of trials *numtrials*.

** PRB 6:randNorm( **

**r e^qi** Sets the mode to polar complex number mode (

**r**).

*e*^q*i*** z re^qi **

**Real** Sets mode to display complex results only when you enter complex numbers.

** z Real **

**real(***value***)** Returns the real part of a complex number or list of complex numbers.

** CPX 2:real( **

**RecallGDB ***n* Restores all settings stored in the graph database variable **GDB***n*.

**y < STO 4:RecallGDB **

**RecallPic ***n* Displays the graph and adds the picture stored in **Pic***n*.

**y < STO 2:RecallPic **

*complex value ***4Rect** Displays *complex value* or list in rectangular format.

** CPX 6:4Rect**

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**TI-83 Plus Tables and Reference Information 680 **

**Function or Instruction/** **Arguments** **Result**

**Key or Keys/** **Menu or Screen/Item**

**RectGC** Sets rectangular graphing coordinates format.

** y . RectGC **

**ref(***matrix***)** Returns the row-echelon form of a *matrix*.

**y > MATH A:ref( **

**:Repeat** *condition* **:***commands* **:End** **:***commands*

**Executes commands until condition is true. **

** CTL 6:Repeat **

**Return** Returns to the calling program. **CTL** **E:Return**

**round(***value*[**,***#decimals*]**)** Returns a number, expression, list, or matrix rounded to *#decimals* ( 9).

** NUM 2:round( **

**row(***value***,***matrix***,***row***)** Returns a matrix with *row* of *matrix* multiplied by *value* and stored in *row*.

**y > MATH E:row( **

**row+(***matrix***,***rowA***,***rowB***)** Returns a matrix with *rowA* of *matrix* added to *rowB* and stored in *rowB*.

**y > MATH D:row+( **

**row+(***value***,***matrix***,** *rowA***,***rowB***)**

**Returns a matrix with rowA of matrix multiplied by value, added to rowB, and stored in rowB. **

**y > MATH F:row+( **

**rowSwap(***matrix***,***rowA***,** *rowB***)**

**Returns a matrix with rowA of matrix swapped with rowB. **

**y > MATH C:rowSwap(**

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**TI-83 Plus Tables and Reference Information 681 **

**Function or Instruction/** **Arguments** **Result**

**Key or Keys/** **Menu or Screen/Item**

**rref(***matrix***)** Returns the reduced row-echelon form of a *matrix*.

**y > MATH B:rref( **

**R4Pr(***x***,***y***)** Returns **R**, given rectangular coordinates *x* and *y* or a list of rectangular coordinates.

**y ; ANGLE 5:R4Pr( **

**R4Pq(***x***,***y***)** Returns **q**, given rectangular coordinates *x* and *y* or a list of rectangular coordinates.

**y ; ANGLE 6:R4Pq( **

**2.SampTest*** *[*listname1***,** *listname2***,***freqlist1***,** *freqlist2***,***alternative***,** *drawflag*] (Data list input)

**Performs a two-sample test. alternative=L1 is <; alternative=0 is ; alternative=1 is >. drawflag=1 draws results; drawflag=0 calculates results. **

** TESTS D:2-SampTest **

**2.SampTest*** Sx1***,***n1***,** *Sx2***,***n2*[**,***alternative***,** *drawflag*] (Summary stats input)

**Performs a two-sample test. alternative=L1 is <; alternative=0 is ; alternative=1 is >. drawflag=1 draws results; drawflag=0 calculates results. **

** TESTS D:2-SampTest **

**2.SampTInt** [*listname1***,** *listname2***,** *freqlist1***,***freqlist2***,** *confidence level***,***pooled*] (Data list input)

**Computes a two-sample t confidence interval. pooled=1 pools variances; pooled=0 does not pool variances. **

** TESTS 0:2-SampTInt **

**2.SampTInt** v*1***,***Sx1***,***n1***,** v*2***,***Sx2***,***n2* [**,***confidence * *level***,***pooled*] (Summary stats input)

**Computes a two-sample t confidence interval. pooled=1 pools variances; pooled=0 does not pool variances. **

** TESTS 0:2-SampTInt**

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**TI-83 Plus Tables and Reference Information 682 **

**Function or Instruction/** **Arguments** **Result**

**Key or Keys/** **Menu or Screen/Item**

**2.SampTTest*** *[*listname1***,** *listname2***,***freqlist1***,** *freqlist2***,***alternative***,** *pooled***,***drawflag*] (Data list input)

**Computes a two-sample t test. alternative=L1 is <; alternative=0 is ; alternative=1 is >. pooled=1 pools variances; pooled=0 does not pool variances. drawflag=1 draws results; drawflag=0 calculates results. **

** TESTS 4:2-SampTTest **

**2.SampTTest **v*1***,***Sx1***,***n1***,** v*2***,***Sx2***,***n2*[**,***alternative***,** *pooled***,***drawflag*] (Summary stats input)

**Computes a two-sample t test. alternative=L1 is <; alternative=0 is ; alternative=1 is >. pooled=1 pools variances; pooled=0 does not pool variances. drawflag=1 draws results; drawflag=0 calculates results. **

** TESTS 4:2-SampTTest **

**2.SampZInt(**s1**,**s2 [**,***listname1***,***listname2***,** *freqlist1***,***freqlist2***,** *confidence level*]**)** (Data list input)

**Computes a two-sample z confidence interval. **

** TESTS 9:2-SampZInt( **

**2.SampZInt(**s1**,**s2**,** v*1***,***n1***,**v*2***,***n2* [**,***confidence level*]**)** (Summary stats input)

**Computes a two-sample z confidence interval. **

** TESTS 9:2-SampZInt( **

**2.SampZTest(**s1,s2 [**,***listname1***,***listname2***,** *freqlist1***,***freqlist2***,** *alternative***,***drawflag*]**)** (Data list input)

**Computes a two-sample z test. alternative=L1 is <; alternative=0 is ; alternative=1 is >. drawflag=1 draws results; drawflag=0 calculates results. **

** TESTS **

**3:2-SampZTest(**

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**TI-83 Plus Tables and Reference Information 683 **

**Function or Instruction/** **Arguments** **Result**

**Key or Keys/** **Menu or Screen/Item**

**2.SampZTest(**s1,s2, v*1***,***n1***,**v*2***,***n2* [**,***alternative***,***drawflag*]**)** (Summary stats input)

**Computes a two-sample z test. alternative=L1 is <; alternative=0 is ; alternative=1 is >. drawflag=1 draws results; drawflag=0 calculates results. **

** TESTS **

**3:2-SampZTest(**

**Sci** Sets scientific notation display mode. z **Sci**

**Select(***Xlistname***,** *Ylistname***)**

**Selects one or more specific data points from a scatter plot or xyLine plot (only), and then stores the selected data points to two new lists, Xlistname and Ylistname. **

**y 9 OPS 8:Select( **

**Send(***variable***)** Sends contents of *variable* to the CBL 2/CBL or CBR System.

** I/O B:Send( **

**seq(***expression***,***variable***,** *begin***,***end*[**,***increment*]**)**

**Returns list created by evaluating expression with regard to variable, from begin to end by increment. **

**y 9 OPS 5:seq( **

**Seq** Sets sequence graphing mode. z **Seq**

**Sequential** Sets mode to graph functions sequentially.

** z Sequential **

**SetUpEditor** Removes all list names from the stat list editor, and then restores list names **L1** through **L6** to columns **1** through **6**.

** EDIT 5:SetUpEditor**

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**TI-83 Plus Tables and Reference Information 684 **

**Function or Instruction/** **Arguments** **Result**

**Key or Keys/** **Menu or Screen/Item**

**SetUpEditor ***listname1* [**,***listname2***,***...***,** *listname20*]

**Removes all list names from the stat list editor, then sets it up to display one or more listnames in the specified order, starting with column 1. **

** EDIT 5:SetUpEditor **

**Shade(***lowerfunc***,** *upperfunc*[**,***Xleft***,***Xright***,** *pattern***,***patres*]**)**

**Draws lowerfunc and upperfunc in terms of X on the current graph and uses pattern and patres to shade the area bounded by lowerfunc, upperfunc, Xleft, and Xright. **

**y < DRAW 7:Shade( **

**Shadec2(***lowerbound***,** *upperbound***,***df***)**

**Draws the density function for the c2 **

**distribution specified by degrees of freedom df and shades the area between lowerbound and upperbound. **

**y = DRAW 3:Shadec2( **

**Shade(***lowerbound***,** *upperbound***,** *numerator df***,** *denominator df***)**

**Draws the density function for the distribution specified by numerator df and denominator df and shades the area between lowerbound and upperbound. **

**y = DRAW 4:Shade( **

**ShadeNorm(***lowerbound***,** *upperbound*[**,**m**,**s]**)**

**Draws the normal density function specified by m and s and shades the area between lowerbound and upperbound. **

**y = DRAW 1:ShadeNorm( **

**Shade_t(***lowerbound***,** *upperbound***,***df***)**

**Draws the density function for the Student-t distribution specified by degrees of freedom df, and shades the area between lowerbound and upperbound. **

**y = DRAW 2:Shade_t(**

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**TI-83 Plus Tables and Reference Information 685 **

**Function or Instruction/** **Arguments** **Result**

**Key or Keys/** **Menu or Screen/Item**

**Simul** Sets mode to graph functions simultaneously.

** z Simul **

**sin(***value***)** Returns the sine of a real number, expression, or list.

**sinL1(***value***)** Returns the arcsine of a real number, expression, or list.

**y ? **

**sinh(***value***)** Returns the hyperbolic sine of a real number, expression, or list.

**y N sinh( **

**sinhL1(***value***)** Returns the hyperbolic arcsine of a real number, expression, or list.

**y N sinhL1( **

**SinReg** [*iterations***,** *Xlistname***,***Ylistname***,** *period***,***regequ*]

**Attempts iterations times to fit a sinusoidal regression model to Xlistname and Ylistname using a period guess, and stores the regression equation to regequ. **

** CALC C:SinReg **

**solve(***expression***,***variable***,** *guess***,{***lower***,***upper***})**

**Solves expression for variable, given an initial guess and lower and upper bounds within which the solution is sought. **

** MATH 0:solve( **

**SortA(***listname***)** Sorts elements of *listname* in ascending order.

**y 9 OPS1:SortA( **

**SortA(***keylistname***,** *dependlist1*[**,***dependlist2***,** **...,***dependlist n*]**)**

**Sorts elements of keylistname in ascending order, then sorts each dependlist as a dependent list. **

**y 9 OPS 1:SortA( **

**SortD(***listname***)** Sorts elements of *listname* in descending order.

**y 9 OPS2:SortD(**

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**TI-83 Plus Tables and Reference Information 686 **

**Function or Instruction/** **Arguments** **Result**

**Key or Keys/** **Menu or Screen/Item**

**SortD(***keylistname***,** *dependlist1*[**,***dependlist2***,** **..., ***dependlist n*]**)**

**Sorts elements of keylistname in descending order, then sorts each dependlist as a dependent list. **

**y 9 OPS 2:SortD( **

**stdDev(***list*[**,***freqlist*]**)** Returns the standard deviation of the elements in *list* with frequency *freqlist*.

**y 9 MATH 7:stdDev( **

**Stop** Ends program execution; returns to home screen.

** CTL F:Stop **

**Store: value!variable Stores value in variable. **

**StoreGDB ***n* Stores current graph in database **GDB***n*.

**y < STO 3:StoreGDB **

**StorePic** *n* Stores current picture in picture **Pic***n*. y < **STO** **1:StorePic**

**String4Equ(***string***,Y=*** var***)** Converts *string* into an equation and stores it in **Y=*** var*.

**y N String4Equ( **

**sub(***string***,***begin***,***length***)** Returns a string that is a subset of another *string*, from *begin* to *length*.

**y N sub( **

**sum(***list*[**,***start***,***end*]**)** Returns the sum of elements of *list* from *start* to *end*.

**y 9 MATH 5:sum( **

**tan(***value***)** Returns the tangent of a real number, expression, or list.

**tanL1(***value***)** Returns the arctangent of a real number, expression, or list.

**y A**

Page 690

**TI-83 Plus Tables and Reference Information 687 **

**Function or Instruction/** **Arguments** **Result**

**Key or Keys/** **Menu or Screen/Item**

**Tangent(***expression***,***value***)** Draws a line tangent to *expression* at **X**=*value*.

**y < DRAW 5:Tangent( **

**tanh(***value***)** Returns hyperbolic tangent of a real number, expression, or list.

**y N tanh( **

**tanhL1(***value***)** Returns the hyperbolic arctangent of a real number, expression, or list.

**y N tanhL1( **

**tcdf(***lowerbound***,** *upperbound***,***df***)**

**Computes the Student- t distribution probability between lowerbound and upperbound for the specified degrees of freedom df. **

**y = DISTR 5:tcdf( **

**Text(***row***,***column***,***text1***,** *text2***,**...**,***text n***)**

**Writes text on graph beginning at pixel (row,column), where 0 row 57 and 0 column 94. **

**y < DRAW 0:Text( **

**Then** *See* **If:Then** **Time** Sets sequence graphs to plot with

**respect to time. y . Time **

**TInterval*** *[*listname***,** *freqlist***,***confidence level*] (Data list input)

**Computes a t confidence interval. TESTS 8:TInterval **

**TInterval*** *v**,***Sx***,***n* [**,***confidence level*] (Summary stats input)

**Computes a t confidence interval. TESTS 8:TInterval **

**tpdf(***x***,***df***)** Computes the probability density function (pdf) for the Student-*t* distribution at a specified *x* value with specified degrees of freedom *df*.

**y = DISTR 4:tpdf(**

Page 691

**TI-83 Plus Tables and Reference Information 688 **

**Function or Instruction/** **Arguments** **Result**

**Key or Keys/** **Menu or Screen/Item**

**Trace** Displays the graph and enters **TRACE** mode.

**r **

**T-Test*** *m*0*[**,***listname***,** * freqlist***,***alternative***,** * drawflag*] (Data list input)

**Performs a t test with frequency freqlist. alternative=L1 is <; alternative=0 is ; alternative=1 is >. drawflag=1 draws results; drawflag=0 calculates results. **

** TESTS 2:T-Test **

**T-Test*** *m*0***,** v**,***Sx***,***n* * *[**,***alternative***,***drawflag*] (Summary stats input)

**Performs a t test with frequency freqlist. alternative=L1 is < ; alternative=0 is ; alternative=1 is >. drawflag=1 draws results; drawflag=0 calculates results. **

** TESTS 2:T-Test **

**tvm_FV**[**(****,****,***PV***,***PMT***,** *P/Y***,***C/Y***)**]

**Computes the future value. 1:Finance CALC 6:tvm_FV **

**tvm_**[**(****,***PV***,***PMT***,***FV***,** *P/Y***,***C/Y***)**]

**Computes the annual interest rate. 1:Finance CALC 3:tvm_( **

**tvm_**[**(****,***PV***,***PMT***,***FV***,** *P/Y***,***C/Y***)**]

**Computes the number of payment periods. **

** 1:Finance CALC 5:tvm_( **

**tvm_Pmt**[**(****,****,***PV***,***FV***,** *P/Y***,***C/Y***)**]

**Computes the amount of each payment. **

** 1:Finance CALC 2:tvm_Pmt **

**tvm_PV**[**(****,****,***PMT***,***FV***,** *P/Y***,***C/Y***)**]

**Computes the present value. 1:Finance CALC 4:tvm_PV**

Page 692

**TI-83 Plus Tables and Reference Information 689 **

**Function or Instruction/** **Arguments** **Result**

**Key or Keys/** **Menu or Screen/Item**

**UnArchive** Moves the specified variables from the user data archive memory to RAM. To archive variables, use **Archive**.

**y L 6:UnArchive **

**uvAxes** Sets sequence graphs to plot **u(n)** on the x-axis and **v(n)** on the y-axis.

** y . uv **

**uwAxes** Sets sequence graphs to plot **u(n)** on the x-axis and **w(n)** on the y-axis.

** y . uw **

**1-Var** **Stats** [*Xlistname***,** *freqlist*]

**Performs one-variable analysis on the data in Xlistname with frequency freqlist. **

** CALC 1:1-Var Stats **

**2-Var** **Stats** [*Xlistname***,** *Ylistname***,***freqlist*]

**Performs two-variable analysis on the data in Xlistname and Ylistname with frequency freqlist. **

** CALC 2:2-Var Stats **

**variance(***list*[**,***freqlist*]**)** Returns the variance of the elements in *list* with frequency *freqlist*.

**y 9 MATH 8:variance( **

**Vertical*** x* Draws a vertical line at *x*. y < **DRAW** **4:Vertical**

**vwAxes** Sets sequence graphs to plot **v(n)** on the x-axis and **w(n)** on the y-axis.

** y . vw **

**Web** Sets sequence graphs to trace as webs.

** y . Web **

**:While** *condition* **:***commands* **:End** **:***command*

**Executes commands while condition is true. **

** CTL 5:While**

Page 693

**TI-83 Plus Tables and Reference Information 690 **

**Function or Instruction/** **Arguments** **Result**

**Key or Keys/** **Menu or Screen/Item**

*valueA* **xor** *valueB* Returns 1 if only *valueA* or *valueB* = 0. *valueA* and *valueB* can be real numbers, expressions, or lists.

**y : LOGIC 3:xor **

**ZBox** Displays a graph, lets you draw a box that defines a new viewing window, and updates the window.

** q ZOOM 1:ZBox **

**ZDecimal** Adjusts the viewing window so that **@X=0.1** and **@Y=0.1**, and displays the graph screen with the origin centered on the screen.

** q ZOOM 4:ZDecimal **

**ZInteger** Redefines the viewing window using these dimensions: **@X=1** **Xscl=10** **@Y=1** **Yscl=10**

** q ZOOM 8:ZInteger **

**ZInterval** s[**,***listname***,** *freqlist***,***confidence level*] (Data list input)

**Computes a z confidence interval. TESTS 7:ZInterval **

**ZInterval** s**,**v**,***n* [**,***confidence level*] (Summary stats input)

**Computes a z confidence interval. TESTS 7:ZInterval **

**Zoom In** Magnifies the part of the graph that surrounds the cursor location.

** q ZOOM 2:Zoom In **

**Zoom Out** Displays a greater portion of the graph, centered on the cursor location.

** q ZOOM 3:Zoom Out**

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**TI-83 Plus Tables and Reference Information 691 **

**Function or Instruction/** **Arguments** **Result**

**Key or Keys/** **Menu or Screen/Item**

**ZoomFit** Recalculates **Ymin** and **Ymax** to include the minimum and maximum **Y** values, between **Xmin** and **Xmax**, of the selected functions and replots the functions.

** q ZOOM 0:ZoomFit **

**ZoomRcl** Graphs the selected functions in a user-defined viewing window.

** q MEMORY 3:ZoomRcl **

**ZoomStat** Redefines the viewing window so that all statistical data points are displayed.

** q ZOOM 9:ZoomStat **

**ZoomSto** Immediately stores the current viewing window.

** q MEMORY 2:ZoomSto **

**ZPrevious** Replots the graph using the window variables of the graph that was displayed before you executed the last **ZOOM** instruction.

** q MEMORY 1:ZPrevious **

**ZSquare** Adjusts the **X** or **Y** window settings so that each pixel represents an equal width and height in the coordinate system, and updates the viewing window.

** q ZOOM 5:ZSquare **

**ZStandard** Replots the functions immediately, updating the window variables to the default values.

** q ZOOM 6:ZStandard**

Page 695

**TI-83 Plus Tables and Reference Information 692 **

**Function or Instruction/** **Arguments** **Result**

**Key or Keys/** **Menu or Screen/Item**

**ZNTest(**m*0***,s**[**,***listname***,** *freqlist***,***alternative***,** *drawflag*]**)** (Data list input)

**Performs a z test with frequency freqlist. alternative=L1 is <; alternative=0 is ; alternative=1 is >. drawflag=1 draws results; drawflag=0 calculates results. **

** TESTS 1:Z.Test( **

**ZNTest(**m*0***,s,v,***n* * *[**,***alternative***,***drawflag*]**)** (Summary stats input)

**Performs a z test. alternative=L1 is <; alternative=0 is ; alternative=1 is >. drawflag=1 draws results; drawflag=0 calculates results. **

** TESTS 1:Z.Test( **

**ZTrig** Replots the functions immediately, updating the window variables to preset values for plotting trig functions.

** q ZOOM 7:ZTrig **

**Factorial: value! Returns factorial of value. PRB 4:! **

**Factorial: list! Returns factorial of list elements. PRB 4:! **

**Degrees notation: value Interprets value as degrees; designates degrees in DMS format. **

**y ; ANGLE 1:( **

**Radian: angler Interprets angle as radians. y ; ANGLE 3:r**

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**TI-83 Plus Tables and Reference Information 693 **

**Function or Instruction/** **Arguments** **Result**

**Key or Keys/** **Menu or Screen/Item**

**Transpose: matrixT Returns a matrix in which each element (row, column) is swapped with the corresponding element (column, row) of matrix. **

**y > MATH 2:T **

*xthroot***x***value* Returns *xthroot* of *value*. **MATH** **5:x(**

*xthroot***x***list* Returns *xthroot* of *list* elements. **MATH** **5:x(**

*list***x***value* Returns *list* roots of *value*. **MATH** **5:x(**

*listA***x***listB* Returns *listA* roots of *listB*. **MATH** **5:x(**

**Cube: value3 Returns the cube of a real or complex number, expression, list, or square matrix. **

** MATH 3:3 **

**Cube root: 3(value) Returns the cube root of a real or complex number, expression, or list. **

** MATH 4:3( **

**Equal: valueA=valueB Returns 1 if valueA = valueB. Returns 0 if valueA valueB. valueA and valueB can be real or complex numbers, expressions, lists, or matrices. **

**y : TEST 1:=**

Page 697

**TI-83 Plus Tables and Reference Information 694 **

**Function or Instruction/** **Arguments** **Result**

**Key or Keys/** **Menu or Screen/Item**

**Not equal: valueAvalueB Returns 1 if valueA valueB. Returns 0 if valueA = valueB. valueA and valueB can be real or complex numbers, expressions, lists, or matrices. **

**y : TEST 2: **

**Less than: valueA<valueB Returns 1 if valueA < valueB. Returns 0 if valueA valueB. valueA and valueB can be real or complex numbers, expressions, or lists. **

**y : TEST 5:< **

**Greater than: valueA>valueB **

**Returns 1 if valueA > valueB. Returns 0 if valueA valueB. valueA and valueB can be real or complex numbers, expressions, or lists. **

**y : TEST 3:> **

**Less than or equal: valueAvalueB **

**Returns 1 if valueA valueB. Returns 0 if valueA > valueB. valueA and valueB can be real or complex numbers, expressions, or lists. **

**y : TEST 6: **

**Greater than or equal: valueAvalueB **

**Returns 1 if valueA valueB. Returns 0 if valueA < valueB. valueA and valueB can be real or complex numbers, expressions, or lists. **

**y : TEST 4: **

**Inverse: valueL1 Returns 1 divided by a real or complex number or expression. **

**Inverse: listL1 Returns 1 divided by list elements. **

**Inverse: matrixL1 Returns matrix inverted. **

**Square: value2 Returns value multiplied by itself. value can be a real or complex number or expression. **

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**TI-83 Plus Tables and Reference Information 695 **

**Function or Instruction/** **Arguments** **Result**

**Key or Keys/** **Menu or Screen/Item**

**Square: list2 Returns list elements squared. **

**Square: matrix2 Returns matrix multiplied by itself. **

**Powers: value^power Returns value raised to power. value can be a real or complex number or expression. **

**Powers: list^power Returns list elements raised to power. **

**Powers: value^list Returns value raised to list elements. **

**Powers: matrix^power Returns matrix elements raised to power. **

**Negation: Lvalue Returns the negative of a real or complex number, expression, list, or matrix. **

**Power of ten: 10^(value) Returns 10 raised to the value power. value can be a real or complex number or expression. **

**y G **

**Power of ten: 10^(list) Returns a list of 10 raised to the list power. **

**y G **

**Square root: (value) Returns square root of a real or complex number, expression, or list. **

**y C **

**Multiplication: valueAvalueB **

**Returns valueA times valueB. **

**Multiplication: valuelist **

**Returns value times each list element. **

**Multiplication: listvalue **

**Returns each list element times value. **

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**TI-83 Plus Tables and Reference Information 696 **

**Function or Instruction/** **Arguments** **Result**

**Key or Keys/** **Menu or Screen/Item**

**Multiplication: listAlistB **

**Returns listA elements times listB elements. **

**Multiplication: valuematrix **

**Returns value times matrix elements. **

**Multiplication: matrixAmatrixB **

**Returns matrixA times matrixB. **

**Division: valueAvalueB Returns valueA divided by valueB. **

**Division: listvalue Returns list elements divided by value. **

**Division: valuelist Returns value divided by list elements. **

**Division: listAlistB Returns listA elements divided by listB elements. **

**Addition: valueA+valueB Returns valueA plus valueB. **

**Addition: list+value Returns list in which value is added to each list element. **

**Addition: listA+listB Returns listA elements plus listB elements. **

**Addition: matrixA+matrixB **

**Returns matrixA elements plus matrixB elements. **

**Concatenation: string1+string2 **

**Concatenates two or more strings. **

**Subtraction: valueANvalueB **

**Subtracts valueB from valueA. **

**Subtraction: valueNlist **

**Subtracts list elements from value. **

Page 700

**TI-83 Plus Tables and Reference Information 697 **

**Function or Instruction/** **Arguments** **Result**

**Key or Keys/** **Menu or Screen/Item**

**Subtraction: listNvalue **

**Subtracts value from list elements. **

**Subtraction: listANlistB **

**Subtracts listB elements from listA elements. **

**Subtraction: matrixANmatrixB **

**Subtracts matrixB elements from matrixA elements. **

**Minutes notation: degreesminutes'seconds" **

**Interprets minutes angle measurement as minutes. **

**y ; ANGLE 2:' **

**Seconds notation: degreesminutes'seconds" **

**Interprets seconds angle measurement as seconds. **

** []**

Page 701

**TI-83 Plus Tables and Reference Information 698 **

**TI-83 Plus Menu Map **

**The TI-83 Plus Menu Map begins at the top-left corner of the keyboard and follows the keyboard layout from left to right. Default values and settings are shown. o **

**(Func mode)** **Plot1 Plot2** **Plot3** **Y1=** **Y2=** **Y3=** **Y4=** **...** **Y9=** **Y0=**

**(Par mode)** **Plot1 Plot2** **Plot3** **X1T=** ** Y1T=** **X2T=** ** Y2T=** **...** **X6T=** ** Y6T=**

**(Pol mode)** **Plot1 Plot2** **Plot3** **r1=** **r2=** **r3=** **r4=** **r5=** **r6=**

**(Seq mode)** **Plot1 Plot2** **Plot3** ** nMin=1** **u(n)=** ** u(nMin)=** **v(n)=** ** v(nMin)=** **w(n)=** ** w(nMin)=**

**y , **

**y , **

**STAT PLOTS** **1:Plot1Off** ** " L1 L2 **

**2:Plot2Off** ** " L1 L2 **

**3:Plot3Off** ** " L1 L2 **

**4:PlotsOff** **5:PlotsOn**

**(PRGM editor)** **PLOTS** **1:Plot1(** **2:Plot2(** **3:Plot3(** **4:PlotsOff** **5:PlotsOn**

**(PRGM editor)** **TYPE** **1:Scatter** **2:xyLine** **3:Histogram** **4:ModBoxplot** **5:Boxplot** **6:NormProbPlot**

**(PRGM editor)** **MARK** **1:**

**2:+** **3:**

Page 702

**TI-83 Plus Tables and Reference Information 699 **

**p **

**(Func mode)** **WINDOW** ** Xmin=-10** ** Xmax=10** ** Xscl=1** ** Ymin=-10** ** Ymax=10** ** Yscl=1** ** Xres=1**

**(Par mode)** **WINDOW** ** Tmin=0** ** Tmax=**p**2** ** Tstep=**p**24** ** Xmin=-10** ** Xmax=10** ** Xscl=1** ** Ymin=-10** ** Ymax=10** ** Yscl=1**

**(Pol mode)** **WINDOW** q**min=0** q**max=**p**2** q**step=**p**24** ** Xmin=-10** ** Xmax=10** ** Xscl=1** ** Ymin=-10** ** Ymax=10** ** Yscl=1**

**(Seq mode)** **WINDOW** ** nMin=1** ** nMax=10** ** PlotStart=1** ** PlotStep=1** ** Xmin=-10** ** Xmax=10** ** Xscl=1** ** Ymin=-10** ** Ymax=10** ** Yscl=1**

**y - **

**y - **

**TABLE SETUP** ** TblStart=0** @**Tbl=1** ** Indpnt:Auto Ask** ** Depend:Auto Ask**

**(PRGM editor)** **TABLE SETUP** ** Indpnt:Auto Ask** ** Depend:Auto Ask**

Page 703

**TI-83 Plus Tables and Reference Information 700 **

**q **

**ZOOM** **1:ZBox** **2:Zoom In** **3:Zoom Out** **4:ZDecimal** **5:ZSquare** **6:ZStandard** **7:ZTrig** **8:ZInteger** **9:ZoomStat** **0:ZoomFit**

**MEMORY** **1:ZPrevious** **2:ZoomSto** **3:ZoomRcl** **4:SetFactors**

**MEMORY** **(Set Factors...)** **ZOOM FACTORS** ** XFact=4** ** YFact=4**

**y . **

**(Func/Par/Pol modes)** **RectGC PolarGC** **CoordOn CoordOff** **GridOff GridOn** **AxesOn AxesOff** **LabelOff LabelOn** **ExprOn ExprOff**

**(Seq mode)** **Time Web uv vw uw** **RectGC PolarGC** **CoordOn CoordOff** **GridOff GridOn** **AxesOn AxesOff** **LabelOff LabelOn** **ExprOn ExprOff**

Page 704

**TI-83 Plus Tables and Reference Information 701 **

**y / **

**(Func mode)** **CALCULATE** **1:value** **2:zero** **3:minimum** **4:maximum** **5:intersect** **6:dy/dx** **7:****f(x)dx**

**(Par mode)** **CALCULATE** **1:value** **2:dy/dx** **3:dy/dt** **4:dx/dt**

**(Pol mode)** **CALCULATE** **1:value** **2:dy/dx** **3:dr/d**q

**(Seq mode)** **CALCULATE** **1:value**

**z **

**Normal Sci Eng** **Float 0123456789** **Radian Degree** **Func Par Pol Seq** **Connected Dot** **Sequential Simul** **Real a+b re^**q **Full Horiz G-T**

Page 705

**TI-83 Plus Tables and Reference Information 702 **

**y 8 **

**SEND** **1:All+** **2:AllN** **3:Prgm** **4:List** **5:Lists to TI82** **6:GDB** **7:Pic** **8:Matrix** **9:Real** **0:Complex** **A:Y-Vars** **B:String** **C:Apps** **D:AppVars** **E:Group** **F:SendId** **G:SendOS** **H:Back Up**

**RECEIVE** **1:Receive**

Page 706

**TI-83 Plus Tables and Reference Information 703 **

**EDIT** **1:Edit** **2:SortA(** **3:SortD(** **4:ClrList** **5:SetUpEditor**

**CALC** **1:1-Var Stats** **2:2-Var Stats** **3:Med-Med** **4:LinReg(ax+b)** **5:QuadReg** **6:CubicReg** **7:QuartReg** **8:LinReg(a+bx)** **9:LnReg** **0:ExpReg** **A:PwrReg** **B:Logistic** **C:SinReg**

**TESTS** **1:Z-Test** **2:T-Test** **3:2-SampZTest** **4:2-SampTTest** **5:1-PropZTest** **6:2-PropZTest** **7:ZInterval** **8:TInterval** **9:2-SampZInt** **0:2-SampTInt** **A:1-PropZInt** **B:2-PropZInt** **C:c2-Test** **D:2-SampTest** **E:LinRegTTest** **F:ANOVA(**

Page 707

**TI-83 Plus Tables and Reference Information 704 **

**y 9 **

**NAMES** **1:listname** **2:listname** **3:listname** **...**

**OPS** **1:SortA(** **2:SortD(** **3:dim(** **4:Fill(** **5:seq(** **6:c*msum(** **7:**@**List(** **8:Select(** **9:augment(** **0:List4matr(** **A:Matr4list(** **B:**

**MATH** **1:min(** **2:max(** **3:mean(** **4:median(** **5:sum(** **6:prod(** **7:stdDev(** **8:variance(**

**MATH** **1:4Frac** **2:4Dec** **3:3**

**4:3(** **5:x**

**6:fMin(** **7:fMax(** **8:nDeriv(** **9:fnInt(** **0:Solver**

**NUM** **1:abs(** **2:round(** **3:iPart(** **4:fPart(** **5:int(** **6:min(** **7:max(** **8:lcm(** **9:gcd(**

**CPX** **1:conj(** **2:real(** **3:imag(** **4:angle(** **5:abs(** **6:4Rect** **7:4Polar**

**PRB** **1:rand** **2:nPr** **3:nCr** **4:!** **5:randInt(** **6:randNorm(** **7:randBin(**

Page 708

**TI-83 Plus Tables and Reference Information 705 **

**y : **

**TEST** **1:=** **2:** **3:>** **4:** **5:<** **6:**

**LOGIC** **1:and** **2:or** **3:xor** **4:not(**

**y > **

**y ; **

**NAMES** **1:[A]** **2:[B]** **3:[C]** **4:[D]** **5:[E]** **6:[F]** **7:[G]** **8:[H]** **9:[I]** **0:[J]**

**MATH** **1:det(** **2:T** **3:dim(** **4:Fill(** **5:identity(** **6:randM(** **7:augment(** **8:Matr4list(** **9:List4matr(** **0:c*msum(** **A:ref(** **B:rref(** **C:rowSwap(** **D:row+(** **E:row(** **F:row+(**

**EDIT** **1:[A]** **2:[B]** **3:[C]** **4:[D]** **5:[E]** **6:[F]** **7:[G]** **8:[H]** **9:[I]** **0:[J]**

**ANGLE** **1:** **2:'** **3:r** **4:4DMS** **5:R4Pr(** **6:R4P**q**(** **7:P4Rx(** **8:P4Ry(**

Page 709

**TI-83 Plus Tables and Reference Information 706 **

**EXEC** **1:***name* **2:***name* **...**

**EDIT** **1:***name* **2:***name* **...**

**NEW** **1:Create New**

** (PRGM editor)** **CTL** **1:If** **2:Then** **3:Else** **4:For(** **5:While** **6:Repeat** **7:End** **8:Pause** **9:Lbl** **0:Goto** **A:IS>(** **B:DS<(** **C:Menu(** **D:prgm** **E:Return** **F:Stop** **G:DelVar** **H:GraphStyle(**

**(PRGM editor)** **I/O** **1:Input** **2:Prompt** **3:Disp** **4:DispGraph** **5:DispTable** **6:Output(** **7:getKey** **8:ClrHome** **9:ClrTable** **0:GetCalc(** **A:Get(** **B:Send(**

**(PRGM editor)** **EXEC** **1:name** **2:name** **...**

Page 710

**TI-83 Plus Tables and Reference Information 707 **

**y < **

**DRAW** **1:ClrDraw** **2:Line(** **3:Horizontal** **4:Vertical** **5:Tangent(** **6:DrawF** **7:Shade(** **8:DrawInv** **9:Circle(** **0:Text(** **A:Pen**

**POINTS** **1:Pt-On(** **2:Pt-Off(** **3:Pt-Change(** **4:Pxl-On(** **5:Pxl-Off(** **6:Pxl-Change(** **7:pxl-Test(**

**STO** **1:StorePic** **2:RecallPic** **3:StoreGDB** **4:RecallGDB**

**VARS** **1:Window** **2:Zoom** **3:GDB** **4:Picture** **5:Statistics** **6:Table** **7:String**

**Y-VARS** **1:Function** **2:Parametric** **3:Polar** **4:On/Off**

Page 711

**TI-83 Plus Tables and Reference Information 708 **

**VARS**

**(Window)** **X/Y** **1:Xmin** **2:Xmax** **3:Xscl** **4:Ymin** **5:Ymax** **6:Yscl** **7:Xres** **8:**@**X** **9:**@**Y** **0:XFact** **A:YFact**

**(Window)** **T/**q **1:Tmin** **2:Tmax** **3:Tstep** **4:**q**min** **5:**q**max** **6:**q**step**

**(Window)** **U/V/W** **1:u(nMin)** **2:v(nMin)** **3:w(nMin)** **4:nMin** **5:nMax** **6:PlotStart** **7:PlotStep**

**VARS**

**(Zoom)** **ZX/ZY** **1:ZXmin** **2:ZXmax** **3:ZXscl** **4:ZYmin** **5:ZYmax** **6:ZYscl** **7:ZXres**

**(Zoom)** **ZT/Z**q **1:ZTmin** **2:ZTmax** **3:ZTstep** **4:Z**q**min** **5:Z**q**max** **6:Z**q**step**

**(Zoom)** **ZU** **1:Zu(nMin)** **2:Zv(nMin)** **3:Zw(nMin)** **4:ZnMin** **5:ZnMax** **6:ZPlotStart** **7:ZPlotStep**

Page 712

**TI-83 Plus Tables and Reference Information 709 **

**VARS**

**(GDB)** **GRAPH DATABASE** **1:GDB1** **2:GDB2** **...** **9:GDB9** **0:GDB0**

**(Picture** **)** **PICTURE** **1:Pic1** **2:Pic2** **...** **9:Pic9** **0:Pic0**

Page 713

**TI-83 Plus Tables and Reference Information 710 **

**VARS**

**(Statistics)** **XY** **1:n** **2:v** **3:Sx** **4:sx** **5:w** **6:Sy** **7:sy** **8:minX** **9:maxX** **0:minY** **A:maxY**

**(Statistics)** **G** **1:Gx** **2:Gx2** **3:Gy** **4:Gy2** **5:Gxy**

**(Statistics)** **EQ** **1:RegEQ** **2:a** **3:b** **4:c** **5:d** **6:e** **7:r** **8:r2**

**9:R2**

**(Statistics)** **TEST** **1:p** **2:z** **3:t** **4:c2**

**5:** **6:df** **7:** **8:1** **9:2** **0:s** **A:1** **B:2** **C:Sx1** **D:Sx2** **E:Sxp** **F:n1** **G:n2** **H:lower** **I:upper**

**(Statistics)** **PTS** **1:x1** **2:y1** **3:x2** **4:y2** **5:x3** **6:y3** **7:Q1** **8:Med** **9:Q3**

Page 714

**TI-83 Plus Tables and Reference Information 711 **

**VARS** **(Table)** **TABLE** **1:TblStart** **2:@Tbl** **3:TblInput**

**(String)** **STRING** **1:Str1** **2:Str2** **3:Str3** **4:Str4** **...** **9:Str9** **0:Str0**

**Y-VARS**

**(Function)** **FUNCTION** **1:Y1** **2:Y2** **3:Y3** **4:Y4** **...** **9:Y9** **0:Y0**

**(Parametric)** **PARAMETRIC** **1:X1T** **2:Y1T** **3:X2T** **4:Y2T** **...** **A:X6T** **B:Y6T**

**(Polar)** **POLAR** **1:r1** **2:r2** **3:r3** **4:r4** **5:r5** **6:r6**

**(On/Off)** **ON/OFF** **1:FnOn** **2:FnOff**

Page 715

**TI-83 Plus Tables and Reference Information 712 **

**y = **

**DISTR** **1:normalpdf(** **2:normalcdf(** **3:invNorm(** **4:tpdf(** **5:tcdf(** **6:c2pdf(** **7:c2cdf(** **8:pdf(** **9:cdf(** **0:binompdf(** **A:binomcdf(** **B:poissonpdf(** **C:poissoncdf(** **D:geometpdf(** **E:geometcdf(**

**DRAW** **1:ShadeNorm(** **2:Shade_t(** **3:Shadec2(** **4:Shade(**

Page 716

**TI-83 Plus Tables and Reference Information 713 **

**1:Finance** **2:CBL/CBR**

**Finance**

**CBL/CBR**

**CALC** **1:TVM** **Solver** **2:tvm_Pmt** **3:tvm_** **4:tvm_PV** **5:tvm_** **6:tvm_FV** **7:npv(** **8:irr(** **9:bal(** **0:GPrn(** **A:GInt(** **B:4Nom(** **C:4Eff(** **D:dbd(** **E:Pmt_End** **F:Pmt_Bgn**

**VARS** **1:** **2:** **3:PV** **4:PMT** **5:FV** **6:P/Y** **7:C/Y**

**1:GAUGE** **2:DATA LOGGER** **3:CBR** **4:QUIT**

Page 717

**TI-83 Plus Tables and Reference Information 714 **

**y L **

**MEMORY**

**MEMORY** **1:About** **2:Mem Mgmt/Del** **3:Clear Entries** **4:ClrAllLists** **5:Archive** **6:UnArchive** **7:Reset** **8:Group**

**(Mem Mgmt/Del)** **RAM FREE 25631** **ARC FREE 131069** **1:All** **2:Real** **3:Complex** **4:List** **5:Matrix** **6:Y-Vars** **7:Prgm** **8:Pic** **9:GDB** **0:String** **A:Apps** **B:AppVars** **C:Group**

Page 718

**TI-83 Plus Tables and Reference Information 715 **

**MEMORY (Reset****)**

**RAM** **1:All RAM** **2:Defaults**

**ARCHIVE** **1:Vars** **2:Apps** **B:Both**

**ALL** **1:All Memory**

**Resetting RAM** **erases all data** **and programs from** **RAM.**

**Resetting Both** **erases all data,** **programs and Apps** **from Archive.**

**Resetting ALL** **erases all data,** **programs and Apps** **from RAM and** **Archive.**

**RAM**

**RESET RAM** **1:No** **2:Reset**

**RESET DEFAULTS** **1:No** **2:Reset**

**Resetting RAM** **erases all data** **and programs from** **RAM.**

Page 719

**TI-83 Plus Tables and Reference Information 716 **

**ARCHIVE**

**RESET ARC VARS** **1:No** **2:Reset**

**RESET ARC APPS** **1:No** **2:Reset**

**RESET ARC BOTH** **1:No** **2:Reset**

**Resetting Vars** **erases all data** **and programs from** **Archive.**

**Resetting Apps** **erases all Apps** **from Archive.**

**Resetting Both** **erases all data,** **programs and Apps** **from Archive.**

**ALL**

**RESET MEMORY** **1:No** **2:Reset** **Resetting ALL** **will delete all** **data, programs &** **Apps from RAM &** **Archive.**

**MEMORY (GROUP...)**

**GROUP UNGROUP** **1:Create New**

Page 720

**TI-83 Plus Tables and Reference Information 717 **

**MEMORY**

**(UNGROUP...)**

**1:***name* **2:***name* **...**

**y N **

**CATALOG** **cosh(** **coshL1(** **...** **Equ4String(** **expr(** **...** **inString(** **...** **length(** **...** **sinh(** **sinhL1(** **...** **String4Equ(** **sub(** **...** **tanh(** **tanhL1(**

Page 721

**TI-83 Plus Tables and Reference Information 718 **

**Variables **

**User Variables**

**The TI-83 Plus uses the variables listed below in various ways. Some variables are restricted to specific data types. **

**The variables A through Z and q are defined as real or complex numbers. You may store to them. The TI-83 Plus can update X, Y, R, q, and T during graphing, so you may want to avoid using these variables to store nongraphing data. **

**The variables (list names) L1 through L6 are restricted to lists; you cannot store another type of data to them. **

**The variables (matrix names) [A] through [J] are restricted to matrices; you cannot store another type of data to them. **

**The variables Pic1 through Pic9 and Pic0 are restricted to pictures; you cannot store another type of data to them. **

**The variables GDB1 through GDB9 and GDB0 are restricted to graph databases; you cannot store another type of data to them. **

**The variables Str1 through Str9 and Str0 are restricted to strings; you cannot store another type of data to them.**

Page 722

**TI-83 Plus Tables and Reference Information 719 **

**Except for system variables, you can store any string of characters, functions, instructions, or variables to the functions Yn, (1 through 9, and 0), XnT/YnT (1 through 6), rn (1 through 6), u(n), v(n), and w(n) directly or through the Y= editor. The validity of the string is determined when the function is evaluated. **

**Archive Variables**

**You can store data, programs or any variable from RAM to user data archive memory where they cannot be edited or deleted inadvertantly. Archiving also allows you to free up RAM for variables that may require additional memory. The names of archived variables are preceded by an asterisk * indicating they are in user data archive. **

**System Variables**

**The variables below must be real numbers. You may store to them. Since the TI-83 Plus can update some of them, as the result of a ZOOM, for example, you may want to avoid using these variables to store nongraphing data. **

** Xmin, Xmax, Xscl, @X, XFact, Tstep, PlotStart, nMin, and other window variables. **

** ZXmin, ZXmax, ZXscl, ZTstep, ZPlotStart, Zu(nMin), and other ZOOM variables.**

Page 723

**TI-83 Plus Tables and Reference Information 720 **

**The variables below are reserved for use by the TI-83 Plus. You cannot store to them. **

**n**, **v**, **Sx**, **sx**, **minX**, **maxX**, **Gy**, **Gy2**, **Gxy**, **a**, **b**, **c**, **RegEQ**, **x1**, **x2**, **y1**, **z**, **t**, **F**, **c2**, ,** v1**, **Sx1**, **n1**, **lower**, **upper**,** r2**, **R2** and other statistical variables.

Page 724

**TI-83 Plus Tables and Reference Information 721 **

**Statistics Formulas **

**This section contains statistics formulas for the Logistic and SinReg regressions, ANOVA, 2.SampTest, and 2.SampTTest. **

**Logistic**

**The logistic regression algorithm applies nonlinear recursive least- squares techniques to optimize the following cost function: **

**2 **

**1 1 = **

**+ = **

*N*

*i* *i*

*ibx* *y*

*ae*

*c* *J*

**which is the sum of the squares of the residual errors, **

**where: x = the independent variable list y = the dependent variable list N = the dimension of the lists **

**This technique attempts to estimate the constants a, b, and c recursively to make J as small as possible.**

Page 725

**TI-83 Plus Tables and Reference Information 722 **

**SinReg**

**The sine regression algorithm applies nonlinear recursive least-squares techniques to optimize the following cost function: **

**( )[ ]2 **

**1 **

**sin = **

**++= N **

*i* *ii* *ydcbxaJ*

**which is the sum of the squares of the residual errors, **

**where: x = the independent variable list y = the dependent variable list N = the dimension of the lists **

**This technique attempts to recursively estimate the constants a, b, c, and d to make J as small as possible. **

**ANOVA(**

**The ANOVA statistic is: **

** MSError **

*MSFactor*=

Page 726

**TI-83 Plus Tables and Reference Information 723 **

**The mean squares ( MS) that make up are: **

*dfFactor*

*SSFactor* *MSFactor* =

*dfError*

*SSError* *MSError* =

**The sum of squares ( SS) that make up the mean squares are: **

** = **

**= I **

*i* *ii* *xxnSSFactor*

**1 **

**2)( **

** = **

**= I **

*i* *ii* *xSnSSError*

**1 **

**2)1( **

**The degrees of freedom df that make up the mean squares are: **

**fornumerator1 dfIdfFactor == **

**forrdenominato)1( 1 **

*dfndfError* *I*

*i* *i* ==

**= **

Page 727

**TI-83 Plus Tables and Reference Information 724 **

**where: I = number of populations xi = the mean of each list **

*Sxi* = the standard deviation of each list *ni* = the length of each list *x* = the mean of all lists

**2.SampTest**

**Below is the definition for the 2.SampTest. **

*Sx*1, *Sx*2 = Sample standard deviations having *n*1-1 and *n*2-1 degrees of freedom *df*, respectively.

** = -statistic = 2 **

**2 **

**1 **

*Sx*

*Sx*

*df*(*x, n*1-1*, n*2-1) = *pdf*( ) with degrees of freedom *df*, *n*1-1, and * n*2-1

*p* = reported *p* value

Page 728

**TI-83 Plus Tables and Reference Information 725 **

**2**.**SampTest** for the alternative hypothesis s1 > s2.

**= F **

*dxnnxfp* )1,1,( 21

**2**.**SampTest** for the alternative hypothesis s1 < s2.

** = F **

*dxnnxfp* 0

**21 )1,1,( **

**2**.**SampTest** for the alternative hypothesis s1 s2. Limits must satisfy

**the following: **

**== bnd **

*bnd*

*U*

*L*

*dxnnxfdxnnxf* *p*

**)1,1,()1,1,( 2 **

**21 0 **

**21 **

**where: [ Lbnd,Ubnd] = lower and upper limits **

**The -statistic is used as the bound producing the smallest integral. The remaining bound is selected to achieve the preceding integrals equality relationship.**

Page 729

**TI-83 Plus Tables and Reference Information 726 **

**2.SampTTest**

**The following is the definition for the 2.SampTTest. The two-sample t statistic with degrees of freedom df is: **

*S*

*xx* *t* 21 =

**where the computation of S and df are dependent on whether the variances are pooled. If the variances are not pooled: **

**2 **

**22 **

**1 **

**21 **

*n*

*Sx*

*n*

*Sx* *S* +=

**2 **

**2 **

**22 **

**2 **

**2 **

**1 **

**21 **

**1 **

**2 **

**2 **

**22 **

**1 **

**21 **

**1 **

**1 **

**1 **

**1 **

** + **

** + **

**= **

*n*

*Sx*

*nn*

*Sx*

*n*

*n*

*Sx*

*n*

*Sx*

*df*

Page 730

**TI-83 Plus Tables and Reference Information 727 **

**otherwise: **

*df*

*SxnSxn* *Sxp*

**222211 )1()1( += **

*pSx* *nn*

*S* 21

**11 += **

**221 += nndf **

**and Sxp is the pooled variance.**

Page 731

**TI-83 Plus Tables and Reference Information 728 **

**Financial Formulas **

**This section contains financial formulas for computing time value of money, amortization, cash flow, interest-rate conversions, and days between dates. **

**Time Value of Money**

**[ ] 1))1(ln( = + xyei **

**where: PMT 0 y = C/Y P/Y x = (.01 I%) C/Y **

*C/Y* = compounding periods per year *P/Y* = payment periods per year *I%* = interest rate per year

**1)( )1( = NPVFVi **

**where: PMT = 0 **

**The iteration used to compute i: **

*N* *N*

*i* *iFV* *i*

*i* *GPMTPV*

**++ **

** ++= )1( **

**)1(1 0**

Page 732

**TI-83 Plus Tables and Reference Information 729 **

**[ ]1/ 100% ))1ln(( = + xyeYCI **

**where: x = i y = P/Y C/Y **

*kiGi* += 1

**where: k = 0 for end-of-period payments k = 1 for beginning-of-period payments **

**)1(ln **

**ln **

*i*

*iPVGPMT*

*iFVGPMT*

*N* *i*

*i*

**+ **

**= + **

**where: i 0 **

*PMTFVPVN* += )(

**where: i = 0 **

** + **

**++= **

**1)1( Ni i **

*FVPV* *PV*

*G*

*i* *PMT*

Page 733

**TI-83 Plus Tables and Reference Information 730 **

**where: i 0 **

*NFVPVPMT* += )(

**where: i = 0 **

*i*

*GPMT*

*i* *FV*

*i*

*GPMT* *PV* *i*

*N* *i*

**+ **

** = **

**)1( **

**1 **

**where: i 0 **

**)( NPMTFVPV += **

**where: i = 0 **

** ++= **

*i*

*GPMT* *PVi*

*i*

*GPMT* *FV* *iNi* )1(

**where: i 0 **

**)( NPMTPVFV += **

**where: i = 0**

Page 734

**TI-83 Plus Tables and Reference Information 731 **

**Amortization**

**If computing bal(), pmt2 = npmt **

**Let bal(0) = RND(PV) **

**Iterate from m = 1 to pmt2 **

**+= = **

**)(I)1()( **

**))]1((12[I **

**m **

**m **

*PMTRNDmbalmbal*

*mbaliRNDRND*

**then: **

**)2()( pmtbalbal = **

**)1()2()(Pr pmtbalpmtbaln = **

**)(Pr)()112()( nPMTRNDpmtpmtInt +=**

Page 735

**TI-83 Plus Tables and Reference Information 732 **

**where: RND = round the display to the number of decimal places **

**selected **

*RND12* = round to 12 decimal places

**Balance, principal, and interest are dependent on the values of PMT, PV, , and pmt1 and pmt2. **

**Cash Flow**

** = **

** +++= **

*N*

*j*

*n* *S*

*j* *i*

*i* *iCFCFnpv*

*j* *j*

**1 0 **

**))1(1( )1()( 1 **

**where: **

**= **

**= = **

**00 **

**1 1 **

*j*

*jn* *S*

*j*

*i* *i*

*j*

**Net present value is dependent on the values of the initial cash flow ( CF0), subsequent cash flows (CFj), frequency of each cash flow (nj), and the specified interest rate (i). **

*irr*() = 100 *i*, where *i* satisfies *npv*() = 0

Page 736

**TI-83 Plus Tables and Reference Information 733 **

**Internal rate of return is dependent on the values of the initial cash flow ( CF0) and subsequent cash flows (CFj). **

*i* = *I*% 100

**Interest Rate Conversions**

**4 Eff = )1(100 )1(ln + xCPe **

**where: x = .01 Nom CP **

**4 Nom = [ ]1100 )1(ln1 + xCPeCP **

**where: x = .01 Eff Eff = effective rate CP = compounding periods **

*Nom* = *nominal rate*

**Days between Dates**

**With the dbd( function, you can enter or compute a date within the range Jan. 1, 1950, through Dec. 31, 2049.**

Page 737

**TI-83 Plus Tables and Reference Information 734 **

**Actual/actual day-count method** (assumes actual number of days per month and actual number of days per year):

*dbd*( (days between dates) = Number of Days II - Number of Days I

**Number of Days I = ( Y1-YB) 365 + (number of days MB to M1) + DT1 **

**+ 4 **

**)1( YBY **

**Number of Days II = ( Y2-YB) 365 + (number of days MB to M2) + DT2 **

**+ 4 **

**)2( YBY **

**where: M1 = month of first date DT1 = day of first date **

*Y*1 = year of first date *M*2 = month of second date

*DT*2 = day of second date *Y*2 = year of second date

*MB* = base month (January) *DB* = base day (1) *YB* = base year (first year after leap year)

Page 738

**TI-83 Plus General Information 735 **

**Appendix B: General Information **

**Battery Information **

**When to Replace the Batteries**

**The TI-83 Plus uses five batteries: four AAA alkaline batteries and one lithium battery. The lithium battery provides auxiliary power to retain memory while you replace the AAA batteries. **

**When the battery voltage level drops below a usable level, the TI-83 Plus: **

**Displays this message when you turn on the unit. **

**Displays this message when you attempt to download an application. **

**Message A Message B**

Page 739

**TI-83 Plus General Information 736 **

**After Message A is first displayed, you can expect the batteries to function for about one or two weeks, depending on usage. (This one- week to two-week period is based on tests with alkaline batteries; the performance of other kinds of batteries may vary.) **

**The low-battery message continues to be displayed each time you turn on the unit until you replace the batteries. If you do not replace the batteries within about two weeks, the calculator may turn off by itself or fail to turn on until you install new batteries. **

**If Message B is displayed, you must to replace the batteries immediately to successfully download an application. **

**Replace the lithium battery every three or four years. **

**Effects of Replacing the Batteries**

**Do not **remove both types of batteries (AAA and lithium auxiliary) at the same time. **Do not** allow the batteries to lose power completely. If you follow these guidelines and the steps for replacing batteries, you can replace either type of battery without losing any information in memory.

Page 740

**TI-83 Plus General Information 737 **

**Battery Precautions**

**Take these precautions when replacing batteries. **

** Do not leave batteries within reach of children **

** Do not mix new and used batteries. Do not mix brands (or types within brands) of batteries. **

** Do not mix rechargeable and nonrechargeable batteries. **

** Install batteries according to polarity (+ and N) diagrams. **

** Do not place nonrechargeable batteries in a battery recharger. **

** Properly dispose of used batteries immediately. Do not leave them within the reach of children. **

** Do not incinerate or dismantle batteries. **

**Replacing the Batteries**

**To replace the batteries, follow these steps. **

**1. Turn off the calculator. Replace the slide cover over the keyboard to avoid inadvertently turning on the calculator. Turn the back of the calculator toward you. **

**2. Hold the calculator upright, push downward on the latch on the top of the battery cover with your finger, and then pull the cover toward you.**

Page 741

**TI-83 Plus General Information 738 **

**Note:** To avoid loss of information stored in memory, you must turn off the calculator. Do not remove the AAA batteries and the lithium battery simultaneously.

**3. Replace all four AAA alkaline batteries simultaneously. Or, replace the lithium battery. **

** To replace the AAA alkaline batteries, remove all four discharged AAA batteries and install new ones according to the polarity (+ and N) diagram in the battery compartment. **

** To replace the lithium battery, remove the screw from the lithium- battery cover, and then remove the cover. Install the new battery, + side up. Replace the cover and secure it with the screw. Use a CR1616 or CR1620 (or equivalent) lithium battery. **

**4. Replace the battery compartment cover. Turn the calculator on and adjust the display contrast, if necessary.**

Page 742

**TI-83 Plus General Information 739 **

**In Case of Difficulty **

**Handling a Difficulty**

**To handle a difficulty, follow these steps. **

**1. If you cannot see anything on the screen, the contrast may need to be adjusted. **

**To darken the screen, press and release y, and then press and hold } until the display is sufficiently dark. **

**To lighten the screen, press and release y, and then press and hold until the display is sufficiently light. **

**2. If an error menu is displayed, follow the steps in Chapter 1. Refer to the Error Conditions table for details about specific errors, if necessary. **

**3. If the busy indicator (dotted line) is displayed, a graph or program has been paused; the TI-83 Plus is waiting for input. Press to continue or press to break. **

**4. If a checkerboard cursor ( # ) is displayed, then either you have entered the maximum number of characters in a prompt, or memory is full. If memory is full:**

Page 743

**TI-83 Plus General Information 740 **

** Press y L 2 to display the MEMORY MANAGEMENT DELETE menu. **

** Select the type of data you want to delete, or select 1:All for a list of all variables of all types. A screen is displayed listing each variable of the type you selected and the number of bytes each variable is using. **

** Press } and to move the selection cursor ( 4) next to the item you want to delete, and then press {. (Chapter 18). **

**5. If the calculator does not seem to work at all, be sure the batteries are fresh and that they are installed properly. Refer to battery information on pages 736 and 737. **

**6. If the calculator still doesnt work even though you are sure the batteries are sufficiently charged, you can try the two solutions in the order they are presented. **

** Download calculator system software as follows: **

**a. Remove one battery from the calculator and then press and hold the { key while re-installing the battery. This will force the calculator to accept a download of system software. **

**b. Connect your calculator to a personal computer with the TI.GRAPH LINK accessory to download current or new software code to your calculator.**

Page 744

**TI-83 Plus General Information 741 **

** II. If the above solution does not work, reset all memory as follows: **

**a. Remove one battery from the calculator and then press and hold down the key while re-installing the battery. While continuing to hold down the key, press and hold down the key. When the home screen is displayed, release the keys. **

**b. Press y L to display the MEMORY menu. **

**c. Select 7:Reset to display the RAM ARCHIVE ALL menu. **

**d. Press ~ ~ to display the ALL menu. **

**e. Select 1:All Memory to display the RESET MEMORY menu. **

**f. To continue with the reset, select 2:Reset. The message MEM cleared is displayed on the home screen.**

Page 745

**TI-83 Plus General Information 742 **

**Error Conditions **

**When the TI-83 Plus detects an error, it displays ERR:message and an error menu. Chapter 1 describes the general steps for correcting errors. This table contains each error type, possible causes, and suggestions for correction. **

**Error Type** **Possible Causes and Suggested Remedies**

**ARCHIVED** You have attempted to use, edit, or delete an archived variable. For example, dim(L1) is an error if L1 is archived.

**ARCHIVE FULL** You have attempted to archive a variable and there is not enough space in archive to receive it.

**ARGUMENT** A function or instruction does not have the correct number of arguments. See Appendix A and the appropriate chapter.

**BAD ADDRESS** You have attempted to send or receive an application and an error (e.g. electrical interference) has occurred in the transmission.

Page 746

**TI-83 Plus General Information 743 **

**Error Type** **Possible Causes and Suggested Remedies**

**BAD GUESS** In a **CALC** operation, you specified a **Guess** that is not between **Left Bound** and **Right Bound**.

** For the solve( function or the equation solver, you specified a guess that is not between lower and upper. **

** Your guess and several points around it are undefined. **

**Examine a graph of the function. If the equation has a solution, change the bounds and/or the initial guess. **

**BOUND** In a **CALC** operation or with **Select(**, you defined **Left Bound** > **Right Bound**.

** In fMin(, fMax(, solve(, or the equation solver, you entered lower upper. **

**BREAK** You pressed the key to break execution of a program, to halt a **DRAW** instruction, or to stop evaluation of an expression.

Page 747

**TI-83 Plus General Information 744 **

**Error Type** **Possible Causes and Suggested Remedies**

**DATA TYPE** You entered a value or variable that is the wrong data type. For a function (including implied multiplication) or an

**instruction, you entered an argument that is an invalid data type, such as a complex number where a real number is required. See Appendix A and the appropriate chapter. **

** In an editor, you entered a type that is not allowed, such as a matrix entered as an element in the stat list editor. See the appropriate chapter. **

** You attempted to store an incorrect data type, such as a matrix, to a list. **

**DIM MISMATCH** You attempted to perform an operation that references more than one list or matrix, but the dimensions do not match.

**DIVIDE BY 0** You attempted to divide by zero. This error is not returned during graphing. The TI-83 Plus allows for undefined values on a graph.

** You attempted a linear regression with a vertical line.**

Page 748

**TI-83 Plus General Information 745 **

**Error Type** **Possible Causes and Suggested Remedies**

**DOMAIN** You specified an argument to a function or instruction outside the valid range. This error is not returned during graphing. The TI-83 Plus allows for undefined values on a graph. See Appendix A and the appropriate chapter.

** You attempted a logarithmic or power regression with a LX or an exponential or power regression with a LY. **

** You attempted to compute GPrn( or GInt( with pmt2 < pmt1. **

**DUPLICATE** You attempted to create a duplicate group name.

**Duplicate Name** A variable you attempted to transmit cannot be transmitted because a variable with that name already exists in the receiving unit.

**EXPIRED** You have attempted to run an application with a limited trial period which has expired.

Page 749

**TI-83 Plus General Information 746 **

**Error Type** **Possible Causes and Suggested Remedies**

**Error in Xmit** The TI-83 Plus was unable to transmit an item. Check to see that the cable is firmly connected to both units and that the receiving unit is in receive mode.

** You pressed to break during transmission. **

** You attempted to perform a backup from a TI.82 to a TI-83 Plus. **

** You attempted to transfer data (other than L1 through L6) from a TI-83 Plus to a TI.82. **

** You attempted to transfer L1 through L6 from a TI-83 Plus to a TI.82 without using 5:Lists to TI82 on the LINK SEND menu. **

**ID NOT FOUND** This error occurs when the SendID command is executed but the proper calculator ID cannot be found.

**ILLEGAL NEST** You attempted to use an invalid function in an argument to a function, such as **seq(** within *expression* for **seq(**.

**INCREMENT** The increment in **seq(** is 0 or has the wrong sign. This error is not returned during graphing. The TI-83 Plus allows for undefined values on a graph.

** The increment in a For( loop is 0.**

Page 750

**TI-83 Plus General Information 747 **

**Error Type** **Possible Causes and Suggested Remedies**

**INVALID** You attempted to reference a variable or use a function where it is not valid. For example, **Y***n* cannot reference **Y**, **Xmin**, **@X**, or **TblStart**.

** You attempted to reference a variable or function that was transferred from the TI.82 and is not valid for the TI-83 Plus. For example, you may have transferred UnN1 to the TI-83 Plus from the TI.82 and then tried to reference it. **

** In Seq mode, you attempted to graph a phase plot without defining both equations of the phase plot. **

** In Seq mode, you attempted to graph a recursive sequence without having input the correct number of initial conditions. **

** In Seq mode, you attempted to reference terms other than (nN1) or (nN2). **

** You attempted to designate a graph style that is invalid within the current graph mode. **

** You attempted to use Select( without having selected (turned on) at least one xyLine or scatter plot.**

Page 751

**TI-83 Plus General Information 748 **

**Error Type** **Possible Causes and Suggested Remedies**

**INVALID DIM** You specified dimensions for an argument that are not appropriate for the operation.

** You specified a list dimension as something other than an integer between 1 and 999. **

** You specified a matrix dimension as something other than an integer between 1 and 99. **

** You attempted to invert a matrix that is not square. **

**ITERATIONS** The **solve(** function or the equation solver has exceeded the maximum number of permitted iterations. Examine a graph of the function. If the equation has a solution, change the bounds, or the initial guess, or both.

** irr( has exceeded the maximum number of permitted iterations. **

** When computing , the maximum number of iterations was exceeded. **

**LABEL** The label in the **Goto** instruction is not defined with a **Lbl** instruction in the program.

Page 752

**TI-83 Plus General Information 749 **

**Error Type** **Possible Causes and Suggested Remedies**

**MEMORY** Memory is insufficient to perform the instruction or function. You must delete items from memory (Chapter 18) before executing the instruction or function.

**Recursive problems return this error; for example, graphing the equation Y1=Y1. **

**Branching out of an If/Then, For(, While, or Repeat loop with a Goto also can return this error because the End statement that terminates the loop is never reached. **

**MemoryFull** You are unable to transmit an item because the receiving units available memory is insufficient. You may skip the item or exit receive mode.

** During a memory backup, the receiving units available memory is insufficient to receive all items in the sending units memory. A message indicates the number of bytes the sending unit must delete to do the memory backup. Delete items and try again. **

**MODE** You attempted to store to a window variable in another graphing mode or to perform an instruction while in the wrong mode; for example, **DrawInv** in a graphing mode other than **Func**.

Page 753

**TI-83 Plus General Information 750 **

**Error Type** **Possible Causes and Suggested Remedies**

**NO SIGN CHNG** The **solve(** function or the equation solver did not detect a sign change.

** You attempted to compute when FV, (PMT), and PV are all 0, or when FV, (PMT), and PV are all 0. **

** You attempted to compute irr( when neither CFList nor CFO is > 0, or when neither CFList nor CFO is < 0. **

**NONREAL ANS** In **Real** mode, the result of a calculation yielded a complex result. This error is not returned during graphing. The TI-83 Plus allows for undefined values on a graph.

**OVERFLOW** You attempted to enter, or you have calculated, a number that is beyond the range of the calculator. This error is not returned during graphing. The TI-83 Plus allows for undefined values on a graph.

**RESERVED** You attempted to use a system variable inappropriately. See Appendix A.

**SINGULAR MAT** A singular matrix (determinant = 0) is not valid as the argument for **L1**.

** The SinReg instruction or a polynomial regression generated a singular matrix (determinant = 0) because it could not find a solution, or a solution does not exist. **

**This error is not returned during graphing. The TI-83 Plus allows for undefined values on a graph.**

Page 754

**TI-83 Plus General Information 751 **

**Error Type** **Possible Causes and Suggested Remedies**

**SINGULARITY** *expression* in the **solve(** function or the equation solver contains a singularity (a point at which the function is not defined). Examine a graph of the function. If the equation has a solution, change the bounds or the initial guess or both.

**STAT** You attempted a stat calculation with lists that are not appropriate.

** Statistical analyses must have at least two data points. **

** Med.Med must have at least three points in each partition. **

** When you use a frequency list, its elements must be 0. **

** ( Xmax N Xmin) Xscl must be 47 for a histogram. **

**STAT PLOT** You attempted to display a graph when a stat plot that uses an undefined list is turned on.

**SYNTAX** The command contains a syntax error. Look for misplaced functions, arguments, parentheses, or commas. See Appendix A and the appropriate chapter.

**TOL NOT MET** You requested a tolerance to which the algorithm cannot return an accurate result.

Page 755

**TI-83 Plus General Information 752 **

**Error Type** **Possible Causes and Suggested Remedies**

**UNDEFINED** You referenced a variable that is not currently defined. For example, you referenced a stat variable when there is no current calculation because a list has been edited, or you referenced a variable when the variable is not valid for the current calculation, such as **a** after **Med.Med**.

**VALIDATION** Electrical interference caused a link to fail or this calculator is not authorized to run the application.

**VARIABLE** You have tried to archive a variable that cannot be archived or you have have.tried to unarchive an application or group.

**Examples of variables that cannot be archived include: **

** Real numbers LRESID, R, T, X, Y, Theta, Statistic variables under Vars, STATISTICS menu, Yvars, and the AppIdList. **

**VERSION** You have attempted to receive an incompatible variable version from another calculator.

Page 756

**TI-83 Plus General Information 753 **

**Error Type** **Possible Causes and Suggested Remedies**

**WINDOW RANGE** A problem exists with the window variables.

** You defined Xmax Xmin or Ymax Ymin. **

** You defined qmax qmin and qstep > 0 (or vice versa). **

** You attempted to define Tstep=0. **

** You defined Tmax Tmin and Tstep > 0 (or vice versa). **

** Window variables are too small or too large to graph correctly. You may have attempted to zoom in or zoom out to a point that exceeds the TI-83 Pluss numerical range. **

**ZOOM** A point or a line, instead of a box, is defined in **ZBox.**

** A ZOOM operation returned a math error.**

Page 757

**TI-83 Plus General Information 754 **

**Accuracy Information **

**Computational Accuracy**

**To maximize accuracy, the TI-83 Plus carries more digits internally than it displays. Values are stored in memory using up to 14 digits with a two- digit exponent. **

** You can store a value in the window variables using up to 10 digits (12 for Xscl, Yscl, Tstep, and qstep). **

** Displayed values are rounded as specified by the mode setting with a maximum of 10 digits and a two-digit exponent. **

** RegEQ displays up to 14 digits in Float mode. Using a fixed-decimal setting other than Float causes RegEQ results to be rounded and stored with the specified number of decimal places. **

**Xmin** is the center of the leftmost pixel, **Xmax** is the center of the next-to- the-rightmost pixel. (The rightmost pixel is reserved for the busy indicator.) **@X** is the distance between the centers of two adjacent pixels.

** In Full screen mode, @X is calculated as (Xmax N Xmin) 94. In G.T split-screen mode, @X is calculated as (Xmax N Xmin) 46. **

** If you enter a value for @X from the home screen or a program in Full screen mode, Xmax is calculated as Xmin + @X 94. In G.T split- screen mode, Xmax is calculated as Xmin + @X 46.**

Page 758

**TI-83 Plus General Information 755 **

**Ymin** is the center of the next-to-the-bottom pixel; **Ymax** is the center of the top pixel. **@Y** is the distance between the centers of two adjacent pixels.

** In Full screen mode, @Y is calculated as (Ymax N Ymin) 62. In Horiz split-screen mode, @Y is calculated as (Ymax N Ymin) 30. In G.T split-screen mode, @Y is calculated as (Ymax N Ymin) 50. **

** If you enter a value for @Y from the home screen or a program in Full screen mode, Ymax is calculated as Ymin + @Y 62. In Horiz split- screen mode, Ymax is calculated as Ymin + @Y 30. In G.T split- screen mode, Ymax is calculated as Ymin + @Y 50. **

**Cursor coordinates are displayed as eight-character numbers (which may include a negative sign, decimal point, and exponent) when Float mode is selected. X and Y are updated with a maximum accuracy of eight digits. **

**minimum** and **maximum** on the **CALCULATE** menu are calculated with a tolerance of 1EL5; **f(x)dx **is calculated at 1EL3. Therefore, the result displayed may not be accurate to all eight displayed digits. For most functions, at least five accurate digits exist. For **fMin(**, **fMax(**, and **fnInt(** on the **MATH** menu and **solve(** in the **CATALOG**, the tolerance can be specified.

Page 759

**TI-83 Plus General Information 756 **

**Function Limits**

**Function** **Range of Input Values**

**sin** *x*, **cos** *x*, **tan** *x* 0 |*x*| < 1012 (radian or degree)

**sinL1** *x*, **cosL1** *x* L1 *x* 1

**ln** *x*, **log** *x* 10L100 < *x* < 10100

**e***x* L10100 < *x* 230.25850929940

**10***x* L10100 < *x* < 100

**sinh** *x*, **cosh** *x* |*x*| 230.25850929940

**tanh** *x* |*x*| < 10100

**sinhL1** *x* |*x*| < 5 1099

**coshL1** *x* 1 *x* < 5 1099

**tanhL1** *x* L1 < *x* < 1

*x *(real mode) 0 *x* < 10100

*x *(complex mode) |*x*| < 10100

*x***!** L.5 *x* 69, where *x* is a multiple of .5

Page 760

**TI-83 Plus General Information 757 **

**Function Results**

**Function** **Range of Result**

**sinL1** *x*, **tanL1** *x* L90 to 90 or Lp2 to p2 (radians)

**cosL1** *x* 0 to 180 or 0 to p (radians)

Page 761

**TI-83 Plus General Information 758 **

**Texas Instruments (TI) Support and Service **

**For General Information**

**Home Page: education.ti.com **

**KnowledgeBase and E-mail Inquiries: education.ti.com/support **

**Phone: (800) TI-CARES; (800) 842-2737 For U.S., Canada, Mexico, Puerto Rico, and Virgin Islands only **

**International Information: education.ti.com/support (Click the International Information link.) **

**For Technical Support**

**KnowledgeBase and Support by E-mail: education.ti.com/support **

**Phone (not toll-free): (972) 917-8324**

Page 762

**TI-83 Plus General Information 759 **

**For Product (hardware) Service**

**Customers in the U.S., Canada, Mexico, Puerto Rico and Virgin** **Islands:** Always contact TI Customer Support before returning a product for service.

**All other customers:** Refer to the leaflet enclosed with this product (hardware) or contact your local TI retailer/distributor.

Page 763

**TI-83 Plus General Information 760 **

**Warranty Information **

**Customers in the U.S. and Canada Only**

**One-Year Limited Warranty for Commercial Electronic Product**

**This Texas Instruments (TI) electronic product warranty extends only to the original purchaser and user of the product. **

**Warranty Duration. **This TI electronic product is warranted to the original purchaser for a period of one (1) year from the original purchase date.

**Warranty Coverage.** This TI electronic product is warranted against defective materials and construction. **THIS WARRANTY IS VOID IF THE PRODUCT HAS** **BEEN DAMAGED BY ACCIDENT OR UNREASONABLE USE, NEGLECT, IMPROPER** **SERVICE, OR OTHER CAUSES NOT ARISING OUT OF DEFECTS IN MATERIALS OR** **CONSTRUCTION.**

**Warranty Disclaimers. ANY IMPLIED WARRANTIES ARISING OUT OF THIS SALE,** **INCLUDING BUT NOT LIMITED TO THE IMPLIED WARRANTIES OF** **MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE, ARE LIMITED IN** **DURATION TO THE ABOVE ONE-YEAR PERIOD. TEXAS INSTRUMENTS SHALL NOT** **BE LIABLE FOR LOSS OF USE OF THE PRODUCT OR OTHER INCIDENTAL OR** **CONSEQUENTIAL COSTS, EXPENSES, OR DAMAGES INCURRED BY THE** **CONSUMER OR ANY OTHER USER.**

**Some states/provinces do not allow the exclusion or limitation of implied warranties or consequential damages, so the above limitations or exclusions may not apply to you.**

Page 764

**TI-83 Plus General Information 761 **

**Legal Remedies.** This warranty gives you specific legal rights, and you may also have other rights that vary from state to state or province to province.

**Warranty Performance.** During the above one (1) year warranty period, your defective product will be either repaired or replaced with a reconditioned model of an equivalent quality (at TIs option) when the product is returned, postage prepaid, to Texas Instruments Service Facility. The warranty of the repaired or replacement unit will continue for the warranty of the original unit or six (6) months, whichever is longer. Other than the postage requirement, no charge will be made for such repair and/or replacement. TI strongly recommends that you insure the product for value prior to mailing.

**Software.** Software is licensed, not sold. TI and its licensors do not warrant that the software will be free from errors or meet your specific requirements. **All software is provided AS IS.**

**Copyright.** The software and any documentation supplied with this product are protected by copyright.

**Australia & New Zealand Customers only**

**One-Year Limited Warranty for Commercial Electronic Product**

**This Texas Instruments electronic product warranty extends only to the original purchaser and user of the product. **

**Warranty Duration.** This Texas Instruments electronic product is warranted to the original purchaser for a period of one (1) year from the original purchase date.

Page 765

**TI-83 Plus General Information 762 **

**Warranty Coverage.** This Texas Instruments electronic product is warranted against defective materials and construction. This warranty is void if the product has been damaged by accident or unreasonable use, neglect, improper service, or other causes not arising out of defects in materials or construction.

**Warranty Disclaimers. Any implied warranties arising out of this sale,** **including but not limited to the implied warranties of merchantability and** **fitness for a particular purpose, are limited in duration to the above one-** **year period. Texas Instruments shall not be liable for loss of use of the** **product or other incidental or consequential costs, expenses, or** **damages incurred by the consumer or any other user.**

**Except as expressly provided in the One-Year Limited Warranty for this** **product, Texas Instruments does not promise that facilities for the repair** **of this product or parts for the repair of this product will be available.**

**Some jurisdictions do not allow the exclusion or limitation of implied warranties or consequential damages, so the above limitations or exclusions may not apply to you. **

**Legal Remedies.** This warranty gives you specific legal rights, and you may also have other rights that vary from jurisdiction to jurisdiction.

**Warranty Performance.** During the above one (1) year warranty period, your defective product will be either repaired or replaced with a new or reconditioned model of an equivalent quality (at TIs option) when the product is returned to the original point of purchase. The repaired or replacement unit will continue for the warranty of the original unit or six (6) months, whichever is longer. Other than your cost to return the product, no charge will be made for

Page 766

**TI-83 Plus General Information 763 **

**such repair and/or replacement. TI strongly recommends that you insure the product for value if you mail it. **

**Software.** Software is licensed, not sold. TI and its licensors do not warrant that the software will be free from errors or meet your specific requirements. All software is provided **AS IS**.

**Copyright.** The software and any documentation supplied with this product are protected by copyright.

**All Other Customers**

**For information about the length and terms of the warranty, refer to your package and/or to the warranty statement enclosed with this product, or contact your local Texas Instruments retailer/distributor.**

Page 767

**TI-83 Plus Index 764 **

**Index ! (factorial), 94, 692 " " (string indicator), 484 " (seconds notation), 97, 697 (annual interest rate variable), 444, **

**462 (degrees notation), 692 (division), 63, 696 (exponent), 14, 20, 661 (graph style, animate), 117 (graph style, dot), 117 (graph style, line), 117 (greater than or equal to), 101, 694 (less than or equal to), 101, 694 (multiplication), 63, 695 M (negation), 49, 66, 695 (not equal to), 101, 694 (number of payment periods **

**variable), 444, 462 p (pi), 66 (plot type, box), 371 (plot type, histogram), 370 (plot type, modified box), 370 (plot type, normal probability), 372 N (subtraction), 63, 696 (user-created list name symbol), 309, **

**668 ! Store, 29, 686 **

**(** (square root) , 64, 695 , (pixel mark), 235, 373 **L1** (inverse), 64, 271, 694 **c2.Test** (chi-square test), 412, 657 **c2cdf(** (chi-square cdf), 429, 657 **c2pdf(** (chi-square pdf), 428, 657 **cdf(**, 430, 662 **4Dec** (to decimal conversion), 67, 659 **!dim(** (assign dimension), 275, 301,

**660 DIST, 471 4DMS (to degrees/minutes/seconds), 99, **

**661 DREF, 471 4Eff( (to effective interest rate), 459, **

**662 f(x)dx operation on a graph, 153 4Frac (to fraction), 67, 664 GInt( (sum of interest), 455, 668 LIGHT, 471 @List(, 303, 669 LREF, 471 4Nom( (to nominal interest rate), 459, **

**672 pdf(, 429, 664 4Polar (to polar), 91, 675 GPrn( (sum of principal), 455, 676**

Page 768

**TI-83 Plus Index 765 **

**4Rect** (to rectangular), 91, 679 **row(**, 282, 680 **row+(**, 282, 680 **@Tbl** (table step variable), 205 **TEMP**, 471 **TREF**, 471 **VOLT**, 471 **VREF**, 471 **@X** window variable, 124 **@Y** window variable, 124 **'** (minutes notation), 97, 697 ( ) (parentheses), 48 **+** (addition), 63, 696 **+** (concatenation), 490, 696 **+** (pixel mark), 235, 373 **:** (colon), 504 **<** (less than), 101, 694 **=** (equal-to relational test), 101, 693 **>** (greater than), 101, 694 ** [ ]** (matrix indicator), 265 **^** (power), 64, 695 **{ }** (list indicator), 288 **1.PropZInt** (one-proportion *z* confidence

**interval), 410, 676 1.PropZTest (one-proportion z test), **

**402, 676 1.Var Stats (one-variable statistics), **

**357, 689 10^( (power of ten), 65, 695 2 (square) , 64, 694 **

**2.PropZInt** (two-proportion *z* confidence interval), 411, 676

**2.PropZTest** (two-proportion *z* test), 403, 677

**2.SampTest** (two-sample -Test), 414, 681

**2.SampTInt** (two-sample *t* confidence interval), 408, 681

**2.SampTTest** (two-sample *t* test), 400, 682

**2.SampZInt** (two-sample *z* confidence interval), 407, 682

**2.SampZTest** (two-sample z test), 399, 682

**2.Var Stats** (two-variable statistics), 358, 689

**3** (cube), 68, 693 **3(** (cube root), 68, 693

**A**

**a+b i** (rectangular complex mode), 24, 84, 656

**about, 596 above graph style(), 117 abs( (absolute value), 79, 90, 271, 655 accuracy information **

**computational and graphing, 754 function limits and results, 756 graphing, 132**

Page 769

**TI-83 Plus Index 766 **

**addition ( +), 63, 696 alpha cursor, 12 alpha-lock, 18 alternative hypothesis, 391 amortization **

**GInt(** (sum of interest), 455, 668 **GPrn( **(sum of principal), 455, 676 **bal(** (amortization balance), 454,

**656 calculating schedules, 454 formula, 731 **

**and** (Boolean operator), 103, 655 ANGLE menu, 97 angle modes, 22 **angle(**, 90, 655 animate graph style (), 117 **ANOVA(** (one-way variance analysis),

**417, 655 formula, 722 **

**Ans** (last answer), 36, 599, 655 APD (Automatic Power Down), 6 applications. *See* examples,

**applications Apps, 27, 598 AppVars, 27, 598 arccosine (cosL1(), 63 Archive, 30, 610, 655 **

**archive full error, 628, 742 garbage collection, 623 memory error, 623 **

**archived variables, 719 arcsine ( sinL1(), 63 arctangent (tanL1(), 63 Asm(, 537, 655 AsmComp(, 537, 655 AsmPrgm(, 537, 655 assembly language programs, 537 augment(, 277, 307, 656 Automatic Power Down (APD), 6 automatic regression equation, 353 automatic residual list (RESID), 352 axes format, sequence graphing, 187 axes, displaying (AxesOn, AxesOff), **

**127, 656 AxesOff, 127, 656 AxesOn, 127, 656 **

**B**

**backing up calculator memory, 638, 650 **

**bal(** (amortization balance), 454, 656 bar, 468 batteries, 7, 735 below graph style (), 117 **binomcdf(**, 431, 656 **binompdf(**, 430, 656 block, 623 Boolean logic, 103 box pixel mark (), 235, 373

Page 770

**TI-83 Plus Index 767 **

**Boxplot** plot type ( ), 371 busy indicator, 11

**C**

**C/Y** (compounding-periods-per-year variable), 444, 463

**CALCULATE menu, 147 Calculate output option, 388, 392 cash flow **

**calculating, 452 formula, 732 irr( (internal rate of return), 453, 668 npv( (net present value), 453, 673 **

**CATALOG, 481 CBL 2/CBL, 464 CBL/CBR **

**Quitting, 480 Running, 464 Selecting, 464 **

**CBL/CBR APP** menu, 467 CBR, 464, 533, 633, 665 check memory, 596 chi-square cdf (**c2cdf(**), 429, 657 chi-square pdf (**c2pdf(**), 428, 657 chi-square test (**c2.Test**), 412, 657 **Circle(** (draw circle), 228, 657 **Clear Entries**, 596, 657 clearing

**all lists ( ClrAllLists), 596, 657 **

**drawing ( ClrDraw), 217, 657 entries (Clear Entries), 596, 657 home screen (ClrHome), 532, 657 list (ClrList), 349, 658 table (ClrTable), 532, 658 **

**ClrAllLists** (clear all lists), 596, 657 **ClrDraw** (clear drawing), 217, 657 **ClrHome** (clear home screen), 532, 657 **ClrList** (clear list), 349, 658 **ClrTable** (clear table), 532, 658 coefficients of determination (**r2**, **R2**,

**354 colon separator ( :), 504 combinations (nCr), 93, 672 compiling an assembly program, 537, **

**655 complex **

**modes ( a+bi, re^qi), 24, 84, 656, 679 **

**numbers, 24, 84, 679 compounding-periods-per-year variable **

**( C/Y), 444, 463 concatenation (+), 490, 696 confidence intervals, 392 conj( (conjugate), 88, 658 Connected (plotting mode), 23, 658 connecting two calculators, 633 contrast (display), 8 convergence, sequence graphing, 195 conversions**

Page 771

**TI-83 Plus Index 768 **

**4Dec** (to decimal), 67, 659 **4DMS** (to degrees/minutes/ seconds),

**99, 661 4Eff (to effective interest rate), 459 4Frac (to fraction conversion), 67, **

**664 4Nom (to nominal interest rate **

**conversion), 459, 672 4Polar (to polar conversion), 91, 675 4Rect (to rectangular conversion), **

**91, 679 Equ4String( (equation-to-string **

**conversion), 491, 662 List4matr( (list-to-matrix **

**conversion), 279, 308, 670 Matr4list( (matrix-to-list conversion), **

**278, 308, 670 P4Rx(, P4Ry( (polar-to-rectangular **

**conversion), 100, 678 R4Pr(, R4Pq( (rectangular-to-polar **

**conversion), 100, 681 String4Equ( (string-to-equation **

**conversion), 493, 686 CoordOff, 126, 658 CoordOn, 126, 658 correlation coefficient (r), 354 cosL1( (arccosine), 63, 658 cos( (cosine), 63, 658 coshM1( (hyperbolic arccosine), 496, 658 cosh( (hyperbolic cosine), 496, 658 **

**cosine ( cos(), 63, 658 cross pixel mark (+), 235, 373 cube (3), 68, 693 cube root (3(), 68, 693 cubic regression (CubicReg), 359, 658 CubicReg (cubic regression), 359, 658 c*msum( (cumulative sum), 279, 303, **

**659 cumulative sum ( c*msum(), 279, 303, **

**659 cursors, 12, 18 **

**D**

**data collection methods, 468 options, 468 results, 471 starting & stopping, 479 **

**Data input option, 388, 390 data logger, 473 data points, 475 data results, 471 days between dates ( dbd(), 460, 659, **

**733 dbd( (days between dates), 460, 659, **

**733 decimal mode (float or fixed), 21 decrement and skip ( DS<(), 521, 661 definite integral, 70, 152, 165**

Page 772

**TI-83 Plus Index 769 **

**defragmenting, 622 Degree angle mode, 22, 97, 659 degrees notation (), 98, 692 delete variable contents (DelVar), 523, **

**659 deleting items from memory, 599 DelVar (delete variable contents), 659 DependAsk, 206, 209, 659 DependAuto, 206, 209, 659 derivative. See numerical derivative det( (determinant), 275, 659 determinant (det(), 275, 659 DiagnosticOff, 354, 660 DiagnosticOn, 354, 660 diagnostics display mode(r r2, R2), 354 differentiation, 72, 152, 165, 175 dim( (dimension), 275, 301, 660 dimensioning a list or matrix, 275, 301, **

**660 directions, 471 DIRECTNS, 471 Disp (display), 528, 529, 660 DispGraph (display graph), 530, 660 display contrast, 8 display cursors, 12 DispTable (display table), 530, 661 DISTR (distributions menu), 424 DISTR DRAW (distributions drawing **

**menu), 434 distribution functions **

**c2cdf(**, 429, 657 **c2pdf(**, 428, 657 **cdf(**, 430, 662 **pdf(**, 429, 664 **binomcdf(**, 431, 656 **binompdf(**, 430, 656 **geometcdf(**, 433, 665 **geometpdf(**, 433, 665 **invNorm(**, 426, 668 **normalcdf(**, 426, 672 **normalpdf(**, 425, 673 **poissoncdf(**, 432, 675 **poissonpdf(**, 432, 675 **tcdf(**, 427, 687 **tpdf(**, 427, 687

**distribution shading instructions Shade(, 437, 684 Shadec2(, 436, 684 Shade_t(, 435, 684 ShadeNorm(, 435, 684 **

**division (), 63, 696 DMS (degrees/minutes/seconds entry **

**notation), 97, 697 Dot (plotting mode), 23, 661 dot graph style (), 117 dot pixel mark (), 235, 373 dr/dq operation on a graph, 175 DRAW menu, 214 Draw output option, 388, 392 DRAW POINTS menu, 233**

Page 773

**TI-83 Plus Index 770 **

**DRAW STO (draw store menu), 239 DrawF (draw a function), 224, 661 drawing on a graph **

**circles ( Circle(), 228 line segments (Line(), 218 lines (Horizontal, Line(, Vertical), **

**221 pixels ( Pxl.Change, Pxl.Off, Pxl.On, **

**pxl.Test)**, 237 points **(Pt.Change**, **Pt.Off**, **Pt.On)**,

**233 tangents ( Tangent), 222 text (Text), 230 using Pen, 232 **

**DrawInv** (draw inverse), 224, 661 **DS<(** (decrement and skip), 521, 661 DuplicateName menu, 644 **dx/dt** operation on a graph, 152, 165 **dy/dx** operation on a graph, 152, 165,

**175 **

**E**

*e *(constant), 65 **e^(** (exponential), 65, 661 edit keys table, 17 **Else**, 514 **End**, 476, 515, 662 **Eng** (engineering notation mode), 20,

**662 **

**ENTRY (last entry key), 33 entry cursor, 12 EOS (Equation Operating System), 47 eqn (equation variable), 72 Equ4String( (equation-to-string **

**conversion), 491, 662 equal-to relational test ( =), 101, 693 Equation Operating System (EOS), 47 Equation Solver, 72 equations with multiple roots, 77 errors **

**diagnosing and correcting, 59 messages, 742 **

**examplesapplications area between curves, 578 areas of regular n-sided polygons, **

**588 box plots, 560 box with lid, 546 **

**defining a, 546 defining a table of values, 547 finding calculated maximum, 557 setting the viewing window, 551 tracing the graph, 553 zooming in on the graph, 555 zooming in on the table, 549 **

**cobweb attractors, 572 fundamental theorem of calculus, **

**584 guess the coefficients, 574**

Page 774

**TI-83 Plus Index 771 **

**inequalities, 566 mortgage payments, 592 parametric equations, ferris wheel **

**problem, 580 piecewise functions, 564 quadratic formula **

**converting to a fraction, 542 displaying complex results, 544 entering a calculation, 540 **

**Sierpinski triangle, 570 solving a system of nonlinear **

**equations, 568 unit circle and trig curves, 576 **

**examplesGetting Started coin flip, 61 compound interest, 442 drawing a tangent line, 212 financing a car, 440 forest and trees, 176 generating a sequence, 283 graphing a circle, 105 mean height of a population, 381 path of a ball, 154 pendulum lengths and periods, 315 polar rose, 166 roots of a function, 203 sending variables, 629 solving a system of linear equations, **

**256 unit circle, 246 **

**volume of a cylinder, 497 examplesmiscellaneous **

**calculating outstanding loan balances, 456 **

**convergence, 195 daylight hours in Alaska, 363 predator-prey model, 197 **

**exponential regression ( ExpReg), 361, 662 **

**expr(** (string-to-expression conversion), 491, 662

**ExpReg** (exponential regression), 361, 662

**expression, 13 converting from string ( expr(), 491, **

**662 turning on and off ( ExprOn, 128, **

**662 ExprOff (expression off), 128, 662 ExprOn (expression on), 128, 662 **

**F**

**factorial ( !), 94, 692 family of curves, 131 Fill(, 276, 663 FINANCE CALC menu, 446 FINANCE VARS menu, 462 financial functions **

**amortization schedules, 454**

Page 775

**TI-83 Plus Index 772 **

**cash flows, 452 days between dates, 460 interest rate conversions, 459 payment method, 461 time value of money (TVM), 448 **

**Fix** (fixed-decimal mode), 21, 663 fixed-decimal mode (**Fix**), 21, 663 **Float** (floating-decimal mode), 21, 663 floating-decimal mode (**Float**), 21, 663 **fMax(** (function maximum), 69, 663 **fMin(** (function minimum), 69, 663 **fnInt(** (function integral), 71, 663 **FnOff** (function off), 115, 663 **FnOn** (function on), 115, 664 **For(**, 515, 664 format settings, 125, 187 formulas

**amortization, 731 ANOVA, 722 cash flow, 732 days between dates, 733 factorial, 94 interest rate conversions, 733 logistic regression, 721 sine regression, 722 time value of money, 728 two-sample -Test, 724 two-sample t test, 726 **

**fPart(** (fractional part), 80, 273, 664 free-moving cursor, 132

**frequency, 357 Full (full-screen mode), 25, 664 full-screen mode (Full), 25, 664 Func (function graphing mode), 23, 664 function graphing **

**@X** and **@Y** window variables, 124 accuracy, 132 CALC (calculate menu), 147 defining and displaying, 107 defining in the Y= editor, 111 defining on the home screen, in a

**program, 112 deselecting, 114, 115 displaying, 108, 121, 129 evaluating, 113 family of curves, 131 format settings, 125 free-moving cursor, 132 graph styles, 117 maximum of ( fMax(), 69, 663 minimum of (fMin(), 663 modes, 23, 109, 664 moving the cursor to a value, 135 overlaying functions on a graph, **

**130 panning, 136 pausing or stopping a graph, 129 Quick Zoom, 136 selecting, 114, 115, 664 shading, 119**

Page 776

**TI-83 Plus Index 773 **

**Smart Graph, 129 tracing, 134 viewing window, 121 window variables, 121, 122, 123 Y= editor, 111 ZOOM MEMORY menu, 144 ZOOM menu, 138 **

**function integral ( fnInt(), 71, 663 function, definition of, 15 functions and instructions table, 654 future value, 444, 451 FV (future-value variable), 444, 462 **

**G**

**G.T** (graph-table split-screen mode), 25, 252, 666

**garbage collecting, 622 GarbageCollect, 626, 664 Gauge, 468 gcd( (greatest common divisor), 82, 665 GDB (graph database), 242 geometcdf(, 433, 665 geometpdf(, 433, 665 Get( (get data from CBL 2/CBL or **

**CBR), 533, 665 GetCalc( (get data from TI.83), 533, **

**665 getKey, 531, 665 **

**Getting Started. See examples, Getting Started **

**Goto**, 519, 665 graph database (GDB), 242 graph styles, 117 graphing modes, 23 graphing-order modes, 24 **GraphStyle(**, 524, 665 graph-table split-screen mode (**G.T**), 25,

**252, 666 greater than ( >), 101, 694 greater than or equal to (), 101, 694 greatest common divisor (gcd(), 82, 665 greatest integer (int(), 81, 273, 668 GridOff, 127, 666 GridOn, 127, 666 grouping, 616 **

**H**

**Histogram** plot type (), 370 home screen, 10 **Horiz** (horizontal split-screen mode),

**25, 250, 666 Horizontal (draw line), 221, 666 hyperbolic functions, 495 hypothesis tests, 396 **

**I**

*i** *(complex number constant), 86

Page 777

**TI-83 Plus Index 774 **

**identity(**, 277, 666 **If** instructions

**If**, 512, 666 **If-Then**, 513, 666 **If-Then-Else**, 514, 667

**imag(** (imaginary part), 89, 667 imaginary part (**imag(**), 89, 667 implied multiplication, 48 increment and skip (**IS>(**), 520, 668 independent variable, 206, 209, 667 **IndpntAsk**, 206, 209, 667 **IndpntAuto**, 206, 209, 667 inferential stat editors, 388 inferential statistics. *See* stat tests;

**confidence intervals alternative hypotheses, 391 bypassing editors, 393 calculating test results ( Calculate), **

**392 confidence interval calculations, 392 data input or stats input, 390 entering argument values, 390 graphing test results ( Draw), 392 input descriptions table, 419 pooled option, 391 STAT TESTS menu, 394 test and interval output variables, **

**422 Input, 526, 527, 667 insert cursor, 12 **

**inString(** (in string), 492, 667 instruction, definition of, 16 **int(** (greatest integer), 81, 273, 668 integer part (**iPart(**), 80, 273, 668 integral. *See* numerical integral interest rate conversions

**4Eff(** (compute effective interest rate), 459

**4Nom(** (compute nominal interest rate), 459

**calculating, 459 formula, 733 **

**internal rate of return ( irr(), 453, 668 intersect operation on a graph, 151 INTRVL (SEC), 475 inverse (L1), 64, 271, 694 inverse cumulative normal distribution **

**( invNorm(), 426, 668 inverse trig functions, 63 invNorm( (inverse cumulative normal **

**distribution), 426, 668 iPart( (integer part), 80, 273, 668 irr( (internal rate of return), 453, 668 IS>( (increment and skip), 520, 668 **

**K**

**keyboard layout, 2 math operations, 63**

Page 778

**TI-83 Plus Index 775 **

**key-code diagram, 532 **

**L**

**LabelOff**, 127, 668 **LabelOn**, 127, 668 labels

**graph, 127, 668 program, 519, 669 **

**Last Entry, 33 Lbl (label), 519, 669 lcm( (least common multiple), 82, 669 least common multiple (lcm(), 82, 669 length( of string, 492, 669 less than (<), 101, 694 less than or equal to (), 101, 694 Light-Time, 468 line graph style (), 117 line segments, drawing, 218 Line( (draw line), 220, 669 lines, drawing, 220, 221 LINK RECEIVE menu, 644 LINK SEND menu, 634 linking **

**receiving items, 644 to a CBL 2/CBL or CBR, 633 to a PC or Macintosh, 633 to a TI.82, 641, 646 transmitting items, 629 two TI.83 Plus units, 638 **

**LinReg(a+bx)** (linear regression), 360, 669

**LinReg(ax+b)** (linear regression), 359, 669

**LinRegTTest** (linear regression *t* test), 415, 669

**LIST MATH menu, 311 LIST NAMES menu, 291 LIST OPS menu, 299 List4matr( (lists-to-matrix conversion), **

**279, 308, 670 lists **

**accessing an element, 289 attaching formulas, 293, 294, 336 clearing all elements, 333 copying, 289 creating, 286, 332 deleting from memory, 289, 599 detaching formulas, 296, 340 dimension, 288 entering list names, 292, 330 indicator ( { }), 288 naming lists, 286 storing and displaying, 288 transmitting to and from TI.73, 642 transmitting to and from TI.82, 641, **

**646 using in expressions, 297 using to graph a family of curves, **

**131, 290**

Page 779

**TI-83 Plus Index 776 **

**using to select data points from a plot, 305 **

**using with math operations, 63, 298 ln(, 65, 670 LnReg (logarithmic regression), 360, **

**670 log(, 65, 670 logic (Boolean) operators, 103 Logistic (regression), 361, 670 logistic regression formula, 721 **

**M**

**marked for deletion, 623 MATH CPX (complex menu), 88 MATH menu, 67 MATH NUM (number menu), 79 math operations, 63 MATH PRB (probability menu), 92 Matr4list( (matrix-to-list conversion), **

**278, 308, 670 matrices **

**accessing elements, 268 copying, 267 defined, 258 deleting from memory, 261 dimensions, 259, 275, 276 displaying a matrix, 267 displaying matrix elements, 260 editing matrix elements, 262 **

**indicator ( [ ]), 265 inverse (L1), 271 math functions, 269 matrix math functions (det(, T, dim(, **

**Fill(**, **identity(**, **randM(**, **augment(**, **Matr4list(**, **List4matr(**, **c*msum(**), 274

**referencing in expressions, 265 relational operations, 272 row operations( ref(, rref(, rowSwap(, **

**row+(**, **row(**, **row+(**), 280 selecting, 258 viewing, 261

**MATRX EDIT menu, 258 MATRX MATH menu, 274 MATRX NAMES menu, 265 max, 470 max( (maximum), 81, 311, 670 maximum of a function (fMax(), 69, 663 maximum operation on a graph, 150 mean(, 312, 671 Med.Med (median-median), 358, 671 median(, 312, 671 Mem Mgmt/Del menu, 597 memory **

**backing up, 650 checking available, 596 clearing all list elements from, 602 clearing entries from, 601 deleting items from, 599**

Page 780

**TI-83 Plus Index 777 **

**error, 626 insufficient during transmission, 653 resetting defaults, 604 resetting memory, 604 **

**MEMORY menu, 596 Menu( (define menu), 521, 671 menus, 39, 40 **

**defining ( Menu(), 521, 671 map, 698 scrolling, 41 **

**meter, 468 min, 470 min( (minimum), 81, 311, 671 minimum of a function (fMin(), 69, 663 minimum operation on a graph, 150 minutes notation ('), 97, 697 ModBoxplot plot type (), 370 mode settings, 19 **

**a+b i** (complex rectangular), 24, 84, 656

**Connected** (plotting), 23, 658 **Degree** (angle), 22, 99, 659 **Dot** (plotting), 23, 661 **Eng** (notation), 20, 662 **Fix** (decimal), 21, 663 **Float** (decimal), 21, 663 **Full** (screen), 25, 664 **Func** (graphing), 23, 664 **G.T** (screen), 25, 666 **Horiz** (screen), 25, 666

**Normal** (notation), 20, 672 **Par/Param** (graphing), 23, 674 **Pol/Polar** (graphing), 23, 675 **Radian** (angle), 22, 99, 678 **r e**^

**q**(complex polar), 24, 84, 679

*i***Real**, 24, 679

**Sci**(notation), 20, 683

**Seq**(graphing), 23, 683

**Sequential**(graphing order), 24, 683

**Simul**(graphing order), 24, 685

**modified box plot type (), 370 multiple entries on a line, 14 multiplication (), 63, 695 multiplicative inverse, 64 **

**N**

**nCr** (number of combinations), 93, 672 **nDeriv(** (numerical derivative), 70, 672 negation (**M**), 49, 66, 695 nonrecursive sequences, 182 normal distribution probability

**( normalcdf(), 426, 672 Normal notation mode, 20, 672 normal probability plot type (), 372 normalcdf( (normal distribution **

**probability), 426, 672 normalpdf( (probability density **

**function), 425, 673 NormProbPlot plot type (), 372**

Page 781

**TI-83 Plus Index 778 **

**not equal to (), 101, 694 not( (Boolean operator), 104, 673 nPr (permutations), 93, 673 npv( (net present value), 453, 673 numerical derivative, 70, 152, 165, 175 numerical integral, 70, 153 **

**O**

**Omit**, 619, 645 **ON/HALT**, 480 one-proportion *z* confidence interval

**( 1.PropZInt), 410, 676 one-proportion z test (1.PropZTest), **

**402, 676 one-sample t confidence interval **

**( TInterval), 406, 687 one-variable statistics (1.Var Stats), **

**357, 689 or (Boolean) operator, 103, 673 order of evaluating equations, 47 Output(, 255, 530, 673 Overwrite, 619, 645 Overwrite All, 619 **

**P**

**P4Rx(**, **P4Ry(** (polar-to-rectangular conversions), 100, 678

**P/Y** (number-of-payment-periods-per- year variable), 444, 463

**panning, 136 Par/Param (parametric graphing mode), **

**23, 674 parametric equations, 159 parametric graphing **

**CALC (calculate operations on a graph), 165 **

**defining and editing, 158, 159 free-moving cursor, 163 graph format, 161 graph styles, 159 moving the cursor to a value, 164 selecting and deselecting, 160 setting parametric mode, 158 tracing, 163 window variables, 160 Y= editor, 158 zoom operations, 165 **

**parentheses, 48 path () graph style, 117 Pause, 518, 674 pausing a graph, 129 Pen, 232 permutations (nPr), 93, 673 phase plots, 197 Pi (p), 66 Pic (pictures), 239 pictures (Pic), 239 pixel, 237 pixels in Horiz/G.T modes, 238, 254**

Page 782

**TI-83 Plus Index 779 **

**PLOT**, 476 **Plot1(**, 373, 674 **Plot2(**, 373, 674 **Plot3(**, 373, 674 **PlotsOff**, 375, 675 **PlotsOn**, 375, 675 plotting modes, 23 plotting stat data, 368 **PMT** (payment amount variable), 444,

**462 Pmt_Bgn (payment beginning variable), **

**461, 675 Pmt_End (payment end variable), 461, **

**675 poissoncdf(, 432, 675 poissonpdf(, 432, 675 Pol/Polar (polar graphing mode), 23, **

**168, 675 polar equations, 169 polar form, complex numbers, 87 polar graphing **

**CALC (calculate operations on a graph), 175 **

**defining and displaying, 168 equations, 169 free-moving cursor, 173 graph format, 171 graph styles, 169 mode ( Pol/Polar), 23, 168, 675 moving the cursor to a value, 174 **

**selecting and deselecting, 169 tracing, 173 window variables, 170 Y= editor, 168 ZOOM operations, 174 **

**PolarGC** (polar graphing coordinates), 126, 676

**pooled option, 388, 391 power ( ^), 64, 695 power of ten (10^(), 65, 695 present value, 444, 450 previous entry (Last Entry), 33 prgm (program name), 522, 676 PRGM CTL (program control menu), **

**511 PRGM EDIT menu, 510 PRGM EXEC menu, 510 PRGM I/O (Input/Output menu), 525 PRGM NEW menu, 500 probability, 92 probability density function **

**( normalpdf(), 425, 673 probe, 468 prod( (product), 313, 676 programming **

**copying and renaming, 509 creating new, 500 defined, 500 deleting, 501 deleting command lines, 508**

Page 783

**TI-83 Plus Index 780 **

**editing, 507 entering command lines, 504 executing, 505 inserting command lines, 508 instructions, 511 name ( prgm), 522, 676 renaming, 509 running assembly language **

**program, 537 stopping, 506 subroutines, 535 **

**Prompt**, 528, 676 **Pt.Change(**, 235, 677 **Pt.Off(**, 234, 677 **Pt.On(**, 233, 677 **PV** (present value variable), 444, 462 p-value, 422 **PwrReg** (power regression), 361, 677 **Pxl.Change(**, 237, 677 **Pxl.Off(**, 237, 677 **Pxl.On(**, 237, 677 **pxl.Test(**, 238, 678

**Q**

**QuadReg** (quadratic regression), 359, 678

**QuartReg** (quartic regression), 360, 678 Quick Zoom, 136 **Quit**, 619, 645

**quitting CBL/CBR, 480 **

**R**

**r** (correlation coefficient), 354 **r** (radian notation), 99, 692 **R4Pr(**, **R4Pq(** (rectangular-to-polar

**conversions), 100, 681 r2, R2 (coefficients of determination), **

**354 Radian angle mode, 22, 99, 678 radian notation (r), 99, 692 RAM ARCHIVE ALL menu, 603 rand (random number), 92, 678 randBin( (random binomial), 96, 678 randInt( (random integer), 95, 679 randM( (random matrix), 277, 679 randNorm( (random Normal), 95, 679 random seed, 92 Ranger, 468 RCL (recall), 31, 297 re^qi (polar complex mode), 24, 84, **

**679 Real mode, 24, 679 real( (real part), 89, 679 RealTme, 476 RecallGDB, 244, 679 RecallPic, 241, 679 rectangular form, complex numbers, 86**

Page 784

**TI-83 Plus Index 781 **

**RectGC** (rectangular graphing coordinates), 126, 680

**recursive sequences, 183 ref( (row-echelon form), 280, 680 reference#, 471 RegEQ (regression equation variable), **

**353, 599 regression model **

**automatic regression equation, 353 automatic residual list feature, 352 diagnostics display mode, 354 models, 357 **

**relational operations, 101, 272 Repeat, 517, 680 RESET MEMORY menu, 608 resetting **

**all memory, 608 archive memory, 606 defaults, 604 memory, 604 RAM memory, 604 **

**residual list (RESID), 352 Return, 523, 680 root (x), 69, 693 root of a function, 148 round(, 80, 271, 680 row+(, 680 rowSwap(, 281, 680 rref( (reduced-row-echelon form), 280, **

**681 **

**S**

**samples (# of), 475 Scatter plot type ("), 369 Sci (scientific notation mode), 20, 683 scientific notation, 14 screen modes, 25 second cursor (2nd), 12 second key (2nd), 4 seconds DMS notation ("), 97 sector, 623 Select(, 304, 683 selecting **

**data points from a plot, 305 functions from the home screen or a **

**program, 115 functions in the Y= editor, 115 stat plots from the Y= editor, 115 **

**Send(** (send to CBL 2/CBL or CBR), 533, 683

**SendID, 634 sending. See transmitting SendOS, 635 Seq (sequence graphing mode), 23, 683 seq( (sequence), 302, 683 sequence graphing **

**axes format, 187 CALC (calculate menu), 191 defining and displaying, 179 evaluating, 192**

Page 785

**TI-83 Plus Index 782 **

**free-moving cursor, 189 graph format, 188 graph styles, 181 moving the cursor to a value, 190 nonrecursive sequences, 182 phase plots, 197 recursive sequences, 183 selecting and deselecting, 181 setting sequence mode, 179 TI.83 Plus versus TI.82 table, 202 tracing, 189 web plots, 193 window variables, 185 Y= editor, 180 ZOOM (zoom menu), 191 **

**Sequential** (graphing order mode), 24, 683

**service information, 759 setting **

**display contrast, 8 graph styles, 118 graph styles from a program, 120 modes, 20 modes from a program, 20 split-screen modes, 248 split-screen modes from a program, **

**255 tables from a program, 206 **

**SetUpEditor**, 350, 683 shade above () graph style, 117

**shade below () graph style, 117 Shade(, 437, 684 Shadec2(, 436, 684 Shade(, 226, 684 Shade_t(, 435, 684 ShadeNorm(, 435, 684 shading graph areas, 119, 226 Simul (simultaneous graphing order **

**mode), 24, 685 sinL1( (arcsine), 63, 685 sin( (sine), 63, 685 sine (sin(), 63, 685 sine regression formula, 722 sinhM1( (hyperbolic arcsine), 496, 685 sinh( (hyperbolic sine), 496, 685 SinReg (sinusoidal regression), 362, **

**685 Smart Graph, 129 solve(, 77, 685 Solver, 72 solving for variables in the equation **

**solver, 75 sonic, 468 sonic probe, 468 sonic-time graph, 468 SortA( (sort ascending), 299, 348, 685 SortD( (sort descending), 299, 348, 685 split-screen modes **

**G.T** (graph-table) mode, 252 **Horiz** (horizontal) mode, 250

Page 786

**TI-83 Plus Index 783 **

**setting, 248, 255 split-screen values, 231, 238, 254 square ( 2), 64, 694 square root ((), 64, 695 STAT CALC menu, 356 STAT EDIT menu, 348 stat list editor **

**attaching formulas to list names, 336 **

**clearing elements from lists, 333 creating list names, 332 detaching formulas from list names, **

**340 displaying, 329 edit-elements context, 344 editing elements of formula- **

**generated lists, 341 editing list elements, 334 entering list names, 330 enter-names context, 346 formula-generated list names, 338 removing lists, 332 restoring list names L1L6, 333 switching contexts, 342 view-elements context, 344 view-names context, 346 **

**STAT PLOTS menu, 373 stat tests and confidence intervals **

**c.Test** (chi-square test), 412

**1.PropZInt** (one-proportion *z* confidence interval), 410

**1.PropZTest** (one-proportion *z* test), 402

**2.PropZInt** (two-proportion *z* confidence interval), 411

**2.PropZTest** (two-proportion *z* test), 403

**2.SampTest** (two-sample .Test), 414

**2.SampTInt** (two-sample *t* confidence interval), 408

**2.SampTTest** (two-sample *t* test), 400

**2.SampZInt** (two-sample *z* confidence interval), 407

**2.SampZTest** (two-sample *z* test), 399

**ANOVA(** (one-way analysis of variance), 415

**LinRegTTest** (linear regression *t* test), 415

**T.Test** (one-sample *t* test), 397 **TInterval** (one-sample *t* confidence

**interval), 406 Z.Test (one-sample z test), 396 ZInterval (one-sample z confidence **

**interval), 405 STAT TESTS menu, 394**

Page 787

**TI-83 Plus Index 784 **

**statistical distribution functions. See distribution functions **

**statistical plotting, 368 Boxplot (regular box plot), 371 defining, 373 from a program, 378 Histogram, 370 ModBoxplot (modified box plot), **

**370 NormProbPlot (normal probability **

**plot), 372 Scatter, 369 tracing, 376 turning on/off stat plots, 115, 375 viewing window, 376 xyLine, 369 **

**statistical variables table, 365 Stats input option, 388, 390 stdDev( (standard deviation), 314, 686 Stop, 523, 686 Store (!), 29, 686 StoreGDB, 242, 686 StorePic, 239, 686 storing **

**graph databases (GDBs), 242 graph pictures, 239 variable values, 29 **

**String4Equ(** (string-to-equation conversions), 493, 686

**strings **

**concatenation ( +), 490, 696 converting, 491 defined, 484 displaying contents, 488 entering, 484 functions in CATALOG, 489 length (length(), 492, 669 storing, 487 variables, 486, 487 **

**student- t distribution probability (tcdf(), 427, 687 probability density function (tpdf(), **

**427, 687 sub( (substring), 493, 686 subroutines, 522 subtraction (N), 63, 696 sum( (summation), 313, 686 system variables, 719 **

**T** **T **(transpose matrix), 275, 693 **T.Test** (one-sample t test), 397, 688 TABLE SETUP screen, 205 tables

**description, 209 variables, 205, 207 **

**tanL1(** (arctangent), 63, 686 **tan(** (tangent), 63, 686 tangent (**tan(**), 63, 686

Page 788

**TI-83 Plus Index 785 **

**tangent lines, drawing, 222 Tangent( (draw line), 222, 687 tanhM1( (hyperbolic arctangent), 496, **

**687 tanh( (hyperbolic tangent), 496, 687 TblStart (table start variable), 205 tcdf( (student-t distribution probability), **

**427, 687 technical support, 758 Temperature, 468 Temp-Time, 468 TEST (relational menu), 101 TEST LOGIC (Boolean menu), 103 Text( **

**instruction, 230, 254, 687 placing on a graph, 230, 254 **

**Then**, 513, 666 thick () graph style, 117 TI.82

**link differences, 646 transmitting to/from, 644 **

**TI.83 Link. See linking **

**TI.83 Plus key code diagram, 532 keyboard, 2 menu map, 698 **

**TI Connect, 632 TI.GRAPH LINK, 632, 633 Time axes format, 187, 687 time value of money (TVM) **

** variable (annual interest rate), 462 **

** variable (number of payment periods), 462 **

**C/Y** variable (number of compounding periods per year), 463

**calculating, 448 formulas, 728 FV variable (future value), 462 P/Y variable (number of payment **

**periods per year), 463 PMT variable (payment amount), **

**462 PV variable (present value), 462 TVM Solver, 444 tvm_ (# payment periods), 450, **

**688 tvm_FV (future value), 451, 688 tvm_I% (interest rate), 449, 688 tvm_Pmt (payment amount), 449, **

**688 tvm_PV (present value), 450, 688 variables, 462 **

**TInterval** (one-sample *t* confidence interval), 406, 687

**tpdf(** (student-*t* distribution probability density function), 427, 687

**TRACE cursor, 135**

Page 789

**TI-83 Plus Index 786 **

**entering numbers during, 135, 164, 173, 189 **

**expression display, 128, 135 Trace instruction in a program, 137, **

**688 transmitting **

**error conditions, 652 from a TI.73 to a TI.83 Plus, 648 from a TI.82 to a TI.83 Plus, 646 lists to a TI.73, 642 lists to a TI.82, 641 lists to a TI.83 Plus, 648 stopping, 637 to an additional TI.83 Plus, 638 **

**transpose matrix( T), 275, 693 TRIGGER, 480 trigonometric functions, 63 turning on and off **

**axes, 127 calculator, 6 coordinates, 126 expressions, 128 functions, 115 grid, 127 labels, 127 pixels, 237 points, 233 stat plots, 115, 375 **

**tvm_** (# payment periods), 450, 688 **tvm_FV** (future value), 451, 688

**tvm_I%** (interest rate), 449, 688 **tvm_Pmt** (payment amount), 449, 688 **tvm_PV** (present value), 450, 688 two-proportion *z* confidence interval

**( 2.PropZInt), 411, 676 two-proportion z test (2.PropZTest), **

**403, 677 two-sample -Test formula, 724 two-sample t test formula, 726 two-variable statistics (2.Var Stats), **

**358, 689 Type **

**Bar or Meter, 469 **

**U**

**u** sequence function, 179 **UnArchive**, 30, 610, 689 ungrouping, 616 units, 470 user variables, 718 **uv**/**uvAxes** (axes format), 187, 689 **uw**/**uwAxes** (axes format), 187, 689

**V**

**v** sequence function, 179 **value** operation on a graph, 147 variables

**complex, 26 displaying and storing values, 30**

Page 790

**TI-83 Plus Index 787 **

**equation solver, 75 graph databases, 26 graph pictures, 26 independent/dependent, 209 list, 26, 286 matrix, 26, 258 real, 26 recalling values, 31 solver editor, 74 statistical, 365 string, 486, 487 test and interval output, 422 types, 26 user and system, 27, 718 VARS and Y.VARS menus, 44 **

**variance of a list ( variance(), 314, 689 variance( (variance of a list), 314, 689 VARS menu **

**GDB, 44 Picture, 44 Statistics, 44 String, 44 Table, 44 Window, 44 Zoom, 44 **

**Vertical** (draw line), 221, 689 viewing window, 121 Volt, 468 Voltage, 468 Volt-Time, 468

**vw**/**uvAxes** (axes format), 187, 689

**W**

**w** sequence function, 179 warranty information, 760 **Web** (axes format), 187, 689 web plots, 193 **While**, 516, 689 window variables

**function graphing, 121 parametric graphing, 161 polar graphing, 170 **

**X** **x** (root), 69, 693 **XFact** zoom factor, 145 x-intercept of a root, 148 **xor** (Boolean) exclusive or operator,

**103, 690 xth root ( x), 69 xyLine () plot type, 369 **

**Y**

**Y.VARS menu Function, 45 On/Off, 45 Parametric, 45 Polar, 45**

Page 791

**TI-83 Plus Index 788 **

**Y= editor function graphing, 111 parametric graphing, 158 polar graphing, 168 sequence graphing, 180 **

**YFact** zoom factor, 145

**Z**

**Z.Test** (one-sample *z* test), 396, 692 **ZBox**, 139, 690 **ZDecimal**, 141, 690 **zero** operation on a graph, 148 **ZInteger**, 143, 690 **ZInterval** (one-sample *z* confidence

**interval), 405, 690 zoom, 138, 139, 140, 141, 142, 143, **

**144, 145, 146 cursor, 139 factors, 145 function graphing, 138 **

**parametric graphing, 165 polar graphing, 174 sequence graphing, 191 **

**Zoom In** (zoom in), 140, 690 ZOOM MEMORY menu, 144 ZOOM menu, 138 **Zoom Out** (zoom out), 140, 690 **ZoomFit** (zoom to fit function), 143,

**691 ZoomRcl (recall stored window), 145, **

**691 ZoomStat (statistics zoom), 143, 691 ZoomSto (store zoom window), 144, **

**691 ZPrevious (use previous window), 144, **

**691 ZSquare (set square pixels), 142, 691 ZStandard (use standard window), 142, **

**691 ZTrig (trigonometric window), 142, 692**

Page 792

**TI-83 Plus Quick-Find Locator i **

**Quick-Find Locator **

**Chapter 1: Operating the TI-83 Plus Silver Edition........................** **1**

**Documentation Conventions.....................................................................1 TI-83 Plus Keyboard .................................................................................2 **

**Keyboard Zones..................................................................................2 Using the Color.Coded Keyboard.......................................................4 Using the y and Keys ...........................................................4 **

**Turning On and Turning Off the TI-83 Plus ..............................................6 Turning On the Calculator...................................................................6 Turning Off the Calculator...................................................................7 Batteries..............................................................................................7 **

**Setting the Display Contrast .....................................................................8 Adjusting the Display Contrast............................................................8 When to Replace Batteries .................................................................9 **

**The Display.............................................................................................10 Types of Displays..............................................................................10 Home Screen ....................................................................................10 Displaying Entries and Answers .......................................................10 Returning to the Home Screen .........................................................11 Busy Indicator ...................................................................................11 Display Cursors.................................................................................12 **

**Entering Expressions and Instructions....................................................13 What Is an Expression? ....................................................................13 Entering an Expression.....................................................................13 Multiple Entries on a Line..................................................................14**

Page 793

**TI-83 Plus Quick-Find Locator ii **

**Entering a Number in Scientific Notation ..........................................14 Functions ..........................................................................................15 Instructions........................................................................................16 Interrupting a Calculation ..................................................................16 **

**TI-83 Plus Edit Keys ...............................................................................17 Setting Modes.........................................................................................19 **

**Checking Mode Settings ...................................................................19 Changing Mode Settings...................................................................20 Setting a Mode from a Program........................................................20 Normal, Sci, Eng ...............................................................................20 Float, 0123456789 ............................................................................21 Radian, Degree.................................................................................22 Func, Par, Pol, Seq...........................................................................23 Connected, Dot .................................................................................23 Sequential, Simul ..............................................................................24 Real, a+bi, re^qi ................................................................................24 Full, Horiz, G-T..................................................................................25 **

**Using TI-83 Plus Variable Names...........................................................26 Variables and Defined Items.............................................................26 Notes about Variables.......................................................................27 **

**Storing Variable Values ..........................................................................29 Storing Values in a Variable..............................................................29 Displaying a Variable Value ..............................................................30 Archiving Variables (Archive, Unarchive)..........................................30 **

**Recalling Variable Values.......................................................................31 Using Recall (RCL) ...........................................................................31 **

**ENTRY (Last Entry) Storage Area..........................................................33 Using ENTRY (Last Entry) ................................................................33**

Page 794

**TI-83 Plus Quick-Find Locator iii **

**Accessing a Previous Entry ..............................................................34 Reexecuting the Previous Entry........................................................34 Multiple Entry Values on a Line ........................................................35 Clearing ENTRY ...............................................................................36 Using Ans in an Expression ..............................................................36 Continuing an Expression .................................................................37 Storing Answers................................................................................38 **

**TI-83 Plus Menus....................................................................................39 Using a TI-83 Plus Menu ..................................................................39 Displaying a Menu ............................................................................40 Moving from One Menu to Another...................................................41 Scrolling a Menu ...............................................................................41 Selecting an Item from a Menu .........................................................41 Leaving a Menu without Making a Selection.....................................43 **

**VARS and VARS Y-VARS Menus ..........................................................44 VARS Menu ......................................................................................44 Selecting a Variable from the VARS Menu or VARS Y-VARS **

**Menu ...........................................................................................45 Equation Operating System (EOS).........................................................47 **

**Order of Evaluation ...........................................................................47 Implied Multiplication.........................................................................48 Parentheses......................................................................................48 Negation............................................................................................49 **

**Special Features of the TI-83 Plus .........................................................50 Flash Electronic Upgradability .......................................................50 1.56 Megabytes (M) of Available Memory ........................................50 Applications.......................................................................................51 Archiving ...........................................................................................51**

Page 795

**TI-83 Plus Quick-Find Locator iv **

**Calculator-Based Laboratory (CBL 2, CBL) and Calculator-Based Ranger (CBR)..........................................52 **

**Other TI-83 Plus Features ......................................................................53 Graphing ...........................................................................................53 Sequences ........................................................................................53 Tables ...............................................................................................54 Split Screen.......................................................................................54 Matrices ............................................................................................54 Lists...................................................................................................55 Statistics............................................................................................55 Inferential Statistics...........................................................................55 Applications.......................................................................................56 CATALOG.........................................................................................56 Programming ....................................................................................57 Archiving ...........................................................................................57 Communication Link .........................................................................57 **

**Error Conditions......................................................................................59 Diagnosing an Error ..........................................................................59 Correcting an Error ...........................................................................60 **

**Chapter 2: Math, Angle, and Test Operations..............................** **61**

**Getting Started: Coin Flip .......................................................................61 Keyboard Math Operations.....................................................................63 **

**Using Lists with Math Operations .....................................................63 + (Addition), N (Subtraction), (Multiplication), (Division) ...............63 Trigonometric Functions ...................................................................63 ^ (Power), 2 (Square), ( (Square Root) ..........................................64 L1 (Inverse)........................................................................................64**

Page 796

**TI-83 Plus Quick-Find Locator v **

**log(, 10^(, ln( .....................................................................................65 e^( (Exponential) .................................................................................65 e (Constant) ......................................................................................65 L (Negation).......................................................................................66 p (Pi) .................................................................................................66 **

**MATH Operations ...................................................................................67 MATH Menu......................................................................................67 4Frac, 4Dec........................................................................................67 3(Cube), 3( (Cube Root) .................................................................68 x (Root)...........................................................................................69 fMin(, fMax( .......................................................................................69 nDeriv( ..............................................................................................70 fnInt(..................................................................................................71 **

**Using the Equation Solver ......................................................................72 Solver................................................................................................72 Entering an Expression in the Equation Solver.................................72 Entering and Editing Variable Values ...............................................74 Solving for a Variable in the Equation Solver....................................75 Editing an Equation Stored to eqn ....................................................77 Equations with Multiple Roots...........................................................77 Further Solutions...............................................................................77 Controlling the Solution for Solver or solve(......................................78 Using solve( on the Home Screen or from a Program ......................78 **

**MATH NUM (Number) Operations..........................................................79 MATH NUM Menu.............................................................................79 abs( ...................................................................................................79 round(................................................................................................80 iPart(, fPart(.......................................................................................80**

Page 797

**TI-83 Plus Quick-Find Locator vi **

**int( ....................................................................................................81 min(, max( .........................................................................................81 lcm(, gcd( ..........................................................................................82 **

**Entering and Using Complex Numbers...................................................84 Complex-Number Modes ..................................................................84 Entering Complex Numbers..............................................................85 Note about Radian Versus Degree Mode .........................................85 Interpreting Complex Results............................................................86 Rectangular-Complex Mode .............................................................86 Polar-Complex Mode ........................................................................87 **

**MATH CPX (Complex) Operations .........................................................88 MATH CPX Menu .............................................................................88 conj( ..................................................................................................88 real(...................................................................................................89 imag( .................................................................................................89 angle( ................................................................................................90 abs( ...................................................................................................90 4Rect .................................................................................................91 4Polar ................................................................................................91 **

**MATH PRB (Probability) Operations.......................................................92 MATH PRB Menu .............................................................................92 rand...................................................................................................92 nPr, nCr.............................................................................................93 ! (Factorial)........................................................................................94 randInt(..............................................................................................95 randNorm(.........................................................................................95 randBin( ............................................................................................96 **

**ANGLE Operations .................................................................................97**

Page 798

**TI-83 Plus Quick-Find Locator vii **

**ANGLE Menu....................................................................................97 Entry Notation ...................................................................................97 (Degree) .........................................................................................98 r (Radians) ........................................................................................99 8DMS................................................................................................99 R8Pr (, R8Pq( , P8Rx(, P8Ry( ........................................................100 **

**TEST (Relational) Operations...............................................................101 TEST Menu.....................................................................................101 =, , >, , <, ..................................................................................101 Using Tests .....................................................................................102 **

**TEST LOGIC (Boolean) Operations .....................................................103 TEST LOGIC Menu.........................................................................103 Boolean Operators..........................................................................103 and, or, xor......................................................................................103 not(..................................................................................................104 Using Boolean Operations ..............................................................104 **

**Chapter 3: Function Graphing.....................................................** **105**

**Getting Started: Graphing a Circle........................................................105 Defining Graphs....................................................................................107 **

**TI-83 PlusGraphing Mode Similarities.........................................107 Defining a Graph.............................................................................107 Displaying and Exploring a Graph ..................................................108 Saving a Graph for Later Use .........................................................108 **

**Setting the Graph Modes......................................................................109 Checking and Changing the Graphing Mode..................................109 Setting Modes from a Program .......................................................110 **

**Defining Functions ................................................................................111**

Page 799

**TI-83 Plus Quick-Find Locator viii **

**Displaying Functions in the Y= Editor .............................................111 Defining or Editing a Function.........................................................111 Defining a Function from the Home Screen or a Program..............112 Evaluating Y= Functions in Expressions.........................................113 **

**Selecting and Deselecting Functions....................................................114 Selecting and Deselecting a Function.............................................114 Turning On or Turning Off a Stat Plot in the Y= Editor....................115 Selecting and Deselecting Functions from the Home Screen **

**or a Program .............................................................................115 Setting Graph Styles for Functions .......................................................117 **

**Graph Style Icons in the Y= Editor..................................................117 Setting the Graph Style...................................................................118 Shading Above and Below..............................................................119 Setting a Graph Style from a Program............................................120 **

**Setting the Viewing Window Variables .................................................121 The TI-83 Plus Viewing Window .....................................................121 Displaying the Window Variables....................................................121 Changing a Window Variable Value ...............................................122 Storing to a Window Variable from the Home Screen or a **

**Program ....................................................................................123 @X and @Y........................................................................................124 **

**Setting the Graph Format .....................................................................125 Displaying the Format Settings .......................................................125 Changing a Format Setting .............................................................125 RectGC, PolarGC ...........................................................................126 CoordOn, CoordOff.........................................................................126 GridOff, GridOn...............................................................................127 AxesOn, AxesOff ............................................................................127**

Page 800

**TI-83 Plus Quick-Find Locator ix **

**LabelOff, LabelOn...........................................................................127 ExprOn, ExprOff..............................................................................128 **

**Displaying Graphs ................................................................................129 Displaying a New Graph .................................................................129 Pausing or Stopping a Graph..........................................................129 Smart Graph ...................................................................................129 Overlaying Functions on a Graph ...................................................130 Graphing a Family of Curves ..........................................................131 **

**Exploring Graphs with the Free-Moving Cursor....................................132 Free-Moving Cursor ........................................................................132 Graphing Accuracy .........................................................................132 **

**Exploring Graphs with TRACE..............................................................134 Beginning a Trace...........................................................................134 Moving the Trace Cursor ................................................................134 Moving the Trace Cursor from Function to Function.......................135 Moving the Trace Cursor to Any Valid X Value...............................135 Panning to the Left or Right ............................................................136 Quick Zoom.....................................................................................136 Leaving and Returning to TRACE...................................................137 Using TRACE in a Program ............................................................137 **

**Exploring Graphs with the ZOOM Instructions......................................138 ZOOM Menu ...................................................................................138 Zoom Cursor ...................................................................................139 ZBox................................................................................................139 Zoom In, Zoom Out.........................................................................140 ZDecimal.........................................................................................141 ZSquare ..........................................................................................142 ZStandard .......................................................................................142**

Page 801

**TI-83 Plus Quick-Find Locator x **

**ZTrig................................................................................................142 ZInteger...........................................................................................143 ZoomStat ........................................................................................143 ZoomFit...........................................................................................143 **

**Using ZOOM MEMORY........................................................................144 ZOOM MEMORY Menu ..................................................................144 ZPrevious........................................................................................144 ZoomSto .........................................................................................144 ZoomRcl..........................................................................................145 ZOOM FACTORS ...........................................................................145 Checking XFact and YFact .............................................................145 Changing XFact and YFact.............................................................146 Using ZOOM MEMORY Menu Items from the Home Screen **

**or a Program .............................................................................146 Using the CALC (Calculate) Operations ...............................................147 **

**CALCULATE Menu.........................................................................147 value ...............................................................................................147 zero .................................................................................................148 minimum, maximum........................................................................150 intersect ..........................................................................................151 dy/dx ...............................................................................................152 f(x)dx ..............................................................................................153 **

**Chapter 4: Parametric Graphing** **.................................................** **154**

**Getting Started: Path of a Ball ..............................................................154 Defining and Displaying Parametric Graphs.........................................158 **

**TI-83 Plus Graphing Mode Similarities ...........................................158 Setting Parametric Graphing Mode.................................................158**

Page 802

**TI-83 Plus Quick-Find Locator xi **

**Displaying the Parametric Y= Editor ...............................................158 Selecting a Graph Style ..................................................................159 Defining and Editing Parametric Equations ....................................159 Selecting and Deselecting Parametric Equations ...........................160 Setting Window Variables ...............................................................160 Setting the Graph Format ...............................................................161 Displaying a Graph .........................................................................161 Window Variables and Y.VARS Menus..........................................161 **

**Exploring Parametric Graphs................................................................163 Free-Moving Cursor ........................................................................163 TRACE............................................................................................163 Moving the Trace Cursor to Any Valid T Value...............................164 ZOOM .............................................................................................165 CALC ..............................................................................................165 **

**Chapter 5: Polar Graphing** **...........................................................** **166**

**Getting Started: Polar Rose..................................................................166 Defining and Displaying Polar Graphs..................................................168 **

**TI-83 Plus Graphing Mode Similarities ...........................................168 Setting Polar Graphing Mode..........................................................168 Displaying the Polar Y= Editor ........................................................168 Selecting Graph Styles ...................................................................169 Defining and Editing Polar Equations .............................................169 Selecting and Deselecting Polar Equations ....................................169 Setting Window Variables ...............................................................170 Setting the Graph Format ...............................................................171 Displaying a Graph .........................................................................171 Window Variables and Y.VARS Menus..........................................171**

Page 803

**TI-83 Plus Quick-Find Locator xii **

**Exploring Polar Graphs.........................................................................173 Free-Moving Cursor ........................................................................173 TRACE............................................................................................173 Moving the Trace Cursor to Any Valid q Value ...............................174 ZOOM .............................................................................................174 CALC ..............................................................................................175 **

**Chapter 6: Sequence Graphing...................................................** **176**

**Getting Started: Forest and Trees ........................................................176 Defining and Displaying Sequence Graphs ..........................................179 **

**TI-83 Plus Graphing Mode Similarities ...........................................179 Setting Sequence Graphing Mode..................................................179 TI-83 Plus Sequence Functions u, v, and w ...................................179 Displaying the Sequence Y= Editor ................................................180 Selecting Graph Styles ...................................................................181 Selecting and Deselecting Sequence Functions.............................181 Defining and Editing a Sequence Function.....................................182 Nonrecursive Sequences................................................................182 Recursive Sequences .....................................................................183 Setting Window Variables ...............................................................185 **

**Selecting Axes Combinations ...............................................................187 Setting the Graph Format ...............................................................187 Setting Axes Format .......................................................................187 Displaying a Sequence Graph ........................................................188 **

**Exploring Sequence Graphs.................................................................189 Free-Moving Cursor ........................................................................189 TRACE............................................................................................189 Moving the Trace Cursor to Any Valid n Value ...............................190**

Page 804

**TI-83 Plus Quick-Find Locator xiii **

**ZOOM .............................................................................................191 CALC ..............................................................................................191 Evaluating u, v, and w.....................................................................192 **

**Graphing Web Plots..............................................................................193 Graphing a Web Plot.......................................................................193 Valid Functions for Web Plots.........................................................193 Displaying the Graph Screen ..........................................................194 Drawing the Web ............................................................................194 **

**Using Web Plots to Illustrate Convergence ..........................................195 Example: Convergence...................................................................195 **

**Graphing Phase Plots ...........................................................................197 Graphing with uv, vw, and uw .........................................................197 Example: Predator-Prey Model.......................................................197 **

**Comparing TI-83 Plus and TI-82 Sequence Variables .........................201 Sequences and Window Variables .................................................201 **

**Keystroke Differences Between TI-83 Plus and TI-82..........................202 Sequence Keystroke Changes .......................................................202 **

**Chapter 7: Tables..........................................................................** **203**

**Getting Started: Roots of a Function ....................................................203 Setting Up the Table .............................................................................205 **

**TABLE SETUP Screen ...................................................................205 TblStart, @Tbl...................................................................................205 Indpnt: Auto, Indpnt: Ask, Depend: Auto, Depend: Ask ..................206 Setting Up the Table from the Home Screen or a Program ............206 **

**Defining the Dependent Variables ........................................................207 Defining Dependent Variables from the Y= Editor ..........................207 Editing Dependent Variables from the Table Editor........................207**

Page 805

**TI-83 Plus Quick-Find Locator xiv **

**Displaying the Table .............................................................................209 The Table........................................................................................209 Independent and Dependent Variables ..........................................209 Clearing the Table from the Home Screen or a Program ...............210 Scrolling Independent-Variable Values...........................................210 Displaying Other Dependent Variables...........................................211 **

**Chapter 8: Draw Instructions.......................................................** **212**

**Getting Started: Drawing a Tangent Line .............................................212 Using the DRAW Menu.........................................................................214 **

**DRAW Menu ...................................................................................214 Before Drawing on a Graph ............................................................215 Drawing on a Graph........................................................................215 **

**Clearing Drawings ................................................................................217 Clearing Drawings When a Graph Is Displayed..............................217 Clearing Drawings from the Home Screen or a Program ...............217 **

**Drawing Line Segments........................................................................218 Drawing a Line Segment Directly on a Graph.................................218 Drawing a Line Segment from the Home Screen or a Program .....219 **

**Drawing Horizontal and Vertical Lines..................................................220 Drawing a Line Directly on a Graph ................................................220 Drawing a Line from the Home Screen or a Program.....................221 **

**Drawing Tangent Lines.........................................................................222 Drawing a Tangent Line Directly on a Graph..................................222 Drawing a Tangent Line from the Home Screen or a Program.......223 **

**Drawing Functions and Inverses ..........................................................224 Drawing a Function .........................................................................224 Drawing an Inverse of a Function ...................................................224**

Page 806

**TI-83 Plus Quick-Find Locator xv **

**Shading Areas on a Graph ...................................................................226 Shading a Graph.............................................................................226 **

**Drawing Circles.....................................................................................228 Drawing a Circle Directly on a Graph..............................................228 Drawing a Circle from the Home Screen or a Program ..................229 **

**Placing Text on a Graph .......................................................................230 Placing Text Directly on a Graph ....................................................230 Placing Text on a Graph from the Home Screen or a Program ......230 Split Screen.....................................................................................231 **

**Using Pen to Draw on a Graph.............................................................232 Using Pen to Draw on a Graph .......................................................232 **

**Drawing Points on a Graph...................................................................233 DRAW POINTS Menu.....................................................................233 Drawing Points Directly on a Graph with Pt.On(.............................233 Erasing Points with Pt .Off( ..............................................................234 Changing Points with Pt.Change( ...................................................235 Drawing Points from the Home Screen or a Program.....................235 **

**Drawing Pixels ......................................................................................237 TI-83 Plus Pixels .............................................................................237 Turning On and Off Pixels with Pxl .On( and Pxl.Off( ......................237 Using pxl.Test( ................................................................................238 Split Screen.....................................................................................238 **

**Storing Graph Pictures (Pic) .................................................................239 DRAW STO Menu...........................................................................239 Storing a Graph Picture ..................................................................239 **

**Recalling Graph Pictures (Pic)..............................................................241 Recalling a Graph Picture ...............................................................241 Deleting a Graph Picture.................................................................241**

Page 807

**TI-83 Plus Quick-Find Locator xvi **

**Storing Graph Databases (GDB) ..........................................................242 What Is a Graph Database? ...........................................................242 Storing a Graph Database ..............................................................242 **

**Recalling Graph Databases (GDB).......................................................244 Recalling a Graph Database...........................................................244 Deleting a Graph Database ............................................................245 **

**Chapter 9: Split Screen** **................................................................** **246**

**Getting Started: Exploring the Unit Circle .............................................246 Using Split Screen ................................................................................248 **

**Setting a Split-Screen Mode ...........................................................248 Horiz (Horizontal) Split Screen..............................................................250 **

**Horiz Mode......................................................................................250 Moving from Half to Half in Horiz Mode ..........................................251 Full Screens in Horiz Mode.............................................................251 **

**G.T (Graph-Table) Split Screen............................................................252 G.T Mode........................................................................................252 Moving from Half to Half in G.T Mode ............................................252 Using r in G.T Mode...............................................................253 Full Screens in G.T Mode...............................................................253 **

**TI-83 Plus Pixels in Horiz and G.T Modes............................................254 TI-83 Plus Pixels in Horiz and G.T Modes......................................254 DRAW POINTS Menu Pixel Instructions ........................................254 DRAW Menu Text( Instruction ........................................................254 PRGM I/O Menu Output( Instruction...............................................255 Setting a Split-Screen Mode from the Home Screen or a **

**Program ....................................................................................255**

Page 808

**TI-83 Plus Quick-Find Locator xvii **

**Chapter 10: Matrices** **....................................................................** **256**

**Getting Started: Systems of Linear Equations......................................256 Defining a Matrix ...................................................................................258 **

**What Is a Matrix? ............................................................................258 Selecting a Matrix ...........................................................................258 Accepting or Changing Matrix Dimensions .....................................259 **

**Viewing and Editing Matrix Elements....................................................260 Displaying Matrix Elements.............................................................260 Deleting a Matrix .............................................................................261 Viewing a Matrix..............................................................................261 Viewing-Context Keys.....................................................................262 Editing a Matrix Element .................................................................262 Editing-Context Keys ......................................................................264 **

**Using Matrices with Expressions ..........................................................265 Using a Matrix in an Expression .....................................................265 Entering a Matrix in an Expression .................................................265 **

**Displaying and Copying Matrices..........................................................267 Displaying a Matrix..........................................................................267 Copying One Matrix to Another.......................................................267 Accessing a Matrix Element............................................................268 **

**Using Math Functions with Matrices .....................................................269 Using Math Functions with Matrices ...............................................269 + (Add), (Subtract), (Multiply) ....................................................269 L (Negation).....................................................................................270 abs( .................................................................................................271 round(..............................................................................................271 M1 (Inverse)......................................................................................271**

Page 809

**TI-83 Plus Quick-Find Locator xviii **

**Powers ............................................................................................272 Relational Operations .....................................................................272 iPart(, fPart(, int(..............................................................................273 **

**Using the MATRX MATH Operations ...................................................274 MATRX MATH Menu ......................................................................274 det(..................................................................................................275 T (Transpose) .................................................................................275 Accessing Matrix Dimensions with dim(..........................................275 Creating a Matrix with dim( .............................................................276 Redimensioning a Matrix with dim( ...................................................276 Fill( ..................................................................................................276 identity( ...........................................................................................277 randM(.............................................................................................277 augment(.........................................................................................277 Matr4list( ..........................................................................................278 List4matr(.........................................................................................279 c*msum(.........................................................................................279 Row Operations ..............................................................................280 ref(, rref( ..........................................................................................280 rowSwap( ........................................................................................281 row+(...............................................................................................281 row(...............................................................................................282 row+(.............................................................................................282 **

**Chapter 11: Lists...........................................................................** **283**

**Getting Started: Generating a Sequence..............................................283 Naming Lists .........................................................................................286 **

**Using TI-83 Plus List Names L1 through L6 ...................................286**

Page 810

**TI-83 Plus Quick-Find Locator xix **

**Creating a List Name on the Home Screen ....................................286 Storing and Displaying Lists..................................................................288 **

**Storing Elements to a List ...............................................................288 Displaying a List on the Home Screen............................................288 Copying One List to Another...........................................................289 Accessing a List Element................................................................289 Deleting a List from Memory ...........................................................289 Using Lists in Graphing...................................................................290 **

**Entering List Names .............................................................................291 Using the LIST NAMES Menu ........................................................291 Entering a User-Created List Name Directly...................................292 **

**Attaching Formulas to List Names........................................................293 Attaching a Formula to a List Name................................................293 Attaching a Formula to a List on the Home Screen or in a **

**Program ....................................................................................294 Detaching a Formula from a List.....................................................296 **

**Using Lists in Expressions....................................................................297 Using a List in an Expression..........................................................297 Using Lists with Math Functions .....................................................298 **

**LIST OPS Menu....................................................................................299 LIST OPS Menu..............................................................................299 SortA(, SortD( .................................................................................299 Using dim( to Find List Dimensions ................................................301 Using dim( to Create a List .............................................................301 Using dim( to Redimension a List ...................................................301 Fill( ..................................................................................................302 seq( .................................................................................................302 c*msum(.........................................................................................303**

Page 811

**TI-83 Plus Quick-Find Locator xx **

**@List( ...............................................................................................303 Select(.............................................................................................304 Before Using Select( .......................................................................304 Using Select( to Select Data Points from a Plot..............................305 augment(.........................................................................................307 List4matr(.........................................................................................308 Matr4list( ..........................................................................................308 **

**LIST MATH Menu .................................................................................311 LIST MATH Menu ...........................................................................311 min(, max( .......................................................................................311 mean(, median(...............................................................................312 sum(, prod(......................................................................................313 Sums and Products of Numeric Sequences ...................................313 stdDev(, variance(...........................................................................314 **

**Chapter 12: Statistics** **...................................................................** **315**

**Getting Started: Pendulum Lengths and Periods..................................315 Setting Up Statistical Analyses .............................................................328 **

**Using Lists to Store Data ................................................................328 Setting Up a Statistical Analysis .....................................................328 Displaying the Stat List Editor .........................................................329 **

**Using the Stat List Editor ......................................................................330 Entering a List Name in the Stat List Editor ....................................330 Creating a Name in the Stat List Editor...........................................332 Removing a List from the Stat List Editor........................................332 Removing All Lists and Restoring L1 through L6............................333 Clearing All Elements from a List....................................................333 Editing a List Element .....................................................................334**

Page 812

**TI-83 Plus Quick-Find Locator xxi **

**Attaching Formulas to List Names........................................................336 Attaching a Formula to a List Name in Stat List Editor ...................336 Using the Stat List Editor When Formula-Generated Lists Are **

**Displayed ..................................................................................338 Handling Errors Resulting from Attached Formulas........................339 **

**Detaching Formulas from List Names ..................................................340 Detaching a Formula from a List Name ..........................................340 Editing an Element of a Formula-Generated List............................341 **

**Switching Stat List Editor Contexts .......................................................342 Stat List Editor Contexts .................................................................342 **

**Stat List Editor Contexts .......................................................................344 View-Elements Context...................................................................344 Edit-Elements Context ....................................................................344 View-Names Context ......................................................................346 Enter-Name Context .......................................................................346 **

**STAT EDIT Menu .................................................................................348 STAT EDIT Menu............................................................................348 SortA(, SortD( .................................................................................348 ClrList..............................................................................................349 SetUpEditor.....................................................................................350 Restoring L1 through L6 to the Stat List Editor ...............................351 **

**Regression Model Features..................................................................352 Regression Model Features............................................................352 Automatic Residual List ..................................................................352 Automatic Regression Equation......................................................353 Diagnostics Display Mode...............................................................354 **

**STAT CALC Menu ................................................................................356 STAT CALC Menu ..........................................................................356**

Page 813

**TI-83 Plus Quick-Find Locator xxii **

**Frequency of Occurrence for Data Points.......................................357 1.Var Stats......................................................................................357 2.Var Stats......................................................................................358 Med.Med (ax+b) .............................................................................358 LinReg (ax+b) .................................................................................359 QuadReg (ax2+bx+c)......................................................................359 CubicReg(ax3+bx2+cx+d) ..........................................................359 QuartReg(ax4+bx3+cx2+ dx+e)..................................................360 LinReg(a+bx)...............................................................................360 LnReg(a+b ln(x)) .........................................................................360 ExpReg(abx) ...............................................................................361 PwrReg(axb) ...............................................................................361 Logisticc/(1+aeLbx) ...................................................................361 SinRega sin(bx+c)+d...................................................................362 SinReg Example: Daylight Hours in Alaska for One Year ...............363 **

**Statistical Variables...............................................................................365 Q1 and Q3 ......................................................................................366 **

**Statistical Analysis in a Program...........................................................367 Entering Stat Data...........................................................................367 Statistical Calculations ....................................................................367 **

**Statistical Plotting..................................................................................368 Steps for Plotting Statistical Data in Lists .......................................368 " (Scatter) .....................................................................................369 (xyLine) ....................................................................................369 (Histogram) ..............................................................................370 (ModBoxplot) ............................................................................370 (Boxplot) ...................................................................................371 (NormProbPlot) ........................................................................372**

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**TI-83 Plus Quick-Find Locator xxiii **

**Defining the Plots............................................................................373 Displaying Other Stat Plot Editors...................................................375 Turning On and Turning Off Stat Plots............................................375 Defining the Viewing Window .........................................................376 Tracing a Stat Plot ..........................................................................376 **

**Statistical Plotting in a Program............................................................378 Defining a Stat Plot in a Program....................................................378 Displaying a Stat Plot from a Program............................................380 **

**Chapter 13: Inferential Statistics and Distributions** **..................** **381**

**Getting Started: Mean Height of a Population ......................................381 Height (in centimeters) of Each of 10 Women ................................381 **

**Inferential Stat Editors ..........................................................................388 Displaying the Inferential Stat Editors .............................................388 Using an Inferential Stat Editor .......................................................388 Selecting Data or Stats ...................................................................390 Entering the Values for Arguments .................................................390 Selecting an Alternative Hypothesis ( < >)....................................391 Selecting the Pooled Option ...........................................................391 Selecting Calculate or Draw for a Hypothesis Test.........................392 Selecting Calculate for a Confidence Interval .................................392 Bypassing the Inferential Stat Editors .............................................393 **

**STAT TESTS Menu ..............................................................................394 STAT TESTS Menu ........................................................................394 Inferential Stat Editors for the STAT TESTS Instructions ...............395 Z.Test .............................................................................................396 T.Test .............................................................................................397 2.SampZTest ..................................................................................399**

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**TI-83 Plus Quick-Find Locator xxiv **

**2.SampTTest ..................................................................................400 1.PropZTest....................................................................................402 2.PropZTest....................................................................................403 ZInterval ..........................................................................................405 TInterval ..........................................................................................406 2.SampZInt .....................................................................................407 2.SampTInt .....................................................................................408 1.PropZInt.......................................................................................410 2.PropZInt.......................................................................................411 c2.Test............................................................................................412 2.SampTest..................................................................................414 LinRegTTest ...................................................................................415 ANOVA( ..........................................................................................417 **

**Inferential Statistics Input Descriptions.................................................419 Test and Interval Output Variables .......................................................422 Distribution Functions ...........................................................................424 **

**DISTR menu ...................................................................................424 normalpdf(.......................................................................................425 normalcdf( .......................................................................................426 invNorm( .........................................................................................426 tpdf(.................................................................................................427 tcdf( .................................................................................................427 c2pdf(..............................................................................................428 c2cdf( ..............................................................................................429 pdf( ...............................................................................................429 cdf(................................................................................................430 binompdf .........................................................................................430 binomcdf( ........................................................................................431**

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**TI-83 Plus Quick-Find Locator xxv **

**poissonpdf( .....................................................................................432 poissoncdf(......................................................................................432 geometpdf(......................................................................................433 geometcdf( ......................................................................................433 **

**Distribution Shading..............................................................................434 DISTR DRAW Menu .......................................................................434 ShadeNorm(....................................................................................435 Shade_t( .........................................................................................435 Shadec2( ........................................................................................436 Shade( ..........................................................................................437 **

**Chapter 14: Applications** **..............................................................** **438**

**The Applications Menu .........................................................................438 Steps for Running the Finance Application.....................................439 **

**Getting Started: Financing a Car ..........................................................440 Getting Started: Computing Compound Interest...................................442 Using the TVM Solver ...........................................................................444 **

**Using the TVM Solver .....................................................................444 Using the Financial Functions...............................................................446 **

**Entering Cash Inflows and Cash Outflows......................................446 FINANCE CALC Menu....................................................................446 TVM Solver .....................................................................................447 **

**Calculating Time Value of Money (TVM) ..............................................448 Calculating Time Value of Money ...................................................448 tvm_Pmt..........................................................................................449 tvm_.............................................................................................449 tvm_PV ...........................................................................................450 tvm_..............................................................................................450**

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**TI-83 Plus Quick-Find Locator xxvi **

**tvm_FV............................................................................................451 Calculating Cash Flows ........................................................................452 **

**Calculating a Cash Flow .................................................................452 npv(, irr(...........................................................................................453 **

**Calculating Amortization .......................................................................454 Calculating an Amortization Schedule ............................................454 bal( ..................................................................................................454 GPrn(, GInt(......................................................................................455 Amortization Example: Calculating an Outstanding Loan **

**Balance .....................................................................................456 Calculating Interest Conversion............................................................459 **

**Calculating an Interest Conversion .................................................459 4Nom(..............................................................................................459 4Eff( .................................................................................................459 **

**Finding Days between Dates/Defining Payment Method ..........................460 dbd(.................................................................................................460 Defining the Payment Method.........................................................461 Pmt_End .........................................................................................461 Pmt_Bgn .........................................................................................461 **

**Using the TVM Variables ......................................................................462 FINANCE VARS Menu ...................................................................462 , , PV, PMT, FV .........................................................................462 P/Y and C/Y ....................................................................................463 **

**The CBL/CBR Application.....................................................................464 Steps for Running the CBLCBR Application .................................464 Selecting the CBL/CBR Application ................................................466 **

**Data Collection Methods and Options ..................................................467**

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**TI-83 Plus Quick-Find Locator xxvii **

**Specifying the Data Collection Method from the CBL/CBR APP Menu.................................................................................467 **

**Specifying Options for Each Data Collection Method .....................468 GAUGE ...........................................................................................468 TYPE...............................................................................................469 MIN and MAX..................................................................................470 UNITS .............................................................................................470 DIRECTNS (Directions) ..................................................................471 Data Collection Comments and Results .........................................471 DATA LOGGER ..............................................................................473 #SAMPLES .....................................................................................475 INTRVL (SEC) ................................................................................475 UNITS .............................................................................................475 PLOT...............................................................................................476 Ymin and Ymax...............................................................................476 DIRECTNS (Directions) ..................................................................476 Data Collection Results...................................................................477 RANGER.........................................................................................478 **

**Starting Data Collection ........................................................................479 Collecting the Data..........................................................................479 **

**Stopping Data Collection ......................................................................480 **

**Chapter 15: CATALOG, Strings, Hyperbolic Functions** **...........** **481**

**Browsing the TI-83 Plus CATALOG......................................................481 What Is the CATALOG?..................................................................481 Selecting an Item from the CATALOG............................................482 **

**Entering and Using Strings ...................................................................484 What Is a String? ............................................................................484**

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**TI-83 Plus Quick-Find Locator xxviii **

**Entering a String .............................................................................484 Storing Strings to String Variables ........................................................486 **

**String Variables...............................................................................486 Storing a String to a String Variable................................................487 Displaying the Contents of a String Variable ..................................488 **

**String Functions and Instructions in the CATALOG..............................489 Displaying String Functions and Instructions in the CATALOG ......489 + (Concatenation)............................................................................490 Selecting a String Function from the CATALOG.............................490 Equ 4String( ......................................................................................491 expr(................................................................................................491 inString(...........................................................................................492 length( .............................................................................................492 String4Equ( ......................................................................................493 sub( .................................................................................................493 Entering a Function to Graph during Program Execution ...............494 **

**Hyperbolic Functions in the CATALOG ................................................495 Hyperbolic Functions ......................................................................495 sinh(, cosh(, tanh( ...........................................................................496 sinh L1(, coshL1(, tanhL1(..................................................................496 **

**Chapter 16: Programming.............................................................** **497**

**Getting Started: Volume of a Cylinder ..................................................497 Creating and Deleting Programs ..........................................................500 **

**What Is a Program? ........................................................................500 Creating a New Program ................................................................500 Managing Memory and Deleting a Program ...................................501 **

**Entering Command Lines and Executing Programs.............................504**

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**TI-83 Plus Quick-Find Locator xxix **

**Entering a Program Command Line ...............................................504 Executing a Program ......................................................................505 Breaking a Program ........................................................................506 **

**Editing Programs ..................................................................................507 Editing a Program ...........................................................................507 Inserting and Deleting Command Lines..........................................508 **

**Copying and Renaming Programs........................................................509 Copying and Renaming a Program.................................................509 Scrolling the PRGM EXEC and PRGM EDIT Menus......................510 **

**PRGM CTL (Control) Instructions.........................................................511 PRGM CTL Menu ...........................................................................511 Controlling Program Flow ...............................................................512 If ..................................................................................................512 If.Then ............................................................................................513 If.Then.Else ....................................................................................514 For( .................................................................................................515 While ...............................................................................................516 Repeat ............................................................................................517 End..................................................................................................518 Pause..............................................................................................518 Lbl, Goto .........................................................................................519 IS>( .................................................................................................520 DS<(................................................................................................521 Menu(..............................................................................................521 prgm................................................................................................522 Return .............................................................................................523 Stop.................................................................................................523 DelVar .............................................................................................523**

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**TI-83 Plus Quick-Find Locator xxx **

**GraphStyle(.....................................................................................524 PRGM I/O (Input/Output) Instructions...................................................525 **

**PRGM I/O Menu .............................................................................525 Displaying a Graph with Input .........................................................526 Storing a Variable Value with Input.................................................527 Prompt ............................................................................................528 Displaying the Home Screen ..........................................................528 Displaying Values and Messages ...................................................529 DispGraph.......................................................................................530 DispTable........................................................................................530 Output( ............................................................................................530 getKey.............................................................................................531 TI-83 Plus Key Code Diagram ........................................................532 ClrHome, ClrTable ..........................................................................532 GetCalc(..........................................................................................533 Get(, Send( .....................................................................................533 **

**Calling Other Programs as Subroutines ...............................................535 Calling a Program from Another Program.......................................535 Notes about Calling Programs ........................................................536 **

**Running an Assembly Language Program ...........................................537 **

**Chapter 17: Activities** **...................................................................** **540**

**The Quadratic Formula.........................................................................540 Entering a Calculation.....................................................................540 Converting to a Fraction..................................................................542 Displaying Complex Results ...........................................................544 **

**Box with Lid ..........................................................................................546 Defining a Function .........................................................................546**

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**TI-83 Plus Quick-Find Locator xxxi **

**Defining a Table of Values..............................................................547 Zooming In on the Table .................................................................549 Setting the Viewing Window ...........................................................551 Displaying and Tracing the Graph ..................................................553 Zooming In on the Graph ................................................................555 Finding the Calculated Maximum....................................................557 **

**Comparing Test Results Using Box Plots .............................................560 Problem...........................................................................................560 Procedure .......................................................................................561 **

**Graphing Piecewise Functions .............................................................564 Problem...........................................................................................564 Procedure .......................................................................................564 **

**Graphing Inequalities............................................................................566 Problem...........................................................................................566 Procedure .......................................................................................566 **

**Solving a System of Nonlinear Equations.............................................568 Problem...........................................................................................568 Procedure .......................................................................................568 **

**Using a Program to Create the Sierpinski Triangle...............................570 Setting up the Program ...................................................................570 Program ..........................................................................................570 **

**Graphing Cobweb Attractors ................................................................572 Problem...........................................................................................572 Procedure .......................................................................................572 **

**Using a Program to Guess the Coefficients..........................................574 Setting Up the Program ..................................................................574 Program ..........................................................................................574 **

**Graphing the Unit Circle and Trigonometric Curves .............................576**

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**TI-83 Plus Quick-Find Locator xxxii **

**Problem...........................................................................................576 Procedure .......................................................................................576 **

**Finding the Area between Curves ........................................................578 Problem...........................................................................................578 Procedure .......................................................................................578 **

**Using Parametric Equations: Ferris Wheel Problem.............................580 Problem...........................................................................................580 Procedure .......................................................................................581 **

**Demonstrating the Fundamental Theorem of Calculus ........................584 Problem 1........................................................................................584 Procedure 1 ....................................................................................584 Problem 2........................................................................................586 Procedure 2 ....................................................................................586 **

**Computing Areas of Regular N-Sided Polygons...................................588 Problem...........................................................................................588 Procedure .......................................................................................588 **

**Computing and Graphing Mortgage Payments ....................................592 Problem...........................................................................................592 Procedure .......................................................................................592 **

**Chapter 18: Memory and Variable Management........................** **596**

**Checking Available Memory .................................................................596 MEMORY Menu..............................................................................596 Displaying the MEMORY MANAGEMENT/DELETE Menu.............597 **

**Deleting Items from Memory.................................................................599 Deleting an Item..............................................................................599 **

**Clearing Entries and List Elements.......................................................601 Clear Entries ...................................................................................601**

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**TI-83 Plus Quick-Find Locator xxxiii **

**ClrAllLists ........................................................................................602 Resetting the TI-83 Plus .......................................................................603 **

**RAM ARCHIVE ALL Menu..............................................................603 Displaying the RAM ARCHIVE ALL Menu ......................................604 Resetting RAM Memory..................................................................604 Resetting Archive Memory..............................................................606 Resetting All Memory......................................................................608 **

**Archiving and UnArchiving Variables....................................................610 Archiving and UnArchiving Variables..............................................610 **

**Grouping and Ungrouping Variables ....................................................616 Grouping Variables .........................................................................616 Ungrouping Variables .....................................................................619 DuplicateName Menu .....................................................................619 **

**Garbage Collection ...............................................................................622 Garbage Collection Message..........................................................622 Responding to the Garbage Collection Message ...........................622 Why Not Perform Garbage Collection Automatically Without a **

**Message?..................................................................................623 Why Is Garbage Collection Necessary? .........................................623 How Unarchiving a Variable Affects the Process............................625 If the MEMORY Screen Shows Enough Free Space......................626 The Garbage Collection Process ....................................................626 Using the GarbageCollect Command .............................................627 **

**ERR:ARCHIVE FULL Message............................................................628**

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**TI-83 Plus Quick-Find Locator xxxiv **

**Chapter 19: Communication Link** **................................................** **629**

**Getting Started: Sending Variables.......................................................629 TI-83 Plus Silver Edition LINK...............................................................632 **

**Connecting Two Calculators with a Unit-to-Unit Cable ...................633 Linking to the CBL/CBR System .....................................................633 Linking to a Computer.....................................................................633 **

**Selecting Items to Send........................................................................634 LINK SEND Menu ...........................................................................634 Sending the Selected Items ............................................................636 Stopping a Transmission ................................................................637 Sending to a TI-83 Plus Silver Edition or TI-83 Plus.......................638 Sending to a TI-83 ..........................................................................640 Sending Lists to a TI-82 ..................................................................641 Sending to a TI-73 ..........................................................................642 **

**Receiving Items ....................................................................................644 LINK RECEIVE Menu .....................................................................644 Receiving Unit.................................................................................644 DuplicateName Menu .....................................................................644 Receiving from a TI-83 Plus Silver Edition or TI-83 Plus ................645 Receiving from a TI-83....................................................................646 Receiving from a TI-82 Resolved Differences............................646 Receiving from a TI-82 Unresolved Differences.........................647 Receiving from a TI-73....................................................................648 **

**Backing Up RAM Memory.....................................................................650 Memory Backup Complete..............................................................651 **

**Error Conditions....................................................................................652 Insufficient Memory in Receiving Unit .............................................653**

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**TI-83 Plus Quick-Find Locator xxxv **

**Appendix A: Tables and Reference Information........................** **654**

**Table of Functions and Instructions......................................................654 TI-83 Plus Menu Map ...........................................................................698 Variables...............................................................................................718 **

**User Variables ................................................................................718 Archive Variables ............................................................................719 System Variables ............................................................................719 **

**Statistics Formulas ...............................................................................721 Logistic............................................................................................721 SinReg ............................................................................................722 ANOVA( ..........................................................................................722 2.SampTest..................................................................................724 2.SampTTest ..................................................................................726 **

**Financial Formulas ...............................................................................728 Time Value of Money ......................................................................728 Amortization ....................................................................................731 Cash Flow .......................................................................................732 Interest Rate Conversions ..............................................................733 Days between Dates.......................................................................733 **

**Appendix B: General Information** **...............................................** **735**

**Battery Information ...............................................................................735 When to Replace the Batteries .......................................................735 Effects of Replacing the Batteries...................................................736 Battery Precautions.........................................................................737 Replacing the Batteries...................................................................737**

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**TI-83 Plus Quick-Find Locator xxxvi **

**In Case of Difficulty ...............................................................................739 Handling a Difficulty ........................................................................739 **

**Error Conditions....................................................................................742 Accuracy Information ............................................................................754 **

**Computational Accuracy .................................................................754 Function Limits................................................................................756 Function Results .............................................................................757 **

**Support and Service Information ..........................................................758 Product Support ..............................................................................758 Product Service...............................................................................759 **

**Warranty Information ......................................................**

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