Texas Instruments TI-83 PLUS User Manual

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83 Plus /

TI-83 Plus Silver Edition

Graphing Calculator Guidebook

First Steps

On/Off Graphing a function Menus Modes Using parentheses Lists

Creating…

Tables Data and lists Matrices Split screen

Beyond the Basics

Inferential statistics Archiving/Unarchiving Programming Menu maps

More Information

Sending and receiving Troubleshooting Formulas Support and service

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.

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:

approved by Texas Instruments may void your authority to operate the equipment.

TI-83 Plus

Any changes or modifications to this equipment not expressly

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.

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

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 Editing Advanced

advanced functions.

Scientific

standard scientific calculator.

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

— Graphing keys access the interactive graphing features.

— Editing keys allow you to edit expressions and values.

— Advanced function keys display menus that access the

— Scientific calculator keys access the capabilities of a

TI-83 Plus

Graphing Keys

Editing Keys Advanced

Function Keys

Scientific Calculator Keys

Colors may vary in actual product.

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

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

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

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

This guidebook describes this keystroke combination as

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

is entered.

[

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

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

key

Turning On and Turning Off the TI-83 Plus

Turning On the Calculator

To turn on the TI-83 Plus, press É.

•

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™ (APDé) 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.

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

Turning Off the Calculator

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

•

All settings and memory contents are retained by Constant

Memory

•

Any error condition is cleared.

Batteries

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

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

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

(darkest) in the top-right corner indicates the current level. You may

to not be able to see the number if contrast is too light or too dark.

(lightest)

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

through

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).

†

•

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

lightens the screen.

}

darkens the screen.

If you adjust the contrast setting to

Note:

blank. To restore the screen, press and release y, and then press and hold

until the display reappears.

}

, the display may become completely

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.

The operating period following the first low-battery message could be

Note:

longer than two weeks if you use the calculator infrequently.

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

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 (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.

editor (Chapter 3), or the program editor

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

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

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.

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

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

Insert Underline

Second Reverse arrow

Alpha Reverse A

Full Checkerboard

rectangle

If you press

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

an underlined # (

during an insertion, the cursor becomes an underlined

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

A character is inserted in front of the cursor location

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

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

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

SOLVE

is executed

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

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

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, pR 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 (EOSé) the answer is displayed.

is an

rules

, and

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

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

. 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

L, O

variables

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

, and G.

Ë 76 ¥ £ Ì 7 Ë 9 Ã y

¤ ¤ Ã 2

Multiple Entries on a Line

To enter two or more expressions or instructions on a line, separate them with colons ( entry (

ENTRY

) .

]). All instructions are stored together in last

[

Entering a Number in Scientific Notation

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

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

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 Ì, 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 (

sin(

name. For example,

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

requires one argument,

) following the

sin(

value

)

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 ( example,

Circle(

requires three arguments,

) at the end of the name. For

Circle(X,Y,

radius

)

Interrupting a Calculation

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

When you interrupt a calculation, a menu is displayed.

•

To return to the home screen, select

•

To go to the location of the interruption, select

1:Quit

2:Goto

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

•

To return to the home screen, press

•

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

‘

or any nongraphing key.

instruction.

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

TI-83 Plus Edit Keys

Keystrokes Result

}

†

y |

y ~

‘

{

y 6

Moves the cursor within an expression; these keys repeat. 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. Moves the cursor to the beginning of an expression. 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. Changes the cursor to an underline (

front of the underline cursor; to end insertion, press y 6 or press |, }, ~, or †.

); inserts characters in

†

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

Keystrokes Result

y 7

„

Changes the cursor to Þ; the next keystroke performs a

2nd

operation (an operation in yellow above a key and to the left); to cancel

, press y again.

2nd

Changes the cursor to Ø; the next keystroke pastes an alpha character (a character in green above a key and to the right) or executes

or press |, }, ~, or †.

SOLVE

(Chapters 10 and 11); to cancel

, press

Changes the cursor to Ø; 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

mode with one keystroke.

Seq

mode, a T in

Func

mode, a q in

Par

mode, or

Pol

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

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

. The current settings are highlighted. Defaults are highlighted below. The following pages describe the mode settings in detail.

Normal Sci Eng

Float 0123456789

Radian Degree

Func Par Pol Seq

Connected Dot

Sequential Simul Real a+bi re^qi

Full Horiz G-T

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

Numeric notation Number of decimal places Unit of angle measure Type of graphing Whether to connect graph points Whether to plot simultaneously Real, rectangular complex, or polar complex Full screen, two split-screen modes

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

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.

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

Normal

to the left and right of the decimal, as in

Sci

notation mode is the usual way we express numbers, with digits

12345.67

(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

Eng

(engineering) notation mode is similar to scientific notation.

, as in

1.234567E4

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 (or the absolute value is less than .001), the TI-83 Plus expresses the answer in scientific notation.

Normal

notation, but the answer cannot display in 10 digits

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 (

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

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

Normal, Sci

, and

Eng

notation modes.

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

•

The regression equation stored after the execution of a regression

CALCULATE

operations (Chapters 3, 4, 5, and 6)

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.

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

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

(Chapter 3).

Par

(parametric) graphing mode plots relations, where X and Y are

functions of

Pol

(polar) graphing mode plots functions, where r is a function of

(Chapter 4).

(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.

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

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

them for the next value of

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+bi, re^

Real

mode does not display complex results unless complex numbers

and then evaluates and plots

are entered as input. Two complex modes display complex results.

a+b

•

(rectangular complex mode) displays complex numbers in the

form a+b

re^

(polar complex mode) displays complex numbers in the form

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

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).

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

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 Complex numbers Matrices Lists Functions Parametric equations Polar functions Sequence functions Stat plots Graph databases

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

, ... ,

A, B A, B

ãAä, ãBä, ãCä

L1, L2, L3, L4, L5, L6 Y1, Y2 X1T r1, r2, r3, r4, r5, r6 u, v, w Plot1, Plot2, Plot3 GDB1, GDB2

, ... ,

, . . . , Y9,

and

Y1T

, ... ,

, . . . ,

ãJä

X6T

, and user-defined names

and

Y6T

GDB9, GDB0

Variable Type Names

Graph pictures Strings Apps Applications AppVars Application variables Groups Grouped variables System variables

Pic1, Pic2 Str1, Str2

Xmin, Xmax

, ... ,

Pic9, Pic0

, ... ,

Str9, Str0

, 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

functions (Chapters 3, 4, 5, and 6).

•

From an editor, you can store to matrices, lists, and

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.

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

•

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

Apps

•

AppVars

are independent applications.which are stored in Flash ROM.

is a variable holder used to store variables created by

cannot be archived (Chapter 18)

independent applications. You cannot edit or change variables in

AppVars

unless you do so through the application which created

them.

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

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

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

key, begin on a blank line and follow these steps.

2. Press

3. Press store the value.

4. Press is stored to the variable.

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

¿. !

and then the letter of the variable to which you want to

. If you entered an expression, it is evaluated. The value

is copied to the cursor location.

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 won’t be able to see its contents or edit it until they are unarchived.

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

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

RCLä

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

•

Press y

[

•

Press y

•

Press

VARS Y.VARS



and then the letter of the variable.

ãLISTä

, and then select the name of the list, or press

, and then select the name of the matrix.

to display the

VARS

menu or

 ~

to display the

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).

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

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.

You can edit the characters pasted to the expression without

Note:

affecting the value in memory.

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

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

To recall

is retained in memory.

ENTRY

, press y

ENTRY

(last entry). When you turn off the TI-83 Plus,

[

. 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.

Í y [

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

Accessing a Previous Entry

The TI-83 Plus retains as many previous entries as possible in to a capacity of 128 bytes. To scroll those entries, press y

[

ENTRY

, up

repeatedly. If a single entry is more than 128 bytes, it is retained for

ENTRY

Í y [

, but it cannot be placed in the

¿ ƒ

If you press y

[

after displaying the oldest stored entry, the

ENTRY

storage area.

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

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

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.

¿ ƒ

Í ƒ

ã:ä

Í Í

Ã 1

¿ ƒ

Multiple Entry Values on a Line

To store to

ENTRY

expression or instruction with a colon, then press and instructions separated by colons are stored in

When you press y

two or more expressions or instructions, separate each

[

, all the expressions and instructions separated

. All expressions

ENTRY

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

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

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.

¿ ƒ

y | Í

Continue until the answer is as accurate as you want.

Í y [

y 6 Ë

[:] y

Clearing ENTRY

Clear Entries

ENTRY

the

(Chapter 18) clears all data that the TI-83 Plus is holding in

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

Ans

called

(last answer).

matrix, or a string. When you turn off the TI-83 Plus, the value in

Ans

may be a real or complex number, a list, a

Ans

retained in memory.

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

You can use the variable Press y

to copy the variable name

the expression is evaluated, the TI-83 Plus uses the value of

Ans

to represent the last answer in most places.

Ans

to the cursor location. When

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.

Ë 7 ¯ 4 Ë

¥ y

147

Continuing an Expression

Ans

You can use the value again or pressing y screen, enter the function. The TI-83 Plus pastes the variable name

as the first entry in the next expression without entering

. On a blank line on the home

Ans

to the screen, then the function.

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

Storing Answers

Ans

To store an answer, store

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 Í ¯ Í ¿ ƒ Í

TI-83 Plus Operating the TI-83 Plus Silver Edition 38

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 also is highlighted.

•

A number or letter identifies each menu item’s place in the menu. The

order is

PRGM EXEC

•

When the menu continues beyond the displayed items, a down arrow

through 9, then 0, then A, B, C, and so on. The

PRGM EDIT

, and

menus only label items 1 through 9 and 0.

($) 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).

, which

LIST NAMES

TI-83 Plus Operating the TI-83 Plus Silver Edition 39

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.

The Menu Map in Appendix A shows each menu, each operation under

Note:

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

MATH

the

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.

TI-83 Plus Operating the TI-83 Plus Silver Edition 40

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 menu items at a time, press

ƒ }

. The green arrows on the

ƒ †

. To page up six

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.

TI-83 Plus Operating the TI-83 Plus Silver Edition 41

•

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.

On the

Note:

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

. If no items begin with that character, the cursor moves beyond it to the next

item.

Calculate

 † † † Í

TI-83 Plus Operating the TI-83 Plus Silver Edition 42

LIST NAMES, PRGM EXEC

27.

‡

, and

PRGM EDIT

menus, only items

Leaving a Menu without Making a Selection

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

•

Press y

•

Press

•

Press a key or key combination for a different menu, such as

y 9

•

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

y 0

‘

to return to the home screen.

to return to the previous screen.



TI-83 Plus Operating the TI-83 Plus Silver Edition 43

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

2: Zoom

3: GDB

4: Picture

5: Statistics

6: Table

7: String

TI-83 Plus Operating the TI-83 Plus Silver Edition 44

...

X/Y ZX/ZY Graph database Picture XY TABLE String

, and

ZT/Z

variables

, G, EQ,

variables

U/V/W

, and ZU variables

TEST

variables

, and

PTS

variables

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

To display the

2:Parametric

, and

VARS Y.VARS

3:Polar

menu, press

display secondary menus of the Y= function

variables.

VARS Y-VARS

1: Function

2: Parametric

3: Polar

4: On/Off

Note: The sequence variables (

...

functions

Lets you select/deselect functions

u, v, w

) are located on the keyboard as the

second functions of ¬, −, and ®.

To select a variable from the

VARS

VARS Y.VARS

steps.

1. Display the

•

Press Press



 ~

VARS

VARS Y.VARS

to display the

menu.

VARS

VARS Y.VARS

2. Select the type of variable, such as

3:Polar

from the

VARS Y.VARS

menu. A secondary menu is displayed.

 ~

menu.

2:Zoom

1:Function

menu, follow these

menu.

from the

VARS

menu or

TI-83 Plus Operating the TI-83 Plus Silver Edition 45

3. If you selected

1:Window, 2:Zoom

5:Statistics

, or

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.

TI-83 Plus Operating the TI-83 Plus Silver Edition 46

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 2

3 4 5 6 7 8 9

Functions that precede the argument, such as Functions that are entered after the argument, such as 2,

, and conversions

Powers and roots, such as Permutations ( Multiplication, implied multiplication, and division Addition and subtraction Relational functions, such as > or Logic operator Logic operators or and

) and combinations (

nPr

and

2^5

xor

‡

)

nCr



(

sin(

, or

log(

, !, ¡,

‡

TI-83 Plus Operating the TI-83 Plus Silver Edition 47

Within a priority level, EOS evaluates functions from left to right.

Note:

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

4sin(46), 5(1+2)

interprets

TI-83 Plus implied multiplication rules, although like theTI.83, differ from

Note:

those of the TI.82. For example, the TI-83 Plus evaluates while the TI.82 evaluates

1à2X

, and

1/(2äX)

(2ä5)7

(Chapter 2).

as implied multiplication.

1à2X

(1à2)äX

Parentheses

All calculations inside a pair of parentheses are completed first. For example, in the expression

1+2

the parentheses,

, and then multiplies the answer, 3, by 4.

4(1+2)

, EOS first evaluates the portion inside

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.

TI-83 Plus Operating the TI-83 Plus Silver Edition 48

An open parenthesis following a list name, matrix name, or

Note:

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

function.

Negation

To enter a negative number, use the negation key. Press Ì 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,

, evaluates to a negative number (or 0). Use

parentheses to square a negative number.

Use the ¹ key for subtraction and the Ì key for negation. If you press

Note:

to enter a negative number, as in subtraction, as in

Ì 7, an error occurs. If you press

interpreted as implied multiplication (

TI-83 Plus Operating the TI-83 Plus Silver Edition 49

¯ ¹ 7, or if you press Ì to indicate

A Ì

B, it is

Special Features of the TI-83 Plus

Flash – Electronic Upgradability

The TI-83 Plus uses Flash technology, which lets you

For details, refer to:

Chapter 19

upgrade to future software versions without buying a new calculator.

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

For details, refer to:

Chapter 18

(random access memory) are available for you to compute and store functions, programs, and data.

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

TI-83 Plus Operating the TI-83 Plus Silver Edition 50

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

For details, refer to:

Chapter 18

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.

Archiving

You can store variables in the TI-83 Plus user data archive, a protected area of memory

For details, refer to:

Chapter 18

separate from RAM. The user data archive lets you:

•

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.

TI-83 Plus Operating the TI-83 Plus Silver Edition 51

Calculator-Based Laboratoryé (CBL 2é, CBLé) and Calculator-Based Rangeré (CBRé)

The TI-83 Plus comes with the CBL/CBR application already installed. When coupled

For details, refer to:

Chapter 14

with the (optional) CBL 2/CBL or CBR accessories, you can use the TI-83 Plus to analyze real world data.

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

CBL 2/CBL and CBR

in their user manuals.

TI-83 Plus Operating the TI-83 Plus Silver Edition 52

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.

DRAW

You can use

instructions to annotate

For graphing details, refer to:

Chapters 3, 4, 5, 6, 8

graphs. The graphing chapters appear in this order:

Sequence

, and

DRAW

Function, Parametric, Polar

Sequences

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

For details, refer to:

Chapter 6

or as phase plots.

TI-83 Plus Operating the TI-83 Plus Silver Edition 53

Tables

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

Split Screen

You can split the screen horizontally to display both a graph and a related editor (such as the

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.

Matrices

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

For details, refer to:

Chapter 7

For details, refer to:

Chapter 9

For details, refer to:

Chapter 10

TI-83 Plus Operating the TI-83 Plus Silver Edition 54

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.

Statistics

You can perform one- and two-variable, listbased 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.

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 11

For details, refer to:

Chapter 12

For details, refer to:

Chapter 13

TI-83 Plus Operating the TI-83 Plus Silver Edition 55

Applications

You can use such applications as Finance or the CBL/CBR. With the Finance application you

TVM

can use time-value-of-money (

) functions to

For details, refer to:

Chapter 14

analyze financial instruments such as annuities, 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 all functions and instructions on the TI-83 Plus.

is a convenient, alphabetical list of

For details, refer to:

Chapter 15

You can paste any function or instruction from the

CATALOG

to the current cursor location.

TI-83 Plus Operating the TI-83 Plus Silver Edition 56

Programming

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

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.

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 16

For details, refer to:

Chapter 16

For details, refer to:

Chapter 19

TI-83 Plus Operating the TI-83 Plus Silver Edition 57

With the

TI™ Connect

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-GRAPH LINK

software and a

TI-GRAPH LINK

cable to upgrade your

TI Connect

TI-83 Plus.

TI-83 Plus Operating the TI-83 Plus Silver Edition 58

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

each error type and possible reasons for the error.

ERR:DOMAIN

. Appendix B describes

•

If you select

1:Quit

(or press y

‘

), 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 execution, then the

TI-83 Plus Operating the TI-83 Plus Silver Edition 59

option returns to the Y= editor, not to the program.

Goto

function during program

Correcting an Error

To correct an error, follow these steps.

ERR:

1. Note the error type (

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.

TI-83 Plus Operating the TI-83 Plus Silver Edition 60

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

display the

7:randBin(

MATH PRB

(random Binomial).

to the home screen. Press

menu. Press 7 to select

number of coin flips. Press ¢. Press

 |

randBin(

is pasted

to enter the

enter the probability of heads. Press ¢. Press

to enter the number of simulations. Press ¤.

TI-83 Plus Math, Angle, and Test Operations 61

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 the list name

¿ y

L1ä

to store the data to

. You then can use the data for another activity, such as plotting a histogram (Chapter 12).

Note: Since your list elements may differ from those in the example.

TI-83 Plus Math, Angle, and Test Operations 62

randBin(

generates random numbers,

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), ä (Multiplication), à (Division)

You can use

(division, ¥) with real and complex numbers, expressions, lists, and

matrices. You cannot use

valueA+valueB valueA

valueA

valueB valueA

Trigonometric Functions

(addition, Ã), N (subtraction, ¹), ä (multiplication, ¯), and

with matrices.

valueB

You can use the trigonometric (trig) functions (sine, and tangent,

) with real numbers, expressions, and lists. The current

angle mode setting affects interpretation. For example,

mode returns

TI-83 Plus Math, Angle, and Test Operations 63

.9880316241

; in

Degree

mode it returns .5.

; cosine,

sin(30)

™

;

Radian

sin(

) cos(

value

) tan(

value

)

You can use the inverse trig functions (arcsine, y

; and arctangent, y

) with real numbers, expressions, and

; arccosine,

lists. The current angle mode setting affects interpretation.

sin

(

) cos

value

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

(

) tan

value

(

value

)

^ (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

value^power value

(Inverse)

You can use

with matrices.

‡

(inverse, œ) with real and complex numbers,

‡

(

value

)

expressions, lists, and matrices. The multiplicative inverse is equivalent

to the reciprocal, 1

value

TI-83 Plus Math, Angle, and Test Operations 64

log(, 10^(, ln(

You can use

log(

(logarithm,

10^(

(power of 10, y G), and

ln(

(natural log, µ) with real or complex numbers, expressions, and lists.

log(

) 10^(

value

power

) ln(

value

)

e^( (Exponential)

e^(

(exponential, y J) returns the constant e raised to a power. You

e^(

can use

e^(

power

with real or complex numbers, expressions, and lists.

)

e (Constant)

(constant, y [e]) is stored as a constant on the TI-83 Plus. Press

] to copy e to the cursor location. In calculations, the TI-83 Plus

[

uses 2.718281828459 for

TI-83 Plus Math, Angle, and Test Operations 65

(Negation)

(negation, Ì) returns the negative of

value

. You can use M with real or

complex numbers, expressions, lists, and matrices.

value

EOS™ rules (Chapter 1) determine when negation is evaluated. For

example,

returns a negative number, because squaring is evaluated

before negation. Use parentheses to square a negated number, as in

(LA)

Note: On the TI-83 Plus, the negation symbol ( subtraction sign (

(Pi)

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

), which is displayed when you press ¹.

the TI-83 Plus uses 3.1415926535898 for

) is shorter and higher than the

TI-83 Plus Math, Angle, and Test Operations 66

MATH Operations

MATH Menu

MATH

To display the

MATH NUM CPX PRB

Frac

2:4Dec

‡

(

‡

6: fMin(

7: fMax(

8: nDeriv(

9: fnInt(

0: Solver

Frac, 4Dec

Frac

You can use

...

(display as a fraction) displays an answer as its rational equivalent.

Frac

menu, press

Displays the answer as a fraction. Displays the answer as a decimal. Calculates the cube. Calculates the cube root. Calculates the Finds the minimum of a function. Finds the maximum of a function. Computes the numerical derivative. Computes the function integral. Displays the equation solver.

with real or complex numbers, expressions, lists, and

root.



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

Frac

following

value

TI-83 Plus Math, Angle, and Test Operations 67

value

use You can only use

value

Frac

Dec

(display as a decimal) displays an answer in decimal form. You can

Dec

with real or complex numbers, expressions, lists, and matrices.

Dec

following

value

(Cube),

(cube) returns the cube of

( (Cube Root)

‡

value

. You can use 3 with real or complex

numbers, expressions, lists, and square matrices.

value

‡

(

(cube root) returns the cube root of

value

. You can use

‡

(

with real or

complex numbers, expressions, and lists.

‡

TI-83 Plus Math, Angle, and Test Operations 68

(

value

)

(Root)

‡

(

root) returns the

xth root

value

. You can use

‡

with real or

complex numbers, expressions, and lists.

xthroot

‡

value

fMin(, fMax(

fMin(

(function minimum) and at which the local minimum or local maximum value of respect to

fMin(

and

tolerance

fMin(

expression,variable,lower,upper

fMax(

Note: In this guidebook, optional arguments and the commas that accompany

them are enclosed in brackets ([ ]).

variable

fMax(

(if not specified, the default is 1

expression,variable,lower,upper

occurs, between

are not valid in

fMax(

(function maximum) return the value

expression

lower

expression

tolerance

[

tolerance

[

upper

and

values for

. The accuracy is controlled by

5).

)

]

)

]

with

variable

TI-83 Plus Math, Angle, and Test Operations 69

nDeriv(

expression

derivative and H (if not specified, the default is 1

(numerical derivative) returns an approximate derivative of

with respect to

variable

, given the

value

at which to calculate the

nDeriv(

3).

is valid only

for real numbers.

nDeriv(

expression,variable,value

uses the symmetric difference quotient method, which

)

[

]

approximates the numerical derivative value as the slope of the secant line through these points.

)(()(

−−+

εε

)('

xfxf

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

You can use calculate

nDeriv(

once in

, the TI-83 Plus can return a false derivative value at a

expression

. Because of the method used to

nondifferentiable point.

TI-83 Plus Math, Angle, and Test Operations 70

fnInt(

(function integral) returns the numerical integral (Gauss-Kronrod method) of and a

tolerance

expression

with respect to

(if not specified, the default is 1

variable

, given

5).

lower

fnInt(

limit,

is valid only for

real numbers.

upper

limit,

fnInt(

expression,variable,lower,upper

Tip: To speed the drawing of integration graphs (when equation), increase the value of the

TI-83 Plus Math, Angle, and Test Operations 71

tolerance

[

Xres

)

]

is used in a Y=

fnInt(

window variable before you press

Using the Equation 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

When you select

•

is valid only for real numbers.

Solver

, one of two screens is displayed.

The equation editor (see step 1 picture below) is displayed when the

eqn

equation variable

is empty.

The interactive solver editor is displayed when an equation is stored

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.

TI-83 Plus Math, Angle, and Test Operations 72

•

Enter the expression directly into the equation solver.

•

Paste a

variable name from the

equation solver.

•

Press y menu, and press

, paste a

variable name from the

. The expression is pasted to the equation

solver.

The expression is stored to the variable

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.

VARS Y.VARS

eqn

as you enter it.

menu to the

VARS Y.VARS

•

The default lower and upper bounds appear in the last line of the editor (

TI-83 Plus Math, Angle, and Test Operations 73

bound={L1å99,1å99}

•

is displayed in the first column of the bottom line if the editor

A continues beyond the screen.

To use the solver to solve an equation such as

Tip:

eqn:0=KN.5MV

in the equation editor.

K=.5MV

, enter

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

and then reference the variables in the equation. The interactive solver

editor displays all variables of all

TI-83 Plus Math, Angle, and Test Operations 74

functions referenced in the equation.

Solving for a Variable in the Equation Solver

To solve for a variable using the equation solver after an equation has

eqn

been stored to

, 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.

TI-83 Plus Math, Angle, and Test Operations 75

The default guess is calculated as

(upper+lower)

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={L1å99,1å99}

5. Move the cursor to the variable for which you want to solve and press

ƒ \

•

The solution is displayed next to the variable for which you solved.

(above the

key).

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.

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

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

eqn

To edit or replace an equation stored to

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=

which you now want to solve and press

diff

disappear. Move the cursor to the variable for

ƒ \

TI-83 Plus Math, Angle, and Test Operations 77

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 program. It returns a solution (root) of initial

guess

sought. The default for

, and

lower

and

lower

upper

bounds within which the solution is

is L1â99. The default for

CATALOG

expression

or from within a

variable

for

upper

, given an is 1â99.

solve(

is valid only for real numbers.

solve(

expression

updated in memory.

expression,variable,guess

is assumed equal to zero. The value of

guess

must be stored for every variable in

expression

TI-83 Plus Math, Angle, and Test Operations 78

is evaluated.

lower,upper

[

}])

variable

will not be

may be a value or a list of two values. Values

lower

and

expression

upper

must be entered in list format.

, except

variable

, before

MATH NUM (Number) Operations

MATH NUM Menu

To display the

MATH NUM CPX PRB 1: abs(

2: round( 3: iPart( 4: fPart( 5: int( 6: min( 7: max( 8: lcm( 9: gcd(

MATH NUM

menu, press

Absolute value Round Integer part Fractional part Greatest integer Minimum value Maximum value Least common multiple Greatest common divisor

 ~

abs(

(absolute value) returns the absolute value of real or complex

(modulus) numbers, expressions, lists, and matrices.

abs(

value

)

Note:

TI-83 Plus Math, Angle, and Test Operations 79

is also available on the

abs(

MATH CPX

menu.

round(

(9). If

returns a number, expression, list, or matrix rounded to

#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(

fPart(

)

value

(fractional part) returns the fractional part or parts of real or complex

numbers, expressions, lists, and matrices.

fPart(

value

)

#decimals

TI-83 Plus Math, Angle, and Test Operations 80

int(

(greatest integer) returns the largest integer  real or complex

numbers, expressions, lists, and matrices.

int(

Note: For a given

nonnegative numbers and negative integers, but one integer less than the result of

value

)

, the result of

value

for negative noninteger numbers.

iPart(

is the same as the result of

int(

iPart(

min(, max(

min(

(minimum value) returns the smaller of

smallest element in

list

. If

listA

and

listB

are compared,

of the smaller of each pair of elements. If

min(

compares each element in

list

with

list

value

valueA

and

valueB

and

min(

returns a list

value

are compared,

or the

for

TI-83 Plus Math, Angle, and Test Operations 81

max(

(maximum value) returns the larger of

largest element in

list

. If

listA

and

listB

the larger of each pair of elements. If compares each element in

list

with

value

valueA

and

are compared,

list

and

value

are compared,

valueB

max(

or the

returns a list of

max(

min(

valueA,valueB

min(

list

min(

listA,listB

min(

list,value

Note:

min(

) max(

and

) max(

also are available on the

max(

valueA,valueB

)

list listA,listB list,value

)

LIST MATH

lcm(, gcd(

lcm(

returns the least common multiple of

must be nonnegative integers. When

listA

valueA

and

listB

returns a list of the lcm of each pair of elements. If

lcm(

specified,

gcd(

returns the greatest common divisor of

finds the lcm of each element in

which must be nonnegative integers. When

gcd(

returns a list of the gcd of each pair of elements. If

gcd(

specified,

finds the gcd of each element in

list

valueA

listA

and

list

menu.

valueB

, both of which

are specified,

list

and and

and

value

and

value

valueB

listB

, both of

are specified,

list

and

value

are

lcm(

value

are

TI-83 Plus Math, Angle, and Test Operations 82

lcm(

valueA,valueB

lcm(

listA,listB

lcm(

list,value

) gcd(

valueA,valueB listA,listB list,value

)

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

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 either of the two modes.

a+b

•

(rectangular-complex mode)

re^

(polar-complex mode)

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

Real

mode, complex-number results return an error, unless you entered a complex number as input. For example, in returns an error; in

a+b

mode

ln(L1)

returns an answer.

, and then select

Real

mode

ln(L1)

TI-83 Plus Math, Angle, and Test Operations 84

Real

mode

a+b

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

) = 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,

sin(45) is treated internally as e^(i45) = cos(p/4) + i sin(p/4). Complex

^(i45) = cos(45)

identities are always true in radian mode.

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

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^

(

and

Radian

modes are set.

Rectangular-Complex Mode

Rectangular-complex mode recognizes and displays a complex number in

a+b

the form component, and

, where a is the real component, b is the imaginary

is a constant equal to -1.

To enter a complex number in rectangular form, enter the value of a (

component

), press Ã or ¹, enter the value of b (

imaginary component

real

), and

press y V (constant).

TI-83 Plus Math, Angle, and Test Operations 86

real component

(+ or N)

imaginary component

Polar-Complex Mode

Polar-complex mode recognizes and displays a complex number in the

re^

form angle, and

, where r is the magnitude, e is the base of the natural log, q is the

is a constant equal to -1.

angle

magnitude

), press

To enter a complex number in polar form, enter the value of r (

press y J (exponential function), enter the value of

y V

magnitude

TI-83 Plus Math, Angle, and Test Operations 87

(constant), and then press ¤.

e^(

angle

)

(

MATH CPX (Complex) Operations

MATH CPX Menu

To display the

MATH NUM CPX PRB 1: conj(

2: real(

3: imag(

4: angle(

5: abs(

6:4Rect

7:4Polar

MATH CPX

menu, press

Returns the complex conjugate. Returns the real part. Returns the imaginary part. Returns the polar angle. Returns the magnitude (modulus). Displays the result in rectangular form. Displays the result in polar form.

 ~ ~

conj(

(conjugate) returns the complex conjugate of a complex number or

list of complex numbers.

conj(a+ conj(re^(

)

returns

))

aNb

returns

e^(

a+b

)

mode.

re^

mode.

TI-83 Plus Math, Angle, and Test Operations 88

real(

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

complex numbers.

real(a+ real(re^(

)

returns a.

))

returns

räcos

(q).

imag(

(imaginary part) returns the imaginary (nonreal) part of a complex

number or list of complex numbers.

imag(a+ imag(re^(

)

returns b.

))

returns

räsin(q)

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

angle(

numbers, calculated as tan

returns the polar angle of a complex number or list of complex

(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

in the third quadrant.

angle(a+bi) angle(re^(

returns

))

returns q, where Lp<q<p.

tan

(b/a)

abs(

(absolute value) returns the magnitude (modulus),

(real2+imag2)

, of

a complex number or list of complex numbers.

abs(a+ abs(re^(

)

returns

))

returns r (magnitude).

(a2+b2)

TI-83 Plus Math, Angle, and Test Operations 90

Rect

(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

Polar

(display as polar) displays a complex result in polar form. It is valid

Rect

returns a+

only at the end of an expression. It is not valid if the result is real.

complex result

TI-83 Plus Math, Angle, and Test Operations 91

Polar

returns

e^(

)

MATH PRB (Probability) Operations

MATH PRB Menu

To display the

MATH NUM CPX PRB

1: rand

2: nPr

3: nCr

4: !

5: randInt(

6: randNorm(

7: randBin(

MATH PRB

menu, press

Random-number generator Number of permutations Number of combinations Factorial Random-integer generator Random # from Normal distribution Random # from Binomial distribution

 |

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

rand[(

numtrials

)

]

(number of trials). The default for

Tip: To generate random numbers beyond the range of 0 to 1, you can include

in an expression. For example,

rand

generates a random number > 0 and

rand5

< 5.

numtrials

is 1.

TI-83 Plus Math, Angle, and Test Operations 92

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

rand

seed value for sequence, store any nonzero seed value to set seed value, store

is 0. To generate a different random-number

rand

. To restore the factory-

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 taken Both

items

nCr

items

integers. Both

number

items

nPr

at a time.

and

number

(number of combinations) returns the number of combinations of

taken

number

items

can be lists.

at a time.

number

and

number

and

items

and

can be lists.

must be nonnegative integers.

number

must be nonnegative

items

TI-83 Plus Math, Angle, and Test Operations 93

nCr

items

number

! (Factorial)

(factorial) returns the factorial of either an integer or a multiple of .5. For

value

a list, it returns factorials for each integer or multiple of .5.

‚L

.5 and 69.

value

Note: The factorial is computed recursively using the relationship (n+1)! = nän!, until n is reduced to either 0 or L1/2. At that point, the definition 0!=1 or the definition (L1à2)!=‡p is used to complete the calculation. Hence:

n!=nä(nN1)ä(nN2)ä ... ä2ä1, if n is an integer ‚0 n!= nä(nN1)ä(nN2)ä ... ä1à2 n! is an error, if neither n nor n+1à2 is an integer ‚0.

, if n+1à2 is an integer ‚0

‡p

must be

(The variable n equals

TI-83 Plus Math, Angle, and Test Operations 94

in the syntax description above.)

value

randInt(

a range specified by random numbers, specify an integer >1 for

(random integer) generates and displays a random integer within

lower

and

upper

integer bounds. To generate a list of

numtrials

(number of trials); if

not specified, the default is 1.

randInt(

lower,upper

numtrials

[

)

]

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,

numtrials

[

)

]

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

randBin(

from a specified Binomial distribution.

‚

(random Binomial) generates and displays a random integer

numtrials

prob

(probability of success) must be ‚ 0 and  1. To generate a list of random numbers, specify an integer > 1 for simulations); if not specified, the default is 1.

randBin(

Note: The seed value stored to

instructions.

numtrials,prob

numsimulations

[

rand

)

]

also affects

(number of trials) must be

numsimulations

randInt(, randNorm(

(number of

, and

randBin(

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

ANGLE Operations

ANGLE Menu

To display the

ANGLE

menu, press y [ angle indicators and instructions. The the TI-83 Plus’s interpretation of

ANGLE

2: '

4:8DMS

5: R8Pr(

6: R8Pq(

7: P8Rx(

8: P8Ry(

Degree notation DMS minute notation Radian notation Displays as degree/minute/second Returns r, given X and Returns q, given X and Returns x, given R and Returns y, given R and

ANGLE

q q

ANGLE

Radian/Degree

]. The

menu entries.

ANGLE

menu displays

mode setting affects

Entry Notation

DMS (degrees/minutes/seconds) entry notation comprises the degree symbol (

), the minute symbol ('), and the second symbol (").

must be a real number;

degrees¡minutes'seconds

minutes

and

seconds

must be real numbers ‚ 0.

degrees

TI-83 Plus Math, Angle, and Test Operations 97

Texas Instruments TI-83 PLUS User Manual

Specifications and Main Features

Frequently Asked Questions

User Manual

Important

US FCC Information Concerning Radio Frequency Interference

Chapter 1: Operating the TI-83 Plus Silver Edition

Documentation Conventions

TI-83 Plus Keyboard

Keyboard Zones

TI-83 Plus

Turning On and Turning Off the TI-83 Plus

Turning On the Calculator

Turning Off the Calculator

Batteries

Setting the Display Contrast

Adjusting the Display Contrast

When to Replace Batteries

The Display

Types of Displays

Home Screen

Displaying Entries and Answers

Returning to the Home Screen

Busy Indicator

Display Cursors

Entering Expressions and Instructions

What Is an Expression?

Entering an Expression

Multiple Entries on a Line

Entering a Number in Scientific Notation

Functions

Instructions

Interrupting a Calculation

TI-83 Plus Edit Keys

Setting Modes

Checking Mode Settings

Changing Mode Settings

Setting a Mode from a Program

Normal, Sci, Eng

Float, 0123456789

Radian, Degree

Func, Par, Pol, Seq

Connected, Dot

Sequential, Simul

Using TI-83 Plus Variable Names

Variables and Defined Items

Notes about Variables

Storing Variable Values

Storing Values in a Variable

Displaying a Variable Value

Archiving Variables (Archive, Unarchive)

Recalling Variable Values

Using Recall (RCL)

ENTRY (Last Entry) Storage Area

Using ENTRY (Last Entry)

Accessing a Previous Entry

Reexecuting the Previous Entry

Multiple Entry Values on a Line

Clearing ENTRY

Using Ans in an Expression

Continuing an Expression

Storing Answers

TI-83 Plus Menus

Using a TI-83 Plus Menu

Displaying a Menu

Moving from One Menu to Another

Scrolling a Menu

Selecting an Item from a Menu

Leaving a Menu without Making a Selection

VARS Menu

Equation Operating System (EOS)

Order of Evaluation

Implied Multiplication

Parentheses

Negation

Special Features of the TI-83 Plus

Flash – Electronic Upgradability

1.56 Megabytes (M) of Available Memory

Applications

Archiving