TI-86/TI-85 ONLINE Graphing Calculator Manual for Dwyer ...

[Pages:48]TI-86/TI-85 ONLINE Graphing Calculator Manual for Dwyer/Gruenwald's

PRECALCULUS

A CONTEMPORARY APPROACH

Dennis Pence

Western Michigan University

Brooks/Cole

Thomson LearningTM Australia ? Canada ? Mexico ? Singapore Spain ? United Kingdom ? United States

COPYRIGHT ? 2004 by Brooks/Cole A division of Thomson Learning The Thomson Learning logo is a trademark used herein under license. For more information, contact: BROOKS/COLE 511 Forest Lodge Road Pacific Grove, CA 93950 USA

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Table of Contents

TI-86/TI-85 Graphing Calculators

Chapter 1

Chapter 2 Chapter 3 Chapter 4 Chapter 5

Foundations and Fundamentals . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5 Calculator Fundamentals . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5 Order of Operation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7 Complex Arithmetic . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8 Scientific Notation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8 Exponents and Radicals . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9 Fractional Arithmetic . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9 Scatter Plots . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10 Function Graphing . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 13 Solving Equations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 15 Graphing a Circle . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 17 Rational Functions and Vertical Asymptotes . . . . . . . . . . . . . 17

Functions and Their Graphs . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 18 Evaluating Functions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 18 Increasing and Decreasing, Turning Points . . . . . . . . . . . . . . 20 Combinations and Composition of Functions . . . . . . . . . . . . 20 Inverse Functions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 20 Graphing a Family of Functions . . . . . . . . . . . . . . . . . . . . . . 21 Piecewise-defined Functions . . . . . . . . . . . . . . . . . . . . . . . . . 21 Least-Squares Best Fit . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 22

Polynomial and Rational Functions . . . . . . . . . . . . . . . . . . . . . . . . 24 Polynomial Functions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 24 Rational Functions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 26

Exponential and Logarithmic Functions . . . . . . . . . . . . . . . . . . . . 26 Exponential Functions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 26 Logarithmic Functions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 27 Regressions Involving Exponentials and Logarithms . . . . . . 27

Trigonometric Functions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 29 Angle Measurement . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 29 Sine, Cosine, and Tangent Function Keys . . . . . . . . . . . . . . . 29 Plotting the Sine, Cosine, and Tangent Functions . . . . . . . . . 30 Families of Trigonometric Functions . . . . . . . . . . . . . . . . . . . 31 Cosecant, Secant, and Cotangent Functions . . . . . . . . . . . . . 31 Plotting the Inverses of Sine, Cosine, and Tangent . . . . . . . . 31

Chapter 6 Trigonometric Identities and Equations . . . . . . . . . . . . . . . . . . . . . 32 Graphical Check of Equations . . . . . . . . . . . . . . . . . . . . . . . . 32 Conditional Trigonometric Equations . . . . . . . . . . . . . . . . . . 33

Chapter 7 Applications of Trigonometry . . . . . . . . . . . . . . . . . . . . . . . . . . . . 34 Complex Numbers Revisited . . . . . . . . . . . . . . . . . . . . . . . . . 34 Polar Coordinates . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 35 Plotting Polar Equations . . . . . . . . . . . . . . . . . . . . . . . . . . . . 35 Vectors . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 37

Chapter 8 Relations and Conic Sections . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 38 Graphing Relations in Pieces . . . . . . . . . . . . . . . . . . . . . . . . . 38 Plotting Parabolas . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 39 Plotting Hyperbolas . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 39 Plotting Parametric Equations . . . . . . . . . . . . . . . . . . . . . . . . 40

Chapter 9 Systems of Equations and Inequalities . . . . . . . . . . . . . . . . . . . . . . 41 Matrices . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 41 Gaussian Elimination . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 41 Identity Matrices, the Inverse of a Matrix, Determinants . . . 42 Systems of Inequalities . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 44 Linear Programming . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 45

Chapter 10 Integer Functions and Probability . . . . . . . . . . . . . . . . . . . . . . . . . . 46 Sequences . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 46 Series . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 48 Permutations, Combinations, Random Numbers . . . . . . . . . . 48

Note that in Acrobat Reader, each chapter and section in this table of contents is linked to the appropriate location in the document. Similarly, chapter and section titles in the document are linked back to this table of contents. Web links are also active if your computer has an internet connection.

TI-86, TI-85

The TI-86 is a good choice for a graphing calculator to use while learning from Precalculus. The older TI-85 will do most of the activities presented here, but it lacks some editing and statistical features of the newer model. The biggest improvements in the TI-86 are the increased memory and the ability to load and run assembly language programs. You can look at the Texas Instruments graphing calculator web pages () to find some programs that can be downloaded using a computer and the GraphLink cable. Thus the TI-86 should be your choice if you are purchasing a new calculator in this family. However Texas Instruments announced several years ago the intention to stop making this line. The TI-86 seems to be heavily discounted now (probably to sell out the remaining stock). If you are buying a new calculator, I would suggest seriously looking at other TI models with flash ROM which can be upgraded.

Chapter 1 - Foundations and Fundamentals

Calculator Fundamentals When you turn on a TI-86 or TI-85, it usually comes up in the Home screen. If not

(because the calculator did an "automatic shutoff" in another screen), press y k to move to the Home screen where immediate computations are performed. The ` key performs two important activities here. While you are typing a new command line (before ?), pressing ` will clear out everything in the command line. If there is nothing in the command line, pressing ` will clear out all of the previous results still showing in the Home screen.

Press y l so that we can check (and explain) the various mode settings.

TI-85/86 MODE Screen

The first two lines determine how the calculator will display real numbers. Normal (the default) tries to show the entire number normally, but switches to scientific notation if a positive number is too large or too small. Sci always uses scientific notation, and Eng uses a special scientific notation where exponents are a multiple of 3. Float (the default)

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? 2004 Brooks/Cole, a division of Thomson Learning, Inc.

Chapter 1 - Foundations and Fundamentals

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moves the decimal point or the scientific exponent to show 10 significant digits (with zero suppression to the right). If we select one of the digits 0123456789, the results are displayed rounded to that many decimal places. For now select the default setting on every line (the left-most choice) by pressing cursor keys to highlight the desired selection and then pressing ?. Briefly, the third line specifies the angle mode, the fourth and seventh lines set ways to report vector components, the fifth line sets the graphing mode, the sixth line fixes the number base, and the last line determines the way to compute the derivative for certain calculus operations.

The keyboard layout is fairly simple. Pressing a key does what is printed on the key. Pressing y (you do not need to hold it down) and then another key gives the operation printed above, left, and in the color orange. Pressing (you do not need to hold it down) and then another key gives the operation printed above, right, and the color blue (usually a capital letter). Pressing twice locks you into this alpha setting so that you can type several letters at once. (Another press or an a will release you from alpha setting.) Pressing y gives lower case letters. Many keys bring a menu to the bottom line of the screen, perhaps with further submenus. The function keys %&'() are used to select the items in the bottom line of the screen. If there is a row of menu items in the next line up from the bottom, first press , and then one of the function keys to get that item via defgh. For example, pressing ,< brings up the MATH menu. Items in all capitols generally are submenus. Pressing % moves those submenu items up and gives a new bottom row of menu selections. Pressing & now pastes the command iPart to find the integer part of a number. Notice that the menus do not go away after you make a selection. Press - to drop the lowest menu (or press anything that brings up a new menu). An arrow means there are more commands to the right. Press . to see these additional commands in the lowest line. The TI85/86 family of graphing calculators also allows you to type commands by typing characters one-by-one using the keys, but this is rather slow. Since the correct spelling and spacing come from the menu, this will be the preferred way. Another alternative to finding a command in a menu is to use ,[CATALOG] on the TI-85 or ,v% on the TI-86 where all commands are listed in alphabetical order.

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? 2004 Brooks/Cole, a division of Thomson Learning, Inc.

Chapter 1 - Foundations and Fundamentals

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Order of Operation Calculators generally follow the traditional algebraic

order of operations. Note that you can control the order of operation with parentheses. This family of calculators allows implied multiplication (no multiplication symbol is needed between the two objects) in many situations where there is no other interpretation. Just be careful with implied multiplication, because if there is any other interpretation possible, something else will happen. Finally the TI-85/86 family allows you to leave off final parentheses. It just assumes all "missing" right parentheses are needed at the end of the expression.

It is very important to recognize the difference between the black subtraction key S above the ? key and the grey negation key ? to the left in the bottom row of keys. In textbook notation we tend to use the same symbol for both, letting the context determine the meaning. Notice on the screen that the negation is slightly higher and shorter. The subtraction operation takes two numbers as arguments, one before the key is pressed and one after. The negation operation takes only one number as an argument coming after the key is pressed. If you start a new command line by pressing the subtraction key ?, the calculator assumes you wish to do a continuation calculation. Thus it assumes that you want to subtract something (yet to be typed) from the previous answer. You can also get the previous answer anywhere within the command line with , which is found above the negation key.

There are many situations where you want to execute essentially the same command repeatedly. There are some nice editing features that make this easy to do. The command ,? found above the ? key causes the last command line to be recalled so that you can edit it. Pressing ,? several times allows you to go back to several previous command lines (limited by the size of some memory buffer). When you edit a previous command line, you do not need to move the cursor point to the end before pressing ?. If you want to execute exactly the same command line, you do not need to recall it. Just repeatedly press ?. In the screen shown here, we have typed 11 ? and then pressed ? 7 ?. As we repeatedly press ? we add 7 to the previous result.

There is also a simple way to store the result of a computation for later use. The command is ? , and it will appear on the screen as an arrow . You follow this command by typing a variable name. Notice that the calculator automatically switches

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? 2004 Brooks/Cole, a division of Thomson Learning, Inc.

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to ALPHA-entry so you do not need to press 0. Variable names must start with a letter and contain no more than eight characters. Variable names are case sensitive, so you may use upper and lower case. There is a way to "delete" a variable name, and you will want to do so to save memory when you no longer need the result. The command DelVar( followed by the variable name will do this, or you can delete individual items in the ~ screen. It saves time if you store intermediate computations rather than copying down a number and retyping it later. Further, most people are lazy, and they copy down only a few of the decimal places. The "storing" operation saves the complete number with all significant decimal places for later use.

Complex Arithmetic The TI-86 and TI-85 can handle complex arithmetic, and there is no turning complex

numbers on and off (for they are always available). A complex number such as 2 + 5i is entered as an ordered pair (2,5). You can then add, subtract, multiply and divide complex numbers. The S menu has other commands for complex numbers.

The absolute value in the < menu, NUM submenu has the traditional meaning for real numbers. For a complex number, abs gives the modulus (or square root of the sum of the squares of the entries). In either case this result is always positive (unless the number is zero).

Scientific Notation Even in our Normal mode, a number may be expressed in scientific notation if it is

too large. Calculators and computers have a short-hand for this. Instead of printing out 5.7319 ? 1025 which is difficult, they simply present 5.731925. You should use the same short-hand when you want to enter a number in scientific notation (avoiding multiplication by a power of 10). Use the Bkey where you want this symbol to be placed. Internally the calculator uses this notation, and 9.99999999999999 is the largest

TI-86/TI-85, Precalculus

? 2004 Brooks/Cole, a division of Thomson Learning, Inc.

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