Trigonometry: A Unit Circle Approach

723 Pages·2012·24.059 MB·English

by  Michael Sullivan

Review “Study for Quizzes and Tests”
Feature Description Benefit Page
Chapter Reviews at the end of each chapter contain…
“Things to A detailed list of important theorems, Review these and you’ll know the 172–174
Know” formulas,and definitions most important material in the chapter!
from the chapter.
“You Should Be Contains a complete list of objectives by Do the recommended exercises and 175
Able to…” section,examples that illustrate the you’ll have mastery over the key
objective,and practice exercises that test material. If you get something wrong,
your understanding of the objective. review the suggested page numbers
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Review These provide comprehensive review and Practice makes perfect.These problems 176–178
Exercises practice of key skills,matched to the combine exercises from all sections,
Learning Objectives for each section. giving you a comprehensive review in
one place.
CHAPTER TEST About 15–20 problems that can be taken Be prepared.Take the sample practice 178–179
as a Chapter Test.Be sure to take the test under test conditions.This will
Chapter Test under test conditions—no get you ready for your instructor’s test.
notes! If you get a problem wrong,watch
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CUMULATIVE These problem sets appear at the end of These are really important.They will 179
REVIEW each chapter,beginning with Chapter 2. ensure that you are not forgetting
They combine problems from previous anything as you go.These will go a long
chapters,providing an ongoing way toward keeping you constantly
cumulative review. primed for the final exam.
CHAPTER The Chapter Project applies what you’ve The Project gives you an opportunity to 180
PROJECTS learned in the chapter.Additional projects apply what you’ve learned in the chapter
are available on the Instructor’s to solve a problem related to the
Resource Center (IRC). opening article. If your instructor allows,
these make excellent opportunities to
work in a group,which is often the
best way of learning math.
NEW!
Internet-based In selected chapters,a web-based The projects allow the opportunity for 180
Projects project is given. students to collaborate and use
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To the Student
As you begin, you may feel anxious about the number of theorems, definitions,
procedures,and equations.You may wonder if you can learn it all in time.Don’t
worry,your concerns are normal.This textbook was written with you in mind.If
you attend class, work hard, and read and study this book, you will build the
knowledge and skills you need to be successful.Here’s how you can use the book
to your benefit.
Read Carefully
When you get busy,it’s easy to skip reading and go right to the problems.Don’t...
the book has a large number of examples and clear explanations to help you break
down the mathematics into easy-to-understand steps.Reading will provide you with
a clearer understanding,beyond simple memorization.Read before class (not after)
so you can ask questions about anything you didn’t understand.You’ll be amazed at
how much more you’ll get out of class if you do this.
Use the Features
I use many different methods in the classroom to communicate.Those methods,
when incorporated into the book, are called “features.”The features serve many
purposes,from providing timely review of material you learned before (just when
you need it),to providing organized review sessions to help you prepare for quizzes
and tests.Take advantage of the features and you will master the material.
To make this easier,I’ve provided a brief guide to getting the most from this
book.Refer to the “Prepare for Class,”“Practice,”and “Review”pages on the inside
front cover of this book.Spend fifteen minutes reviewing the guide and familiarizing
yourself with the features by flipping to the page numbers provided.Then,as you
read,use them.This is the best way to make the most of your textbook.
Please do not hesitate to contact me, through Pearson Education, with any
questions,suggestions,or comments that would improve this text.I look forward to
hearing from you,and good luck with all of your studies.
Best Wishes!
Michael Sullivan

To the Memory of Joe and Rita
and my sister Maryrose
TRIGONOMETRY
A UNIT CIRCLE APPROACH
NINTH EDITION
Michael Sullivan
Chicago State University
Prentice Hall
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1 2 3 4 5 6 7 8 9 10—CRK—15 14 13 12 11
ISBN-10:0-321-71657-4
ISBN-13:978-0-321-71657-6
Table of Contents
To the Student ii
Preface to the Instructor xi
Applications Index xviii
Photo Credits xxiii
1
Graphs and Functions 1
1.1 The Distance and Midpoint Formulas 2
1.2 Graphs of Equations in Two Variables;Circles 9
1.3 Functionsand Their Graphs 24
1.4 Properties of Functions 42
1.5 Library of Functions;Piecewise-defined Functions 53
1.6 Graphing Techniques:Transformations 61
1.7 One-to-OneFunctions;Inverse Functions 75
Chapter Review 87
Chapter Test 93
Chapter Projects 94
2
Trigonometric Functions 95
2.1 Angles and Their Measure 96
2.2 Trigonometric Functions:Unit Circle Approach 109
2.3 Properties of the Trigonometric Functions 125
2.4 Graphs of the Sine and Cosine Functions 139
2.5 Graphs of the Tangent,Cotangent,Cosecant,and Secant
Functions 154
2.6 Phase Shift;Sinusoidal Curve Fitting 161
Chapter Review 172
Chapter Test 178
Cumulative Review 179
Chapter Projects 180
3
Analytic Trigonometry 181
3.1 The Inverse Sine,Cosine,and Tangent Functions 182
3.2 The Inverse Trigonometric Functions (Continued) 194
3.3 Trigonometric Equations 200
3.4 Trigonometric Identities 210
3.5 Sum and Difference Formulas 218
3.6 Double-angle and Half-angle Formulas 230
3.7 Product-to-Sum and Sum-to-Product Formulas 240
vii
viii
Table of Contents
Chapter Review 244
Chapter Test 248
Cumulative Review 248
Chapter Projects 249
4
Applications of Trigonometric Functions 250
4.1 Right Triangle Trigonometry;Applications 251
4.2 The Law of Sines 263
4.3 The Law of Cosines 274
4.4 Area of a Triangle 281
4.5 Simple Harmonic Motion;Damped Motion;
Combining Waves 287
Chapter Review 296
Chapter Test 300
Cumulative Review 301
Chapter Projects 301
5
Polar Coordinates;Vectors 303
5.1 Polar Coordinates 304
5.2 Polar Equations and Graphs 313
5.3 The Complex Plane;De Moivre’s Theorem 328
5.4 Vectors 335
5.5 The Dot Product 349
5.6 Vectors in Space 356
5.7 The Cross Product 366
Chapter Review 371
Chapter Test 375
Cumulative Review 375
Chapter Projects 376
6
Analytic Geometry 377
6.1 Conics 378
6.2 The Parabola 379
6.3 The Ellipse 388
6.4 The Hyperbola 398
6.5 Rotation of Axes;General Form of a Conic 411
6.6 Polar Equations of Conics 419
6.7 Plane Curves and Parametric Equations 424
Chapter Review 437
Chapter Test 440
Cumulative Review 440
Chapter Projects 441
ix
Table of Contents
7
Exponential and Logarithmic Functions 442
7.1 Exponential Functions 443
7.2 Logarithmic Functions 459
7.3 Properties of Logarithms 472
7.4 Logarithmic and Exponential Equations 481
7.5 Financial Models 488
7.6 Exponential Growth and Decay Models;Newton’s Law;
Logistic Growth and Decay Models 498
7.7 Building Exponential,Logarithmic,and Logistic Models
from Data 508
Chapter Review 516
Chapter Test 521
Cumulative Review 521
Chapter Projects 522
Appendix A Review A1
A.1 Algebra Essentials A1
A.2 Geometry Essentials A14
A.3 Factoring Polynomials;Completing the Square A22
A.4 Solving Equations A28
A.5 Complex Numbers;Quadratic Equations in the Complex
Number System A38
A.6 Interval Notation;Solving Inequalities A46
A.7 nth Roots;Rational Exponents A55
A.8 Lines A64
A.9 Building Linear Models from Data A79
Appendix B Graphing Utilities B1
B.1 The Viewing Rectangle B1
B.2 Using a Graphing Utility to Graph Equations B3
B.3 Using a Graphing Utility to Locate Intercepts
and Check for Symmetry B5
B.4 Using a Graphing Utility to Solve Equations B6
B.5 Square Screens B8
B.6 Using a Graphing Utility to Graph a Polar Equation B9
B.7 Using a Graphing Utility to Graph Parametric
Equations B9
Answers AN1
Index I1