Algebra & Trigonometry

1172 Pages·2016·60.67 MB·English

by  Michael Sullivan

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
For the Family
Katy (Murphy) and Pat Shannon,Patrick,Ryan
Mike and Yola Michael,Kevin,Marissa
Dan and Sheila Maeve,Sean,Nolan
Colleen (O’Hara) and Bill Kaleigh,Billy,Timmy
ALGEBRA & TRIGONOMETRY
NINTH EDITION
ALGEBRA & TRIGONOMETRY
NINTH EDITION
Michael Sullivan
Chicago State University
Prentice Hall
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Text Font: Times Ten Roman
Credits and acknowledgments borrowed from other sources and reproduced,with
permission,in this textbook appear on page xxx.
Many of the designations used by manufacturers and sellers to distinguish their
products are claimed as trademarks.Where those designations appear in this book,
and Pearson was aware of a trademark claim,the designations have been printed in
initial caps or all caps.
The Student Edition of this book has been cataloged as follows:
Library of Congress Cataloging-in-Publication Data
Sullivan,Michael,1942-
Algebra & trigonometry / Michael Sullivan.—9th ed.
p.cm.
ISBN 978-0-321-71656-9
1.Algebra—Textbooks.2. Trigonometry—Textbooks. I.Title. II.Title:Algebra and trigonometry.
QA154.3.S73 2012
512¿.13—dc22
2010027085
Copyright © 2012,2008,2005,and 2002 by Pearson Education,Inc.All rights reserved.No part of this
publication may be reproduced,stored in a retrieval system,or transmitted,in any form or by any
means,electronic,mechanical,photocopying,recording,or otherwise,without the prior written
permission of the publisher.Printed in the United States of America.For information on obtaining
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to 617-671-3447,or e-mail at http://www.pearsoned.com/legal/permissions.htm.
1 2 3 4 5 6 7 8 9 10—CRK—14 13 12 11 10
ISBN-10:0-321-71656-6
ISBN-13:978-0-321-71656-9
Table of Contents
To the Student ii
Preface to the Instructor xvi
Applications Index xxiii
Photo Credits xxx
R
Review 1
R.1 Real Numbers 2
R.2 Algebra Essentials 17
R.3 Geometry Essentials 30
R.4 Polynomials 39
R.5 Factoring Polynomials 49
R.6 Synthetic Division 58
R.7 Rational Expressions 62
R.8 nth Roots;Rational Exponents 73
1
Equations and Inequalities 81
1.1 Linear Functions 82
1.2 Quadratic Equations 92
1.3 Complex Numbers;Quadratic Equations in the Complex
Number System 104
1.4 Radical Equations;Equations Quadratic in Form;Factorable
Equations 113
1.5 Solving Inequalities 119
1.6 Equations and Inequalities Involving Absolute Value 130
1.7 Problem Solving:Interest,Mixture,Uniform Motion,
Constant Rate Job Applications 134
Chapter Review 143
Chapter Test 147
Chapter Projects 148
2
Graphs 149
2.1 The Distance and Midpoint Formulas 150
2.2 Graphs of Equations in Two Variables;Intercepts;
Symmetry 157
2.3 Lines 167
2.4 Circles 182
2.5 Variation 188
ix
x Table of Contents
Chapter Review 194
Chapter Test 197
Cumulative Review 197
Chapter Project 197
3
Functions and Their Graphs 199
3.1 Functions 200
3.2 The Graph of a Function 214
3.3 Properties of Functions 222
3.4 Library of Functions;Piecewise-defined Functions 234
3.5 Graphing Techniques:Transformations 244
3.6 Mathematical Models:Building Functions 257
Chapter Review 263
Chapter Test 268
Cumulative Review 269
Chapter Projects 269
4
Linear and Quadratic Functions 271
4.1 Linear Functions and Their Properties 272
4.2 Linear Models:Building Linear Functions from Data 282
4.3 Quadratic Functions and Their Properties 288
4.4 Build Quadratic Models from Verbal Descriptions
and from Data 300
4.5 Inequalities Involving Quadratic Functions 309
Chapter Review 313
Chapter Test 316
Cumulative Review 317
Chapter Projects 318
5
Polynomial and Rational Functions 319
5.1 Polynomial Functions and Models 320
5.2 Properties of Rational Functions 342
5.3 The Graph of a Rational Function 353
5.4 Polynomial and Rational Inequalities 368
5.5 The Real Zeros of a Polynomial Function 374
5.6 Complex Zeros;Fundamental Theorem
of Algebra 387
Chapter Review 393
Chapter Test 397
Cumulative Review 397
Chapter Projects 398
Table of Contents xi
6
Exponential and Logarithmic Functions 400
6.1 Composite Functions 401
6.2 One-to-One Functions;Inverse Functions 408
6.3 Exponential Functions 421
6.4 Logarithmic Functions 437
6.5 Properties of Logarithms 450
6.6 Logarithmic and Exponential Equations 459
6.7 Financial Models 466
6.8 Exponential Growth and Decay Models;Newton’s Law;
Logistic Growth and Decay Models 476
6.9 Building Exponential,Logarithmic,and Logistic Models
from Data 486
Chapter Review 494
Chapter Test 500
Cumulative Review 500
Chapter Projects 501
7
Trigonometric Functions 503
7.1 Angles and Their Measure 504
7.2 Right Triangle Trigonometry 517
7.3 Computing the Values of Trigonometric Functions
of Acute Angles 529
7.4 Trigonometric Functions of Any Angle 540
7.5 Unit Circle Approach;Properties of the Trigonometric
Functions 550
7.6 Graphs of the Sine and Cosine Functions 561
7.7 Graphs of the Tangent,Cotangent,Cosecant,and Secant
Functions 576
7.8 Phase Shift;Sinusoidal Curve Fitting 583
Chapter Review 594
Chapter Test 600
Cumulative Review 601
Chapter Projects 602
8
Analytic Trigonometry 603
8.1 The Inverse Sine,Cosine,and Tangent Functions 604
8.2 The Inverse Trigonometric Functions (Continued) 616
8.3 Trigonometric Equations 622
8.4 Trigonometric Identities 632
8.5 Sum and Difference Formulas 640
8.6 Double-angle and Half-angle Formulas 652
8.7 Product-to-Sum and Sum-to-Product Formulas 662
xii Table of Contents
Chapter Review 666
Chapter Test 670
Cumulative Review 670
Chapter Projects 671
9
Applications of Trigonometric Functions 672
9.1 Applications Involving Right Triangles 673
9.2 The Law of Sines 678
9.3 The Law of Cosines 689
9.4 Area of a Triangle 696
9.5 Simple Harmonic Motion;Damped Motion;
Combining Waves 702
Chapter Review 711
Chapter Test 714
Cumulative Review 715
Chapter Projects 716
10
Polar Coordinates;Vectors 717
10.1 Polar Coordinates 718
10.2 Polar Equations and Graphs 727
10.3 The Complex Plane;De Moivre’s Theorem 742
10.4 Vectors 749
10.5 The Dot Product 763
Chapter Review 770
Chapter Test 773
Cumulative Review 774
Chapter Projects 774
11
Analytic Geometry 776
11.1 Conics 777
11.2 The Parabola 778
11.3 The Ellipse 787
11.4 The Hyperbola 797
11.5 Rotation of Axes;General Form of a Conic 810
11.6 Polar Equations of Conics 818
11.7 Plane Curves and Parametric Equations 823
Chapter Review 836
Chapter Test 839
Cumulative Review 840
Chapter Projects 840