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 494–495 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 495–496 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 and try again.
Review These provide comprehensive review and Practice makes perfect.These problems 496–499 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 500 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 the Chapter Test Prep video. CUMULATIVE These problem sets appear at the end of These are really important. They will 500–501 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 501–502 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). 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 501–502 Projects project is given. students to collaborate and use mathematics to deal with issues that come up in their lives.
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. 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 Step-by-step solutions on video for all chapter test exercises from the text English and Spanish Subtitles Available CHAPTER TEST PREP VIDEOS AR E ACCE SSIB LE T HROUG H T HE FO LLOWIN G: Interactive DVD Lecture Series 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 This page intentionally left blank ALGEBRA & TRIGONOMETRY NINTH EDITION Michael Sullivan Chicago State University Prentice Hall Editor in Chief: Anne Kelly Sponsoring Editor: Dawn Murrin Assistant Editor: Joseph Colella Executive Marketing Manager: Roxanne McCarley Marketing Assistant: Katherine Minton Senior Managing Editor: Karen Wernholm Associate Managing Editor: Tamela Ambush Senior Production Project Manager: Peggy McMahon Production Editor: Bob Walters, Prepress Management, Inc. Senior Design Supervisor: Andrea Nix Art Direction and Cover Design: Barbara T. Atkinson Interior Design: Tamara Newnam Image Manager/Image Management Services: Rachel Youdelman Photo Researcher: Caroline Commins Permissions Project Supervisor: Michael Joyce Media Producer: Vicki Dreyfus Senior Author Support/Technology Specialist: Joe Vetere Manufacturing Manager: Evelyn Beaton Senior Manufacturing Buyer: Carol Melville Composition: MPS Limited, a Macmillan Company Technical Illustrations: Precision Graphics and Laserwords Printer/Binder: Courier/Kendallville Cover Printer: Lehigh-Phoenix Color/Hagerstown 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. Title: Algebra and trigonometry.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 permission for use of material in this work, please submit a written request to Pearson Education, Inc., Rights and Contracts Department, 501 Boylston Street, Suite 900, Boston, MA 02116, fax your request to 617-671-3447, or e-mail at http://www.com/legal/permissions.
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.8 nth Roots; Rational Exponents 73 1 Equations and Inequalities 81 1.3 Complex Numbers; Quadratic Equations in the Complex Number System 104 1.4 Radical Equations; Equations Quadratic in Form; Factorable Equations 113 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 2.5 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 3.2 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 6.2 One-to-One Functions; Inverse Functions 408 6.5 Properties of Logarithms 450 6.6 Logarithmic and Exponential Equations 459 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 8.5 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 10.2 Polar Equations and Graphs 727 10.3 The Complex Plane; De Moivre’s Theorem 742 10.5 The Dot Product 763 Chapter Review 770 Chapter Test 773 Cumulative Review 774 Chapter Projects 774 11 Analytic Geometry 776 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 Table of Contents xiii 12 Systems of Equations and Inequalities 842 12.1 Systems of Linear Equations: Substitution and Elimination 843 12.2 Systems of Linear Equations: Matrices 858 12.3 Systems of Linear Equations: Determinants 873 12.5 Partial Fraction Decomposition 899 12.6 Systems of Nonlinear Equations 907 12.7 Systems of Inequalities 916 12.8 Linear Programming 923 Chapter Review 930 Chapter Test 935 Cumulative Review 936 Chapter Projects 936 13 Sequences; Induction; the Binomial Theorem 938 13.3 Geometric Sequences; Geometric Series 955 13.5 The Binomial Theorem 970 Chapter Review 976 Chapter Test 979 Cumulative Review 979 Chapter Projects 980 14 Counting and Probability 981 14.2 Permutations and Combinations 987 14.3 Probability 996 Chapter Review 1006 Chapter Test 1008 Cumulative Review 1009 Chapter Projects 1009 xiv Table of Contents Appendix Graphing Utilities A1 1 The Viewing Rectangle A1 2 Using a Graphing Utility to Graph Equations A3 3 Using a Graphing Utility to Locate Intercepts and Check for Symmetry A5 4 Using a Graphing Utility to Solve Equations A6 5 Square Screens A8 6 Using a Graphing Utility to Graph Inequalities A9 7 Using a Graphing Utility to Solve Systems of Linear Equations A9 8 Using a Graphing Utility to Graph a Polar Equation A11 9 Using a Graphing Utility to Graph Parametric Equations A11 Answers AN1 Index I1 Three Distinct Series Students have different goals, learning styles, and levels of preparation. Instructors have different teaching philosophies, styles, and techniques. Rather than write one series to fit all, the Sullivans have written three distinct series. All share the same goal—to develop a high level of mathematical understanding and an appreciation for the way mathematics can describe the world around us.
