Analytic trigonometry with applications PDF
Preview Analytic trigonometry with applications
Barnett Ziegler Byleen 11 Edition th ANALYTIC TRIGONOMETRY W I T H A P P L I C A T I O N S This page intentionally left blank 11 E ANALYTIC TRIGONOMETRY with Applications Raymond A. Barnett Merritt College Michael R. Ziegler Marquette University Karl E. Byleen Marquette University John Wiley & Sons, Inc. VICE PRESIDENT AND PUBLISHER Laurie Rosatone ACQUISITIONS EDITOR Joanna Dingle EDITORIAL ASSISTANT Elizabeth Baird DEVELOPMENT EDITOR Anne Scanlan-Rohrer MARKETING MANAGER Jonathan Cottrell PROJECT MANAGER Paul Lopez MEDIA EDITOR Melissa Edwards PRODUCT DESIGNER Thomas Kulesa ASSISTANT CONTENT EDITOR Beth Pearson DESIGN DIRECTOR Harold Nolan SENIOR DESIGNER Madelyn Lesure PRODUCTION MANAGER Juanita Thompson SENIOR PRODUCTION EDITOR Kerry Weinstein PRODUCTION MANAGEMENT SERVICES Suzanne Ingrao COVER/CHAPTER OPENER IMAGE Brazil2/Vetta/Getty Images, Inc. COVER DESIGN Madelyn Lesure This book was set in 10/12 Times by Preparé, Inc. and printed and bound by QUADVersailles. The cover was printed by QUADVersailles. ∞ This book is printed on acid-free paper. Copyright © 2012 John Wiley & Sons, 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, scanning, or otherwise, except as permitted under Sections 107 or 108 of the 1976 United States Copyright Act, without either the prior written permission of the Publisher, or authorization through payment of the appropriate per-copy fee to the Copyright Clearance Center, Inc., 222 Rosewood Drive, Danvers, MA 01923, (978) 750-8400, fax (978) 750-4470 or on the web at www.copyright.com. Requests to the Publisher for permission should be addressed to the Permissions Department, John Wiley & Sons, Inc., 111 River Street, Hoboken, NJ 07030-5774, (201) 748-6011, fax (201) 748-6008, or online at http://www.wiley.com/go/permissions. Evaluation copies are provided to qualified academics and professionals for review purposes only, for use in their courses during the next academic year. These copies are licensed and may not be sold or transferred to a third party. Upon completion of the review period, please return the evaluation copy to Wiley. Return instructions and a free of charge return shipping label are available at HYPERLINK “http://www.wiley.com/go/return” www.wiley.com/go/returnlabel. Outside of the United States, please contact your local representative. ISBN-13 978-0-470-64805-6 ISBN-10 0-470-64805-8 Printed in the United States of America 10 9 8 7 6 5 4 3 2 1 PREFACE TThe 11thedition of Analytic Trigonometry with Applicationsis designed for a one-term course in trigonometry and for students who have had 11>2–2 years of high school algebra or the equivalent. The choice and independence of topics make the text readily adaptable to a variety of courses (see the starred sections in the table of contents). Fundamental to a book’s growth and effectiveness is classroom use and feedback. Now in its 11th edition, Analytic Trigonometry with Applicationshas had the benefit of having a substantial amount of both. ■■ Emphasis and Style The text is written for student comprehension.Great care has been taken to write a book that is mathematically correct and accessible to students. An informal style is used for exposition, definitions, and theorems. Precision, however, is not com- promised. General concepts and results are usually presented only after particular cases have been discussed. To gain reader interest quickly, the text moves directly into trigonometric concepts and applications in the first chapter. Review material from prerequisite courses is either integrated in certain developments (particularly in Chapters 4 and 5)or can be found in the appendixes. This material can be reviewed as needed by the student or taught in class by an instructor. ■■ Examples and Matched Problems Over 180 completely worked numbered examples are used to introduce con- cepts and to demonstrate problem-solving techniques. Many examples have let- tered parts, significantly increasing the total number of worked examples. Each example is followed by a similar matched problem for the student to work while reading the material. This actively involves the student in the learning process. The answers to these matched problems are included at the end of each section for easy reference. ■■ Exploration and Discussion Every section contains Explore-Discuss problems interspersed at appropriate places to encourage a student to think about a relationship or process before a re- sult is stated or to investigate additional consequences of a development in the text. Verbalization of mathematical concepts, results, and processes is encour- aged in these Explore-Discuss boxes, as well as in some matched problems, and in particular problems in almost every exercise set. The Explore-Discuss material can also be used as an in-class or out-of-class group activity.In addition, at the end of every chapter, before the chapter review, is a special Chapter Group Activitythat in- volves a number of the concepts discussed in the chapter. The Explore-Discuss v vi PREFACE boxes and the group activities are highlighted with a light screen to emphasize their im- portance. Problems involving these elements are indicated by color problem numbers. ■■ Exercise Sets The book contains over 3,200 numbered problems. Many problems have let- tered parts, significantly increasing the total number of problems. Each exercise set is designed so that an average or below-average student will experience success and a very capable student will be challenged. Exercise sets are mostly divided into A (routine, easy mechanics), B (more difficult mechanics), and C (difficult mechanics and some theory)levels. ■■ Applications A major objective of this book is to give the student substantial experience in modeling and solving real world problems. Enough applications are in- cluded to convince even the most skeptical student that mathematics is really useful (see the Applications Index). Most of the applications are simplified versions of actual real-world problems taken from professional journals and books. No specialized experience is required to solve any of the applications. ■■ Technology The term calculator refers to any scientific calculator that can evaluate trigono- metric and inverse trigonometric functions. No tables are included in the text, so access to a calculator is assumed. Access to a more sophisticated graphing calcu- lator is not assumed,although it is likely that many students will want to use one of these devices. To assist these students, optional graphing calculator activities are included in appropriate places in the book. The 11th edition features optional applications including using graphing calculators for regression. The activities in- clude brief discussions in the text, examples or portions of examples solved on a graphing calculator, and problems for the student to solve. All of the optional graphing calculator material is clearly identified by and can be omitted without loss of continuity, if desired. ■■ Graphs All graphs are computer generated to ensure mathematical accuracy. Graphing calculator screens displayed in the text are actual output from a graphing calculator. ■■ Changes in the 11th Edition Throughout the book, the exposition has been supplemented and clarified to strengthen intuition and encourage a conceptual understanding of trigonometry. Hundreds of new exercises have been added, including many that require a verbal explanation (marked by red problem numbers). In particular, there are many more "reading comprehension" questions, located at the beginning of the exercise sets. They test whether the student has grasped the basic concepts of a section by an initial reading, and should be answered before tackling the exercises that build vii PREFACE computational and problem-solving skills. In Section 2.3, we have given greater emphasis to the unit circle in the definition of the trigonometric functions, and also in the examples that follow the definition. In Section 5.3, we have improved the diagrams that are used to solve trigonometric equations algebraically. In Chapter 6, vectors are given a streamlined treatment. Section 6.4 replaces the two sections on vectors of the previous edition. ■■ Student Aids Functional use of color improves the clarity of many illustrations, graphs, and developments and guides students through certain critical steps (see Sections 1.3, 4.2, and 5.3). Think boxes(dashed boxes)are used to enclose steps that are usu- ally performed mentally (see Sections 1.1, 2.4, and 6.5). Screened boxesare used to highlight important definitions, theorems, results, and step-by-step processes (see Sections 1.3, 4.2, and 6.5). Caution statements appear throughout the text where student errors often occur (see Sections 1.3, 2.3, and 4.2). Boldface typeis used to introduce new terms and highlight important comments. Chapter review sections include a review of all important terms and symbols and a comprehen- sive review exercise. Cumulative review sections follow Chapters 3, 5, and 7. Answers to most review exercises, keyed to appropriate sections, are included in the back of the book. Additionally, answers to all odd-numbered problems are also in the back of the book. Formulas and symbols (keyed to sections in which they are first introduced) and the metric system are summarized on the front and back end papers of the book for convenient reference. ■■ Ancillaries for Students A Student Solutions Manual (9781118115831) contains detailed solutions to all chapter review, cumulative review, and odd-numbered problems in the book. ■■ Ancillaries for Instructors An Instructor’s Resource Manual contains answers to the even-numbered problems not found in the back of the text, plus hints and solutions for the chapter group activities and Explore/Discuss material. An Instructor’s Solutions Manual (9781118115824) contains solutions to the even-numbered problems. Aprinted test bankcontains quizzes and exams, plus answers. ■■ WileyPLUS WileyPLUS is your complete solution for online teaching and learning, including an entire digital textbook and remediation to help students get help in and out of the classroom. The best part is, instructors don't have to do a thing! With the click of a mouse, precreated assignments are ready and available for students to get essentially endless practice. To learn more, contact your Wiley sales representative or visit wileyplus.com. viii PREFACE ■■ Error Check This book has been carefully checked by a number of mathematicians. If any errors are detected, the authors would be grateful if they were sent to [email protected]. ■■ Acknowledgments In addition to the authors, the publication of a book requires the effort and skills of many people. We would like to extend thanks to: All the people at John Wiley & Sons, who contributed their efforts to the production of this book, especially Joanna Dingle, Liz Baird, Jonathan Cottrell, Beth Pearson, Anne Scanlan-Rohrer, Kerry Weinstein, Suzanne Ingrao, Madelyn Lesure, and Laurie Rosatone. Fred Safier and Hossein Hamedani, for preparing the student’s and instructor’s solutions manuals, respectively, and Jeanne Wallace, for producing the manuals. Fred and Gitta Safier, for checking the mathematical accuracy of the book. All the people at Scientific Illustrators for their effective illustrations and accurate graphs. We also wish to thank the many users and reviewers of the 11th and earlier editions: Doug Aichele Rodney Chase Oklahoma State University Oakland Community College George Alexander Barbara Chudilowsky University of Wisconsin De Anza College John Alford Thomas F. Davis Sam Houston State University Sam Houston State University Robert Banik Jody DeVoe Mississippi State University Valencia Community College Loretta Bartolini Jorge Dioses Oklahoma State University Okahoma State University Charlene Beckman Gay Ellis Grand Valley State University Southeast Missouri State University Steve Butcher University of Central Arkansas Richard L. Francis Southeast Missouri State University Ronald Bzoch University of North Dakota Al Giambrone Anne Cavagnaro Sinclair Community College Yosemite Community College Frank Glaser Robert A. Chaffer California State Polytechnic Central Michigan University University—Pomona ix PREFACE Jack Goebel Stephanie H. Kurtz Montana College of Mineral Louisiana State University Science and Technology Ted Laetsch Deborah Gunter University of Arizona Langston University Vernon H. Leach Pierce College Shellie Gutierrez Butler County Community College Lauri Lindberg Pierce College Charles Hale California State University Pomona Christopher Lippi Peralta College Yuichi Handa California State University Chico John Lofberg South Dakota School of Mines James Hart Middle Tennessee State University Babbette Lowe Victoria College Pamala Heard Langston University Van Ma Nicholls State University Steven Heath Southern Utah State College LaVerne McFadden Parkland College Robert Henkel Pierce College John Martin Santa Rosa Junior College John G. Henson Mesa College Susan Meriwether University of Mississippi Fred Hickling University of Central Arkansas Eldon Miller University of Mississippi Quin Higgins Louisiana State University Georgia Miller Millsaps College JoAnnah Hill Montana State University Margaret Ullmann Miller Skyline College Norma F. James New Mexico State University— Kathy Monaghan Las Cruces American River College Judith M. Jones Michael Montano Valencia Community College Riverside Community College Lisa Juliano Charles Mullins Collin County Community College University of Central Arkansas Sally Keely Karen Murany Clark College Oakland Community College x PREFACE Karla Neal M. Vali Siadat Louisiana State University Richard J. Daley College Harald M. Ness Thomas Spradley University of Wisconsin American River College J.F. Nystrom Lowell Stultz Ferris State University Kalamazoo Valley Community Nagendra N. Pandey College Montana College of Mineral Donna Szott Science and Technology Community College of Allegheny William Paulsen County Arkansas State University Richard Tebbs Shahrokh Parvini Southern Utah State College San Diego Mesa College Roberta Tugenberg Howard Penn Southwestern College El Centro College Susan Walker David Platt Montana Tech Front Range Community College Carolyn Warren Tammy Potter Northwest Mississippi State Gadsden State University Community College Gladys Rockin Steve Waters Oakland Community College Pacific Union College Jean-Pierre Rosay Laura Watkins University of Wisconsin Maricopa Community College Miguel San Miguel Randall Wills Texas A & M International University Southeastern Louisiana C. Robert Secrist University Kellogg Community College Bobby Winters Michael Seery Pittsburgh State University Scottsdale Community College Kristin Wolesensky Angelo Segalla University of Nebraska California State University Long Beach Thomas Worthington Charles Seifert Grand Rapids Community College University of Central Arkansas W. Xie Robyn Elaine Serven California State Polytechnic University of Central Arkansas University—Pomona Producing this new edition with the help of all these extremely competent people has been a most satisfying experience. Raymond A. Barnett Michael R. Ziegler Karl E. Byleen
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