Analytic Trigonometry with Applications, 11th

620 Pages·2012·13.1 MB·English

by  Raymond A. Barnett

Barnett Ziegler Byleen 11 Edition
th
ANALYTIC TRIGONOMETRY
W I T H A P P L I C A T I O N S
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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,
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Evaluation copies are provided to qualified academics and professionals for review purposes only,
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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