Trigonometry

407 Pages·15.798 MB·English

by  Robert Blitzer

A Brief Guide to Getting the Most from this Book
1 Read the Book
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Section-Opening Every section opens with a scenario presenting a unique Realizing that trigonometry is everywhere will help motivate
Scenarios application of trigonometry in your life outside the classroom. your learning. (See page 71.)
Detailed Examples are clearly written and provide step-by-step The blue annotations will help you understand the solutions
Worked-Out solutions. No steps are omitted, and each step is thoroughly by providing the reason why every trigonometric step is true.
Examples explained to the right of the mathematics. (See page 198.)
Applications Interesting applications from nearly every discipline, supported Ever wondered how you’ll use trigonometry? This feature
Using Real-World by up-to-date real-world data, are included in every section. will show you how trigonometry can solve real problems.
Data (See page 89.)
Great Question! Answers to students’ questions offer suggestions for problem By seeing common mistakes, you’ll be able to avoid them.
solving, point out common errors to avoid, and provide This feature should help you not to feel anxious or threatened
informal hints and suggestions. when asking questions in class. (See page 112.)
Brief Reviews Brief Reviews cover algebraic and geometric skills you already Having these refresher boxes easily accessible will help ease
learned but may have forgotten. anxiety about skills you may have forgotten. (See page 191.)
Achieving NEW to this edition. Achieving Success boxes offer strategies Follow these suggestions to help achieve your full academic
Success for persistence and success in college mathematics courses. potential in college mathematics. (See page 34.)
Explanatory Voice balloons help to demystify trigonometry. They Does math ever look foreign to you? This feature often
Voice Balloons translate mathematical language into plain English, clarify translates math into everyday English. (See page 81.)
problem-solving procedures, and present alternative ways of
understanding.
Learning Every section begins with a list of objectives. Each objective is The objectives focus your reading by emphasizing what is
Objectives restated in the margin where the objective is covered. most important and where to find it. (See page 192.)
Technology The screens displayed in the technology boxes show how Even if you are not using a graphing utility in the course,
graphing utilities verify and visualize trigonometric results. this feature will help you understand different approaches to
problem solving. (See page 145.)
2 Work the Problems
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Check Point Each example is followed by a matched problem, called a You learn best by doing. You’ll solidify your understanding of
Examples Check Point, that offers you the opportunity to work a similar worked examples if you try a similar problem right away to be
exercise. The answers to the Check Points are provided in the sure you understand what you’ve just read. (See page 219.)
answer section.
Concept and These short-answer questions, mainly fill-in-the-blank and It is difficult to learn trigonometry without knowing its special
Vocabulary true/false items, assess your understanding of the definitions language. These exercises test your understanding of the
Checks and concepts presented in each section. vocabulary and concepts. (See page 35.)
Extensive and An abundant collection of exercises is included in an Exercise The parallel order of the Practice Exercises lets you refer
Varied Exercise Set at the end of each section. Exercises are organized to the worked examples and use them as models for
Sets within several categories. Your instructor will usually provide solving these problems. (See page 220.)
guidance on which exercises to work. The exercises in the
first category, Practice Exercises, follow the same order as the
section’s worked examples.
Practice Plus This category of exercises contains more challenging It is important to dig in and develop your problem-solving
Problems problems that often require you to combine several skills or skills. Practice Plus Exercises provide you with ample
concepts. opportunity to do so. (See page 179.)
Retaining the NEW to this edition. Beginning with Chapter 2, each Exercise These exercises improve your understanding of the topics
Concepts Set contains review exercises under the header “Retaining the and help maintain mastery of the material. (See page 95.)
Concepts.”
Preview Each Exercise Set concludes with three problems to help you These exercises let you review previously covered material
Problems prepare for the next section. that you’ll need to be successful for the forthcoming section.
Some of these problems will get you thinking about concepts
you’ll soon encounter. (See page 169.)
3 Review for Quizzes and Tests
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Mid-Chapter At approximately the midway point in the chapter, an By combining exercises from the first half of the chapter,
Check Points integrated set of review exercises allows you to review the the Mid-Chapter Check Points give a comprehensive review
skills and concepts you learned separately over several before you move on to the material in the remainder of the
sections. chapter. (See page 182.)
Chapter Review Each chapter contains a review chart that summarizes the Review this chart and you’ll know the most important material
Grids definitions and concepts in every section of the chapter. in the chapter! (See page 259.)
Examples that illustrate these key concepts are also
referenced in the chart.
Chapter Review A comprehensive collection of review exercises for each of Practice makes perfect. These exercises contain the most
Exercises the chapter’s sections follows the grid. significant problems for each of the chapter’s sections.
(See page 261.)
Chapter Tests Each chapter contains a practice test with problems that You can use the chapter test to determine whether you
cover the important concepts in the chapter. Take the have mastered the material covered in the chapter.
practice test, check your answers, and then watch the (See page 68.)
Chapter Test Prep Videos to see worked-out solutions for any
exercises you miss.
Chapter Test These videos contain worked-out solutions to every exercise The videos let you review any exercises you miss on the
Prep Videos in each chapter test and can be found in MyMathLab and on chapter test.
YouTube.
Objective Videos NEW to this edition. These fresh, interactive videos walk you The videos provide you with active learning at your own pace.
through the concepts from every objective of the text.
Cumulative Beginning with Chapter 3, each chapter concludes with Ever forget what you’ve learned? These exercises ensure that
Review Exercises a comprehensive collection of mixed cumulative review you are not forgetting anything as you move forward.
exercises. These exercises combine problems from previous (See page 325.)
chapters and the present chapter, providing an ongoing
cumulative review.
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EDITION
Robert Blitzer
Miami Dade College
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Library of Congress Cataloging-in-Publication Data
Names: Blitzer, Robert.
Title: Trigonometry / Robert Blitzer, Miami Dade College.
Description: Second edition. | Hoboken, New Jersey : Pearson Prentice Hall, [2018] |
Includes answers to selected exercises. | Includes subject index.
Identifiers: LCCN 2016042564 | ISBN 9780134469966
Subjects: LCSH: Trigonometry—Textbooks.
Classification: LCC QA531 .B635 2018 | DDC 516.24—dc23
LC record available at https://lccn.loc.gov/2016042564

ISBN 13: 978-0-13-446996-6
ISBN 10: 0-13-446996-8
CONTENTS
Preface vii 2 Graphs of the Trigonometric
To the Student xv Functions; Inverse Trigonometric
About the Author xvi Functions 69
Applications Index xvii 2.1 Graphs of Sine and Cosine Functions 71
2.2 Graphs of Other Trigonometric Functions 96
1 Angles and
Mid-Chapter Check Point 109
the Trigonometric Functions 1
2.3 Inverse Trigonometric Functions 111
1.1 Angles and Radian Measure 2 2.4 Applications of Trigonometric Functions 127
1.2 Right Triangle Trigonometry 21 Summary, Review, and Test 139
1.3 Trigonometric Functions of Any Angle 39 Review Exercises 140
Mid-Chapter Check Point 53 Chapter 2 Test 142
1.4 Trigonometric Functions: The Unit Circle 55
Summary, Review, and Test 64
Review Exercises 66
Chapter 1 Test 68
v
vi Contents
3 Trigonometric Identities
and Equations 143
3.1 Verifying Trigonometric Identities 144
3.2 Sum and Difference Formulas 158
3.3 Double-Angle, Power-Reducing,
and Half-Angle Formulas 170
Mid-Chapter Check Point 182
3.4 Product-to-Sum and Sum-to-Product Formulas 183
3.5 Trigonometric Equations 192 5 Complex Numbers, Polar
Summary, Review, and Test 207 Coordinates, and Parametric
Review Exercises 208 Equations 263
Chapter 3 Test 210
5.1 Complex Numbers 265
Cumulative Review Exercises (Chapters 1–3) 210
5.2 Complex Numbers in Polar Form;
DeMoivre’s Theorem 272
4 Laws of Sines and Cosines;
5.3 Polar Coordinates 286
Vectors 211
Mid-Chapter Check Point 298
4.1 The Law of Sines 212 5.4 Graphs of Polar Equations 299
4.2 The Law of Cosines 224 5.5 Parametric Equations 311
Mid-Chapter Check Point 233 Summary, Review, and Test 321
4.3 Vectors 234 Review Exercises 323
4.4 The Dot Product 249 Chapter 5 Test 324
Summary, Review, and Test 259 Cumulative Review Exercises (Chapters 1–5) 325
Review Exercises 261
Chapter 4 Test 262 Appendix: Where Did That Come From? Selected Proofs 327
Cumulative Review Exercises (Chapters 1–4) 262 Answers to Selected Exercises AA1
Subject Index I1
Photo Credits C1
PREFACE
I’ve written Trigonometry, Second Edition, to help diverse I’ve written every page of the Second Edition with the
students, with different backgrounds and future goals, to intent of eliminating these two objections. The ideas and
succeed. The book has three fundamental goals: tools I’ve used to do so are outlined for the student in
“A Brief Guide to Getting the Most from This Book,”
1. To help students acquire a solid foundation in
which appears at the front of the book.
trigonometry, preparing them for other courses such as
calculus and business calculus, as well as for students
What’s New in the Second Edition?
taking trigonometry as their final mathematics course.
2. To show students how trigonometry can model and • Retaining the Concepts. Beginning with Chapter 2,
solve authentic real-world problems. Section 2.1, each Exercise Set contains three review
exercises under the header “Retaining the Concepts.”
3. To enable students to develop problem-solving skills,
These exercises are intended for students to review
while fostering critical thinking, within an interesting
previously covered objectives in order to improve their
setting.
understanding of the topics and to help maintain their
One major obstacle in the way of achieving these goals
mastery of the material. If students are not certain how
is the fact that very few students actually read their
to solve a review exercise, they can turn to the section
textbook. This has been a regular source of frustration
and worked example given in parentheses at the end
for me and for my colleagues in the classroom. Anecdotal
of each exercise. The Second Edition contains 66 new
evidence gathered over years highlights two basic reasons
exercises in the “Retaining the Concepts” category.
that students do not take advantage of their textbook:
• Achieving Success. The Achieving Success boxes
• “I can’t follow the explanations.”
offer strategies for persistence and success in college
• “I’ll never use this information.”
mathematics courses.
• Updated Learning Guide. Organized by the textbook’s
learning objectives, this updated Learning Guide helps
students make the most of their textbook for test
preparation. Projects are now included to give students
an opportunity to discover and reinforce the concepts
in an active learning environment and are ideal for
group work in class.
• Updated Graphing Calculator Screens. All screens
have been updated using the TI-84 Plus C.
• Section 1.1 (Angles and Radian Measure) has new
examples involving radians expressed in decimal
form, including converting 2.3 radians to degrees
(Example 3(d)) and finding a coterminal angle for a
-10.3 angle (Example 7(d)). Additional Great
Question! features provide hints for locating terminal
sides of angles in standard position.
• Section 1.2 (Right Triangle Trigonometry) has a new
Discovery feature on the use of parentheses when
evaluating trigonometric functions with a graphing
calculator, supported by new calculator screens
throughout the section. A Great Question! has been
added urging students not to become too calculator
dependent.
vii