Mark Dugopolski  
Total pages
November 2013
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Dugopolski’s Trigonometry, Third Edition gives students the essential strategies to help them develop the comprehension and confidence they need to be successful in this course. Students will find enough carefully placed learning aids and review tools to help them do the math without getting distracted from their objectives. Regardless of their goals beyond the course, all students will benefit from Dugopolski’s emphasis on problem solving and critical thinking, which is enhanced by the addition of nearly 1,000 exercises in this edition.

Instructors will also find this book a pleasure to use, with the support of an Annotated Instructor’s Edition which maps each group of exercises back to each example within the section; pop quizzes for every section; and answers on the page for most exercises plus a complete answer section at the back of the text. An Insider’s Guide provides further strategies for successful teaching with Dugopolski.


  • Strategies for success. Learning aids are strategically placed throughout the text giving students guidance right when they need it.
    • Chapter Openers discuss real-world situations that use mathematics from that chapter. Examples and exercises then relate back to the opening scenarios.
    • Try This exercises after every example give students the opportunity to immediately try a problem that is just like the example and to check their work. Solutions are contained in the appendix of the student edition.
    • Summaries of important concepts are included to help students clarify ideas that have multiple parts.
    • Strategies contain general guidelines for accomplishing tasks, and are useful for sharpening students’ problem-solving skills.
    • Procedures are similar to Strategies, but are more specific and more algorithmic, designed to give students a step-by-step approach for problems.
    • Function Galleries show families of functions and their graphs, helping students link the visual aspects with the mathematical properties. These occurring throughout the text as appropriate, and are also gathered together at the beginning of the text for easy reference.
    • Hints suggest ways of approaching a problem and give a starting point to solve the application problem. These are given for approximately five application problems in every exercise set.
    • Graphing calculator discussions throughout the text support and enhance algebraic conclusions, but are not used to arrive at those conclusions. These are optional and may be skipped, although students who do not use a graphing calculator may still benefit from the graphs and technology discussions
  • Milestones along the way. Section exercises and review material include the following exercise types so students can practice and check their progress.
    • NEW! Fill-in-the-blank exercises begin every set of section exercises helping students learn the definitions, rules, and theorems.
    • For Thought exercises are ten true/false questions that review the basic concepts in the section, check student understanding before beginning the exercises, and offer opportunities for writing and discussion. Answers are included in the back of the student edition.
    • Exercises are arranged by difficulty, from easy to challenging. Exercises that require a graphing calculator are marked with an icon and may be skipped.
    • NEW! Cumulative review exercises at the end-of-section exercises are designed to keep current the skills learned in previous sections and chapters. These exercises are under the heading “Rethinking.”
    • Writing/Discussion andCooperative Learning Exercises deepen students’ understanding by giving them the opportunity to express mathematical ideas in writing and to their classmates during small group or team discussions.
    • Thinking Outside the Box problems are designed to get students (and instructors) to do some mathematics just for fun, encouraging students to apply their creativity to unique problems. The problems can be used for individual or group work. Answers are given in the Annotated Instructor’s Edition and complete solutions can be found in the Instructor’s Solutions Manual.
    • Pop Quizzes in every section of the text give instructors convenient eight- to ten-question quizzes that can be used in the classroom, covering the basic concepts. Answers are included in the Annotated Instructor’s Edition.
    • Linking Concepts are multi-part exercises that require the use of concepts from previous sections to illustrate the links among various concepts. These can be found at the end of nearly every exercise set. Answers are given in the Annotated Instructor’s E

New to this Edition

  • Updated real-world data in examples, exercises, and chapter and section openers make the text relevant for today’s students.
  • Fill-in-the-blank exercises begin every set of section exercises now begins with fill-in-the-blank exercises, helping students learn the definitions, rules, and theorems.
  • Cumulative review exercises at the end-of-section exercises are designed to keep current the skills learned in previous sections and chapters. These exercises are under the heading “Rethinking.”
  • Tying It All Together exercises have been expanded to include fill-in-the-blank vocabulary exercises.
  • Complex Numbers The section on Complex Numbers has been moved to the end of Chapter P so that it now follows the more basic review material on polynomial operations.
  • Polynomial and Rational Inequalities are now solved with one method, the test-point method.
  • Limit notation is now introduced and used to describe the asymptotic behavior of exponential, logarithmic, rational, and trigonometric functions.

Table of Contents

P. Algebraic Prerequisites

P.1 The Cartesian Coordinate System

P.2 Functions

P.3 Families of Functions, Transformations, and Symmetry

P.4 Compositions and Inverses

   Chapter P Highlights

   Chapter P Review Exercises

   Chapter P Test


1. Angles and the Trigonometric Functions

1.1 Angles and Degree Measure

1.2 Radian Measure, Arc Length, and Area

1.3 Angular and Linear Velocity

1.4 The Trigonometric Functions

1.5 Right Triangle Trigonometry

1.6 The Fundamental Identity and Reference Angles

   Chapter 1 Highlights

   Chapter 1 Review Exercises

   Chapter 1 Test


2. Graphs of the Trigonometric Functions

2.1 The Unit Circle and Graphing

2.2 The General Sine Wave

2.3 Graphs of the Secant and Cosecant Functions

2.4 Graphs of the Tangent and Cotangent Functions

2.5 Combining Functions

   Chapter 2 Highlights

   Chapter 2 Review Exercises

   Chapter 2 Test

   Tying it all Together


3. Trigonometric Identities

3.1 Basic Identities

3.2 Verifying Identities

3.3 Sum and Difference Identities for Cosine

3.4 Sum and Difference Identities for Sine and Tangent

3.5 Double-Angle and Half-Angle Identities

3.6 Product and Sum Identities

   Chapter 3 Highlights

   Chapter 3 Review Exercises

   Chapter 3 Test

   Tying it all Together


4. Solving Conditional Trigonometric Equations

4.1 The Inverse Trigonometric Functions

4.2 Basic Sine, Cosine, and Tangent Equations

4.3 Multiple-Angle Equations

4.4 Trigonometric Equations of Quadratic Type

   Chapter 4 Highlights

   Chapter 4 Review Exercises

   Chapter 4 Test

   Tying it all Together


5. Applications of Trigonometry

5.1 The Law of Sines

5.2 The Law of Cosines

5.3 Area of a Triangle

5.4 Vectors

5.5 Applications of Vectors

   Chapter 5 Highlights

   Chapter 5 Review Exercises

   Chapter 5 Test

   Tying it all Together


6. Complex Numbers, Polar Coordinates, and Parametric Equations

6.1 Complex Numbers

6.2 Trigonometric Form of Complex Numbers

6.3 Powers and Roots of Complex Numbers

6.4 Polar Equations

6.5 Parametric Equations

   Chapter 6 Highlights

   Chapter 6 Review Exercises

   Chapter 6 Test

   Tying it all Together


Appendix A:  Solutions to Try This Exercise

Appendix B:  More Thinking Outside the Box

Answers to All Exercises