Trigonometry, 5th edition

Published by Pearson (January 28, 2019) © 2020
Mark Dugopolski

Title overview

For courses in Plane Trigonometry. Can also be used in co-requisite courses, and in courses with students requiring some skill remediation.

Prepares students to succeed in trigonometry and beyond

Emphasizing problem solving and critical thinking,  Trigonometry with Integrated Review, 5th Edition helps students develop the comprehension and confidence they need to succeed in and out of the classroom. Learning aids are strategically placed throughout, giving students guidance where they need it. Abundant chapter review material offers features such as Highlights, Chapter Review Exercises and Chapter Tests to help students review and synthesize the material as they prepare for the road ahead.

Hallmark features of this title

  • Chapter Openers discuss real-world situations that use mathematics from that chapter.
  • Try This exercises let students immediately try a problem that is just like the example and check their work.
  • For Thought exercises are 10 true/false questions that review the basic concepts in the section, check student understanding before beginning the exercises, and promote writing and discussion.
  • Hints suggest ways of approaching a problem and give a starting point to solve the application problem.
  • Highlights contain an overview all of the chapter concepts along with brief examples to illustrate the concept.
  • Chapter Review Exercises give a comprehensive review of the chapter without reference to individual sections to prepare students for the chapter test.

New and updated features of this title

  • All graphing calculator screenshots have been redone using the TI-84 Plus CE.
  • Updated data: Data used in examples, exercises and chapter openers has been revised for currency.
  • Many new nonstandard exercises ranging from easy to challenging (see exercise 33 on the Law of Sines) have been added.
  • Section 2.5, Combining Functions, has been rewritten to put more emphasis on producing the graphs with a graphing calculator versus drawing by hand. Section 3.2, Verifying Identities, has been rewritten to provide six examples corresponding to the six-point strategy for verifying identities.
  • Multiplying trigonometric binomials  and  factoring trigonometric expressions have been moved from Section 3.2 to Section 3.1. Section 3.2 now focuses solely on verifying identities using the six-point strategy.
  • A new section 6.6, Fun with Polar and Parametric Equations, experiments with polar and parametric equations, producing interesting graphs on a calculator that would be impossible to draw by hand.

Key features

Features of MyLab Math for the 5th Edition

  • Integrated Review Notebook is available in MyLab Math for download. It aligns to the Integrated Review topics and gives students a structured place to take notes as they work through the prerequisite objectives. Definitions, unique examples, and important concepts are highlighted. The notebook is also available in print format.
  • Worked Example Videos engage and support students outside the classroom, covering all Integrated Review prerequisite topics and key examples from the book, hand-picked by the author.
    • Lightboard technology creates a personal experience and simulates an in-class environment.
    • Accompanying assessment questions in MyLab Math make these brand-new videos assignable.
  • Guided Visualizations bring mathematical concepts to life, helping students visualize appropriate Integrated Review topics and key concepts from the main text through directed explorations and purposeful manipulation.
    • Guided Visualizations and accompanying assessment exercises can be assigned in MyLab Math to encourage active learning, critical thinking and conceptual understanding.

Table of contents

  • The table of contents below shows the review topics that are integrated into the MyLab® Math course. The Integrated Review includes worksheets, videos, and other materials designed to help students master these important topics.

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

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 Integrated Review Topics:
    • Multiplying simple rational expressions
    • Using Rational Expressions in Conversions
    • Finding area and circumference of a circle using the standard formula.
    • Simplifying square roots.
    • Performing operations with square roots.
    • Using the Pythagorean theorem to find missing sides of a right triangle.
    • Finding center and radius of a circle given the equation for the circle.
    • Finding the inverse of a function.

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 Integrated Review Topics:
    • Shifting graphs of algebraic functions horizontally and vertically.
    • Finding domain and range of algebraic functions; Reflecting, stretching, and shrinking of algebraic functions.
    • Writing equations of horizontal and vertical lines.
    • Performing arithmetic with fractions involving pi.
    • Finding horizontal and vertical asymptotes for rational functions.
    • Identifying domain and range of rational functions.

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 Integrated Review Topics:
    • Recognizing identities in algebra.
    • Using the Fundamental Identity from Trigonometry to simplify expressions.
    • Using reciprocal identities to simplify expressions.
    • Multiplying binomials.
    • Squaring a binomial.
    • Factoring expressions into a product of two binomials.
    • Finding compositions of algebraic functions.
    • Proving that an equation is not an identity.
    • Operations with rational expressions in algebra.

4. Solving Conditional Trigonometric Equations

  • 4.1 The Inverse Trigonometric Functions
  • 4.2 Basic Sine, Cosine, and Tangent Equations
  • 4.3 Equations Involving Compositions
  • 4.4 Trigonometric Equations of Quadratic Type
  • Chapter 4 Integrated Review Topics:
    • Evaluating a composition of algebraic functions.
    • Identifying identities in trigonometry.
    • Solving proportions for a variable.
    • Solving for a variable in an algebraic equation.
    • Solving quadratic equations by factoring.
    • Solve quadratic equations by using the square root property.
    • Solve quadratic equations by using the quadratic formula.
    • Squaring each side of an equation and getting extraneous roots.
    • Domain and range of the trig functions.
    • Finding the exact values of the sine function.
    • Finding the exact values of secant, cosecant, and cotangent.

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 Integrated Review Topics:
    • Solving proportions for x.
    • Solving proportions using the inverse sine function.
    • Finding the area of a triangle using the standard formula.
    • Solving right triangles.
    • Finding the distance between two points with the distance formula.

6. Complex Numbers, Polar Coordinates, and Parametric Equations

  • 6.1 Complex Numbers
  • 6.2 Trigonometric Form of Complex Numbers
  • 6.3 Powers of Roots of Complex Numbers
  • 6.4 Polar Equations
  • 6.5 Parametric Equations
  • New - 6.6 Fun with Polar and Parametric Equations
  • Chapter 6 Integrated Review Topics:
    • Simplifying square roots.
    • Adding and subtracting binomials.
    • Multiplying binomials.
    • Finding nth roots with 1/n notation.
    • Solving cubic equations.
    • Finding sine and cosine of large angles.

Author bios

About our author

Mark Dugopolski was born in Menominee, Michigan. After receiving a BS from Michigan State University, he taught high school in Illinois for 4 years. He received an MS in mathematics from Northern Illinois University at DeKalb. He then received a PhD in the area of topology and an MS in statistics from the University of Illinois at Champaign - Urbana. Mark taught mathematics at Southeastern Louisiana University in Hammond for 25 years and now holds the rank of Professor Emeritus of Mathematics. He has been writing textbooks since 1988. He is married and has 2 daughters. In his spare time he enjoys tennis, jogging, bicycling, fishing, kayaking, gardening, bridge, and motorcycling.

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