Trigonometry: A Right Triangle Approach [With CDROM] / Edition 5

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Overview

These authors understand what it takes to be successful in mathematics, the skills that students bring to this course, and the way that technology can be used to enhance learning without sacrificing math skills. As a result, they have created a textbook with an overall learning system involving preparation, practice, and review to help students get the most out of the time they put into studying. In sum, Sullivan and Sullivan's Trigonometry: Enhanced with Graphing Utilities gives students a model for success in mathematics.

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Product Details

Meet the Author

Mike Sullivan is a Professor of Mathematics at Chicago State University and received a Ph.D. in mathematics from Illinois Institute of Technology. Mike has taught at Chicago State for over 30 years and has authored or co-authored over fifty books. Mike has four children, all of whom are involved with mathematics or publishing: Kathleen, who teaches college mathematics; Mike III, who co-authors this series and teaches college mathematics; Dan, who is a Pearson Education sales representative; and Colleen, who teaches middle-school mathematics. When he's not writing, Mike enjoys gardening or spending time with his family, including nine grandchildren.

Mike Sullivan III is a professor of mathematics at Joliet Junior College. He holds graduate degrees from DePaul University in both mathematics and economics. Mike is an author or co-author on more than 20 books, including a statistics book and a developmental mathematics series. Mike is the father of three children and an avid golfer who tries to spend as much of his limited free time as possible on the golf course.

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Table of Contents

Chapter 1 Graphs and Functions

1.1 Rectangular Coordinates; Introduction to Graphing Equations

1.2 Intercepts; Symmetry; Graphing Key Equations; Circles

1.3 Functions

1.4 The Graph of a Function

1.5 Properties of Functions

1.6 Library of Functions; Piecewise-defined Functions

1.7 Graphing Techniques: Transformations

1.8 One-to-One Functions; Inverse Functions

Chapter 2 Trigonometric Functions

2.1 Angles and Their Measure

2.2 Right Triangle Trigonometry

2.3 Evaluating Trigonometric Functions of Acute Angles

2.4 Evaluating Trigonometric Functions of General Angle

2.5 Unit Circle Approach; Properties of the Trigonometric Functions

2.6 Graphs of the Sine and Cosine Functions

2.7 Graphs of the Tangent, Cotangent, Cosecant, and Secant Functions

2.8 Phase Shift; Building Sinusoidal Models

Chapter 3 Analytic Trigonometry

3.1 The Inverse Sine, Cosine, and Tangent Functions

3.2 The Inverse Trigonometric Functions (Continued)

3.3 Trigonometric Identities

3.4 Sum and Difference Formulas

3.5 Double-angle and Half-angle Formulas

3.6 Product-to-Sum and Sum-to-Product Formulas

3.7 Trigonometric Equations (I)

3.8 Trigonometric Equations (II)

Chapter 4 Applications of Trigonometric Functions

4.1 Applications Involving Right Triangles

4.2 The Law of Sines

4.3 The Law of Cosines

4.4 Area of a Triangle

4.5 Simple Harmonic Motion; Damped Motion; Combining Waves

Chapter 5 Polar Coordinates; Vectors

5.1 Polar Coordinates

5.2 Polar Equations and Graphs

5.3 The Complex Plane; DeMoivre’s Theorem

5.4 Vectors

5.5 The Dot Product

5.6 Vectors in Space

5.7 The Cross Product

Chapter 6 Analytic Geometry

6.1 Conics

6.2 The Parabola

6.3 The Ellipse

6.4 The Hyperbola

6.5 Rotation of Axes; General Form of a Conic

6.6 Polar Equations of Conics

6.7 Plane Curves and Parametric Equations

Chapter 7 Exponential and Logarithmic Functions

7.1 Exponential Functions

7.2 Logarithmic Functions

7.3 Properties of Logarithms

7.4 Logarithmic and Exponential Equations

7.5 Financial Models

7.6 Exponential Growth and Decay Models; Newton’s Law; Logistic Growth and Decay Models

7.7 Building Exponential, Logarithmic, and Logistic Models from Data

Appendix A Review

A.1 Algebra Essentials

A.2 Geometry Essentials

A.3 Factoring Polynomials

A.4 Solving Equations Algebraically

A.5 Solving Equations Using a Graphing Utility

A.6 Complex Numbers; Quadratic Equations in the Complex Number System

A.7 Interval Notation; Solving Inequalities

A.8 nth Roots; Rational Exponents

A.9 Lines

A.10 Building Linear Models from Data

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Introduction

As professors at both an urban public university and a community college, Michael Sullivan and Michael Sullivan III are aware of the varied needs of trigonometry students. As a teacher, and as an author of engineering calculus, finite mathematics, and business calculus texts, Michael understands what students must know if they are to be focused and successful in upper level mathematics courses. As a father of four, including the co-author, he also understands the realities of college life. His co-author and son, Michael III, belies passionately in the value of technology as a tool for learning that enhances understanding without sacrificing important skills.

Together, Michael and Michael III have taken great pains to ensure that this text contains solid, student-friendly examples and exercises, as well as a clear, seamless writing style. Please share with them your experiences teaching from this text.

The Third Edition

The Third Edition builds upon a strong foundation by integrating new features and techniques that further enhance student interest and involvement. The elements of previous editions that have proved successful remain, while many changes, some obvious, others subtle, have been made. One important benefit of authoring a successful series is the broad-based feedback upon which improvements and additions are ultimately based. Virtually every change to this edition is the result of thoughtful comments and suggestions from colleagues and students who used previous editions. We are sincerely grateful for this feedback and have tried to make changes that improve the usefulness of the text for both instructors and students.

New to theThird Edition

Preparing for This Section
Most sections now open with a referenced list (by section and page number) of key items to review in preparation for the section ahead. This provides a just-in-time review for students.

Objectives
Each section also contains a numbered list of learning objectives. As the learning objective is addressed in the text, its number will appear.

Concepts and Vocabulary
At the end of every section, there is a short list of Fill-in-the-Blank and True/False items that test concepts and vocabulary in a short answer format. Several quick-answer questions are also included.

Cumulative Reviews
At the end of Chapters 2-6, exercises are provided that require skills learned in the earlier chapters. These cumulative reviews serve to continually reinforce the important concepts of trigonometry. They also make it easier for the student to prepare for a comprehensive final examination.

Content

  • The formula for the area of a sector and related exercises are now part off Section 2.1 Angles and Their Measure.
  • Combining Waves is a new subsection in Section 4.5 Simple Harmonic Motion; Damped Motion; Combining Waves.
  • The Cross Product is a new section in Chapter 5 Polar Coordinates; Vectors.
  • Section 7.1, Exponential Functions, now contains a subsection on exponential equations; Section 7.2, Logarithmic Functions, now contains a subsection on logarithmic equations.
  • The Appendix has been expanded to include more review material appropriate to trigonometry.
  • New Chapter Projects have been added that discuss topics of current interest.

Organization

  • Scatter Diagrams, formerly found in Section 1.1, has been relocated to the. Appendix as part of Section A.8. This change positions the content to, where it is being used.
  • Graphs of the Trigonometric Functions and Sinusoidal Graphs; Sinusoidal Curve Fitting, formerly Sections 2.6 and 2.7, now is covered in three sections, 2.6, 2.7, and 2.8. This change makes it possible to teach the sections in one period each.
  • The Inverse Trigonometric Functions, formerly Section 3.5, now is covered in two sections at the beginning of the chapter. This change makes it possible to teach the sections in one period each. It also places the content closer to the discussion of the trigonometric functions and their graphs.

Features in the 3rd Edition

  • Section OBJECTIVES appear in a numbered list to begin each section.
  • NOW WORK PROBLEM XX. Appears after a concept has been introduced. This directs the student to a problem in the exercises that tests the concept, insuring that the concept has been mastered before moving on. The Now Work problems are identified in the exercises using orange numbers and a pencil icon.
  • References to Calculus are identified by a calculus icon.
  • Discussion, Writing, and Research problems appear in most exercise sets, identified by an icon and red numbers. These problems provide a basis for class discussion, writing projects, and library projects.
  • Historical Perspectives, sometimes with exercises, are presented in context, and provide interesting anecdotal information.
  • Varied applications and real-world, sourced data are abundant in Examples and Exercises.
  • Concepts and Vocabulary, a short list of Fill-in-the-Blank, True/False, and open-ended questions that test concepts and vocabulary in a quick-answer format, are given at the end of every section.
  • An extensive Chapter Review provides a list of important formulas and key definitions and theorems. The objectives of the chapter are listed by section, with page references and review exercises that relate to the objective. The authors' suggestions for a practice test are indicated by a blue number in the review exercise set.
  • Chapter Projects that are relevant and current, many based on newspaper articles, appear at the end of each chapter. These can serve as the basis for collaborative learning experiences.
  • Cumulative Reviews appear at the end of Chapters 2-6. These problem sets serve to continually reinforce skills from earlier chapters.

Using the 3rd Edition Effectively and Efficiently with Your Syllabus.

To meet the varied needs of diverse syllabi, this book contains more content than expected in a trigonometry course. The illustration shows the dependencies of chapters on each other.

As the chart indicates, this book has been organized with flexibility of use in mind. Even within a given chapter, certain sections are optional and can be skipped without fear of future problems.

Chapter 1: Functions and Their Graphs
A quick coverage of this chapter, which is mainly review material, will enable you to get to Chapter 2 Trigonometric Functions earlier.

Chapter 2: Trigonometric Functions
The sections follow in sequence. Section 2.8 is optional.

Chapter 3: Analytic Trigonometry
The sections follow in sequence. Sections 3.2, 3.6, and 3.8 may be skipped in a brief course.

Chapter 4: Applications of Trigonometry
The sections follow in sequence. Sections 4.4 and 4.5 are optional.

Chapter 5: Polar Coordinates; Vectors
Sections 5.1-5.3 and Sections 5.4-5.7 are independent and may be covered separately.

Chapter 6: Analytic Geometry
Sections 6.1-6.4 follow in sequence. Sections 6.5, 6.6, and 6.7 are independent of each other, but do depend on sections 6.1-6.4.

Chapter 7: Exponential and Logarithmic Functions
Sections 7.1-7.4 follow in sequence. Sections 7.5, 7.6, and 7.7 each require Section 7.3.

Appendix Review
This consists of review material, which can be used as the first part of a course in trigonometry or as a just-in-time review. Specific references to this material occur throughout the text to assist in the review process.

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