For undergraduate courses in College Algebra, Algebra and Trigonometry, Trigonometry and Precalculus. The Sullivan Enhanced with Graphing Utilities series fully integrates the graphing calculator. This widely adopted text is known for its precise careful presentation of mathematics. This precision permeates the text and is particularly evident in the examples, pedagogy and exercises.

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**TO THE INSTRUCTOR**

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 Algebra & Trigonometry students, ranging from those who have little mathematical background and a fear of mathematics courses, to those having a strong mathematical education and a high level of motivation. For some of your students, this will be their last course in mathematics, while others will further their mathematical education. This text is written for both groups.

As a teacher, and as an author of precalculus, engineering calculus, finite math, and business calculus texts, Michael understands what students must know if they are to be focused and successful in upper level math courses. However, as a father of four, including the coauthor, he also understands the realities of college life. His co-author and son, Michael Sullivan III, believes passionately in the value of technology as a tool for learning that enhances understanding without sacrificing important skills. Together, both authors have taken great pains to ensure that the text contains solid, student-friendly examples and problems, as well as a clear and seamless writing style.

**In 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 made by colleagues and students who have used previous editions. This feedback has proved invaluable and has been used to make changes that improve the flow, usability, and accessibility of the text. For example, some topics have been moved to better reflect the way teachers approach the course and problems have been added where more practice was needed. The supplements package has been enhanced through upgrading traditional supplements and adding innovative media components.

**Reorganized Content for Algebra and Trigonometry**

- Appendix Review
- Now expanded, this material appears in the beginning of the book as Chapter R
- Chapter 1
- Scatter diagrams now appear in Section 2.2 Linear Functions and Models
- Section 1.2 has been split into two sections. In 3/e Section 1.2 contains point plotting, graphing equations on a graphing utility, and intercepts. Section 3.1 covers symmetry and graphing key equations. This adheres to the "just in time approach" by placing symmetry and key equations closer to functions.
- Section 1.3 from 2/e has been split into two sections—1.3 and 1.5. Section 1.5 has been expanded to include quadratic in form equations.
- Chapter 2
- Section 2.2 now includes the discussion on scatter diagrams.
- Quadratic equations now appears earlier as part of Section 13.
- Chapter 3
- Section 3.1 contains the discussion on symmetry and graphing key equations.
- Section 3.1 from 2/e is now two sections: Section 3.2 covers properties of functions, while Section 3.3 covers the library of functions and piecewise-defined functions.
- Chapter 4
- This chapter contains Sections 4.1, 4.2, 4.7 and 4.8 from 2/e. The section on rational functions has been split into two sections to accommodate a single lecture for each section.
- Chapter 5
- This chapter contains the remaining sections of Chapter 4 from 2/e.
- Chapter 6 (Formerly Chapter 5)
- Section 6.2 now includes a discussion of basic exponential equations.
- Section 6.3 now includes a discussion of basic logarithmic equations.
- Chapter 7 (Formerly Chapter 6)
- Chapter 8 (Formerly Chapter 7)
- Graphs of Trigonometric Functions has been split into two sections. Section 8.6 discusses the graphs of the sine and cosine functions, including sinusoidal graphs. Section 8.7 discusses the graphs of the tangent, cotangent, secant and cosecant functions.
- Chapter 9 (Formerly Chapter 8)
- Section 8.5 has been split into two sections as 9.1 and 9.2 to accommodate a single lecture for each section.
- Chapter 10 (Formerly Chapter 9)
- Section 10.5 now includes a discussion on combining waves (the method of adding
*y*-coordinates to obtain graphs). - Chapter 11 (Formerly Chapter 10)
- Chapter 12 (Formerly Chapter 11)
- Chapter 13 (Formerly Chapter 12)
- Chapter 14 (Formerly Chapter 13)

**Specific Content Changes**

In this edition emphasis is placed on the role of modeling in algebra and trigonometry. To this end, dedicated sections appear on Linear Functions and Models, Quadratic Models, Power Functions and Models, Polynomial Functions and Models, Exponential and Logarithmic Functions and Models, and Trigonometric Models. Many of these applications focus on the areas of business, finance, and economics.

Chapter R review is a robust expansion of the appendix review of the second edition.

New to this edition is a discussion of quadratic in form equations.

A section on combining waves (the method of adding *y*-coordinates to obtain graphs) has been added.

As a result of these changes, this edition will be an improved teaching device for professors and a better learning tool for students.

**Features in the 3rd Edition**

- Section
appear in a numbered list to begin each section.*OBJECTIVES* - "Now Work" problems identified by the yellow pencil icon appear 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.
- References to calculus are identified by a calculus icon.
- Historical Perspectives, sometimes with exercises, are presented in context and provide interesting anecdotal information.
- Varied applications and real-world data are abundant in Examples and in Exercises. Many contain sourced data.
- Discussion, Writing, and Research problems appear in each exercise set, identified by an icon and red numbers. These problems challenge students to expand the parameters of their understanding by providing the basis for class discussions, writing projects and collaboration.
- An extensive Chapter Review provides a list of important formulas, definitions, theorems, and objectives. Each objective is listed with a page reference and review exercises that test the student's understanding of the objective. The authors' suggestions for practice tests are indicated in blue.
- A cumulative review appears at the end of every chapter, beginning with Chapter 2. These cumulative reviews serve to continually reinforce skills from previous chapters. This makes study for the final examination easier.

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

To meet the varied needs of diverse syllabi, this book contains more content than a typical algebra and 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 can be skipped without fear of future problems.

**Chapter R. Review**

This chapter is a revision of the old Appendix. It may be used as the first part of the course, or as a "just-in-time" review when the content is required in a later chapter. Specific references to this chapter occur throughout the book to assist in the review process.

**Chapter 1. Graphs**

This chapter presents an introduction to graphing and the graphing utility. Equations and inequalities are solved algebraically with graphical support. For those who prefer to treat complex numbers and negative discriminants early, Section 5.3 can be covered any time after Section 1.3.

**Chapter 2. Linear and Quadratic Functions**

This chapter provides an introduction to functions and then discusses two specific types of functions: linear functions and quadratic functions, along with models that utilize these functions.

**Chapter 3. Functions and Their Graphs**

Perhaps the most important chapter. Section 3.6 can be skipped without adverse effects.

**Chapter 4. Polynomial and Rational Functions**

Topic selection is dependent on your syllabus.

**Chapter 5. The Zeros of a Polynomial Function**

Topic selection is dependent on your syllabus. Section 5.1 is not absolutely necessary, but its coverage makes some computation easier.

**Chapter 6. Exponential and Logarithmic Functions**

Sections 6.1-6.5 follow in sequence; Sections 6.6, 6.7, and 6.8 each require Section 6.3.

**Chapter 7. Systems of Equations and Inequalities**

Sections 7.1-7.2 follow in sequence; Sections 7.3-7.7 require Sections 7.1 and 7.2, and may be covered in any order.

**Chapter 8. Trigonometric Functions**

The sections follow in sequence. Section 10.1 on Applications Involving Right Triangles, may be covered immediately after Section 8.3, if so desired.

**Chapter 9. Analytic Trigonometry**

The sections follow in sequence. Sections 9.2, 9.6, and 9.8 may be skipped in a brief course.

**Chapter 10. Applications of Trigonometric Functions**

The sections follow in sequence. Sections 10.4 and 10.5 may be skipped in a brief course.

**Chapter 11. Polar Coordinates; Vectors**

Sections 11.1-11.3 and Sections 11.4-11.5 are independent and may be covered separately.

**Chapter 12. Analytic Geometry**

Sections 12.1-12.4 follow in sequence. Sections 12.5,12.6, and 12.7 are independent of each other, but do depend on Sections 12.112.4. Section 12.8 is independent of Sections 12.5-12.7, but does depend on Sections 12.1-12.4 as well as Sections 7.1-7.2.

**Chapter 13. Sequences; Induction; The Binomial Theorem**

There are three independent parts: (1) Sections 13.1-13.3; (2) Section 13.4; (3) Section 13.5

**Chapter 14. Counting and Probability** Sections 14.1-14.4 follow in order.

**TO THE STUDENT**

As you begin your study of Algebra and Trigonometry, you may feel overwhelmed by the numbers of theorems, definitions, procedures, and equations that confront you. You may even wonder whether or not you can learn all of this material in the time allotted. These concerns are normal. Keep in mind that the elements of algebra and trigonometry are all around us as we go through our daily routines. Many of the concepts you will learn to express mathematically, you already know intuitively. For many of you, this may be your last math course, while for others, just the first in a series of many. Either way; this text was written with you in mind. We have spent countless hours teaching Algebra and Trigonometry courses. We know what you're going through. You'll find that we have written a text that doesn't overwhelm, or unnecessarily complicate Algebra and Trigonometry, but at the same time gives you the skills and practice you need to be successful.

This text is designed to help you, the student, master the terminology and basic concepts of Algebra and Trigonometry. These aims have helped to shape every aspect of the book. Many learning aids are built into the format of the text to make your study of the material easier and more rewarding. This book is meant to be a "machine for learning," that can help you focus your efforts, ensuring that you get the most from the time and energy you invest.

Please do not hesitate to contact us through Prentice Hall with any suggestions or comments that would improve this text.

Best Wishes!

*Michael SullivanMichael Sullivan, III*

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(2002)

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