The Eighth Edition of this highly dependable book retains its best features–accuracy, precision, depth, and abundant exercise sets–while substantially updating its content and pedagogy. Striving to teach mathematics as a way of life, Sullivan provides understandable, realistic applications that are consistent with the abilities of most readers. Chapter topics include Graphs; Trigonometric Functions; Exponential and Logarithmic Functions; Analytic Geometry; Analytic Trigonometry; Counting and Probability; and more. For individuals with an interest in learning algebra and trigonometry as it applies to their everyday lives.

Why I Wrote This Book:

As a professor of mathematics at an urban public university for over 35 years, I understand the varied needs of precalculus students who range from having little mathematical background and a fear of mathematics courses to those who have had a strong mathematical education and are highly motivated.  For some of your students, this will be their last course in mathematics, while others may decide to further their mathematical education.  I have written this text for both groups.  As the author of precalculus, engineering calculus, finite math and business calculus texts, and, as a teacher, I understand what students must know if they are to be focused and successful in upper level mathematics courses.  However, as a father of four, I also understand the realities of college life.  I have taken great pains to insure that this text contains solid, student-friendly examples and problems, as well as a clear writing style.  I encourage you to share with me your experiences teaching from this text.

The eighth edition of this series builds upon a solid foundation by integrating new features and techniques that further enhance student interest and involvement.  The elements of the previous edition that have proved successful remain, while many changes, some obvious, others subtle, have been made.  A huge 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 from colleagues and students who have used the previous edition.  I am sincerely grateful for this feedback and have tried to make changes that improve the flow and usability of this text.

TABLE OF CONTENTS

Chapter R Review

R.1 Real Numbers

R.2 Algebra Essentials

R.3 Geometry Essentials

R.4 Polynomials

R.5 Factoring Polynomials

R.6 Synthetic Division

R.7 Rational Expressions

R.8 nth Roots; Rational Exponents

Chapter Review

Chapter Test

 Chapter 1 Equations and Inequalities

1.1 Linear Equations

1.2 Quadratic Equations

1.3 Complex Numbers; Quadratic Equations in the Complex Number System

1.4 Radical Equations; Equations Quadratic in Form;  Factorable Equations

1.5 Solving Inequalities

1.6 Equations and Inequalities Involving Absolute Value

1.7 Problem Solving: Interest, Mixture, Uniform Motion, and Constant Rate Jobs  Applications

Chapter Review

Chapter Test

Chapter Projects

 Chapter 2 Graphs

2.1 The Distance and Midpoint Formulas

2.2 Graphs of Equations; Intercepts; Symmetry

2.3 Lines

2.4 Circles

2.5 Variation

Chapter Review

Chapter Test

Cumulative Review

Chapter Projects

Chapter 3 Functions and Their Graphs

3.1 Functions

3.2 The Graph of a Function

3.3 Properties of Functions

3.4 Library of Functions; Piecewise-defined Functions

3.5 Graphing Techniques: Transformations

3.6 Mathematical Models: Building Functions

Chapter Review

Chapter Test

Cumulative Review

Chapter Projects

Chapter 4 Linear and Quadratic Functions

4.1 Linear Functions and Their Properties

4.2 Building Linear Functions from Data

4.3 Quadratic Functions and Their Properties

4.4 Quadratic Models; Building Quadratic Functions From Data

4.5 Inequalities Involving Quadratic Functions

Chapter Review

Chapter Test

Cumulative Review

Chapter Projects

Chapter 5 Polynomial and Rational Functions

5.1 Polynomial Functions and Models

5.2 Properties of Rational Functions

5.3 The Graph of a Rational Function

5.4 Polynomial and Rational Inequalities

5.5 The Real Zeros of a Polynomial Function

5.6 Complex Zeros: Fundamental Theorem of Algebra

Chapter Review

Chapter Test

Cumulative Review

Chapter Projects

Chapter 6   Exponential and Logarithmic Functions

6.1 Composite Functions

6.2 One-to-One Functions; Inverse Functions

6.3 Exponential Functions

6.4 Logarithmic Functions

6.5 Properties of Logarithms

6.6 Logarithmic and Exponential Equations

6.7 Compound Interest

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

6.9 Building Exponential, Logarithmic, and Logistic Functions from Data

Chapter Review

Chapter Test

Cumulative Review

Chapter Projects

Chapter 7   Trigonometric Functions

7.1 Angles and Their Measure

7.2 Right Triangle Trigonometry

7.3 Computing the Values of Trigonometric Functions of Acute Angles

7.4 Trigonometric Functions of General Angles

7.5 Unit Circle Approach: Properties of the Trigonometric Functions

7.6 Graphs of the Sine and Cosine Functions

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

7.8 Phase Shift; Building Sinusoidal Functions from Data

Chapter Review

Chapter Test

Cumulative Review

Chapter Projects

Chapter 8   Analytic Trigonometry

8.1 The Inverse Sine, Cosine, and Tangent Functions

8.2 The Inverse Trigonometric Functions (continued)

8.3 Trigonometric Identities

8.4 Sum and Difference Formulas

8.5 Double-Angle and Half-Angle Formulas

8.6 Product-to-Sum and Sum-to-Product Formulas

8.7 Trigonometric Equations (I)

8.8 Trigonometric Equations (II)

Chapter Review

Chapter Test

Cumulative Review

Chapter Projects

Chapter 9   Applications of Trigonometric Functions

9.1 Applications Involving Right Triangles

9.2 Law of Sines

9.3 Law of Cosines

9.4 Area of a Triangle

9.5 Simple Harmonic Motion; Damped Motion; Combining Waves

Chapter Review

Chapter Test

Cumulative Review

Chapter Projects

Chapter 10  Polar Coordinates; Vectors

10.1 Polar Coordinates

10.2 Polar Equations and Graphs

10.3 The Complex Plane; DeMoivre’s Theorem

10.4 Vectors

10.5 The Dot Product

Chapter Review

Chapter Test

Cumulative Review

Chapter Projects

Chapter 11  Analytic Geometry

11.1 Conics

11.2 The Parabola

11.3 The Ellipse

11.4 The Hyperbola

11.5 Rotation of Axes; General Form of a Conic

11.6 Polar Equations of Conics

11.7 Plane Curves and Parametric Equations

Chapter Review

Chapter Test

Cumulative Review

Chapter Projects

Chapter 12  Systems of Equations and Inequalities

12.1 Systems of Linear Equations: Substitution and Elimination

12.2 Systems of Linear Equations: Matrices

12.3 Systems of Linear Equations: Determinants

12.4 Matrix Algebra

12.5 Partial Fraction Decomposition

12.6 Systems of Nonlinear Equations

12.7 Systems of Inequalities

12.8 Linear Programming

Chapter Review

Chapter Test

Cumulative Review

Chapter Projects

Chapter 13  Sequences; Induction; The Binomial Theorem

13.1 Sequences

13.2 Arithmetic Sequences

13.3 Geometric Sequences; Geometric Series

13.4 Mathematical Induction

13.5 The Binomial Theorem

Chapter Review

Chapter Test

Cumulative Review

Chapter Projects

Chapter 14  Counting and Probability

14.1 Sets and Counting

14.2 Permutations and Combinations

14.3 Probability

Chapter Review

Chapter Test

Cumulative Review

Chapter Projects

Appendix Graphing Utilities

1 The Viewing Rectangle

2 Graphing Equations in Two Variables

3 Locating Intercepts and Checking for Symmetry

4 Solving Equations Using a Graphing Utility

5 Square Screens

6 Graphing Inequalities in Two Variables

7 Solving Systems of Linear Equations

8 Graphing a Polar Equation

9 Graphing Parametric Equations