## Description

**Mike Sullivan’s**time-tested approach focuses students on the fundamental skills they need for the course:

*preparing*for class,

*practicing*with homework, and

*reviewing*the concepts. In the

**Ninth Edition**,

**Algebra and Trigonometry**has evolved to meet today’s course needs, building on these hallmarks by integrating projects and other interactive learning tools for use in the classroom or online. New Internet-based Chapter Projects apply skills to real-world problems and are accompanied by assignable MathXL exercises to make it easier to incorporate these projects into the course. In addition, a variety of new exercise types, Showcase examples, and video tutorials for MathXL exercises give instructors even more flexibility, while helping students build their conceptual understanding.

**CourseSmart textbooks do not include any media or print supplements that come packaged with the bound book.**

## Table of Contents

**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

**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

**2. Graphs**

2.1 The Distance and Midpoint Formulas

2.2 Graphs of Equations in Two Variables; Intercepts; Symmetry

2.3 Lines

2.4 Circles

2.5 Variation

**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

**4. Linear and Quadratic Functions**

4.1 Linear Functions and Their Properties

4.2 Linear Models: Building Linear Functions from Data

4.3 Quadratic Functions and Their Properties

4.4 Building Quadratic Models from Data

4.5 Inequalities Involving Quadratic Functions

**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

**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 Financial Models

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

6.9 Building Exponential, Logarithmic, and Logistic Models from Data

**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 Any Angle

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; Sinusoidal Curve Fitting

**8. Analytic Trigonometry**

8.1 The Inverse Sine, Cosine, and Tangent Functions

8.2 The Inverse Trigonometric Functions (continued)

8.3 Trigonometric Equations

8.4 Trigonometric Identities

8.5 Sum and Difference Formulas

8.6 Double-Angle and Half-Angle Formulas

8.7 Product-to-Sum and Sum-to-Product Formulas

**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

**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

**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

**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

**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

**14. Counting and Probability**

14.1 Sets and Counting

14.2 Permutations and Combinations

14.3 Probability

**Appendix: Graphing Utilities**

1. The Viewing Rectangle

2. Using a Graphing Utility to Graph Equations

3. Using a Graphing Utility to Graph Equations Locating Intercepts and Checking for Symmetry

4. Using a Graphing Utility to Solve Equations

5. Square Screens

6. Using a Graphing Utility to Graph Inequalities

7. Using a Graphing Utility to Solve Systems of Linear Equations

8. Using a Graphing Utility to Graph a Polar Equation

9. Using a Graphing Utility to Graph Parametric Equations### Digital

Algebra and Trigonometry, CourseSmart eTextbook, 9th Edition

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