Algebra and Trigonometry, 8th Edition

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