## Table of Contents

**1. Graphs and Functions **

1.1 The Distance and Midpoint Formulas

1.2 Graphs of Equations; Circles

1.3 Functions and Their Graph

1.4 Properties of Functions

1.5 Library of Functions; Piecewise-defined Functions

1.6 Graphing Techniques: Transformations

1.7 One-to-One Functions; Inverse Functions

**2. Trigonometric Functions**

2.1 Angles and Their Measure

2.2 Trigonometric Functions: Unit Circle Approach

2.3 Properties of the Trigonometric Functions

2.4 Graphs of the Sine and Cosine Functions

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

2.6 Phase Shift; Sinusoidal Curve Fitting

**3. Analytic Trigonometry**

3.1 The Inverse Sine, Cosine, and Tangent Functions

3.2 The Inverse Trigonometric Functions (continued)

3.3 Trigonometric Equations

3.4 Trigonometric Identities

3.5 Sum and Difference Formulas

3.6 Double-angle and Half-angle Formulas

3.7 Product-to-Sum and Sum-to-Product Formulas

**4. Applications of Trigonometric Functions**

4.1 Right Triangle Trigonometry; Applications

4.2 Law of Sines

4.3 Law of Cosines

4.4 Area of a Triangle

4.5 Simple Harmonic Motion; Damped Motion; Combining Waves

**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

**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

**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; Completing the Square

A.4 Solving Equations

A.5 Complex Numbers; Quadratic Equations in the Complex Number System

A.6 Interval Notation; Solving Inequalities

A.7 nth Roots; Rational Exponents

A.8 Lines

A.9 Building Linear Models from Data

**Appendix B. Graphing Utilities**

B.1 The Viewing Rectangle

B.2 Using a Graphing Utility to Graph Equations

B.3 Using a Graphing Utility to Locate Intercepts and Check for Symmetry

B.4 Using a Graphing Utility to Solve Equations

B.5 Square Screens

B.6 Using a Graphing Utility to Graph a Polar Equation

B.7 Using a Graphing Utility to Graph Parametric Equations