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