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Table of Contents

Note: Chapters end with a Chapter Review and Chapter Project. Chapters 2-7 also end with a Cumulative Review.

Preface to the Instructor.


Preface to the Student.


List of Applications.


Photo and Illustration Credits.


1. Functions and Their Graphs.

Rectangular Coordinates. Graphs of Equations; Circles. Functions. Properties of Functions; Library of Functions. Graphing Techniques: Transformations. One-to-One Functions; Inverse Functions.

2. Trigonometric Functions.

Angles and Their Measure. Trigonometric Functions: Unit Circle Approach. Properties of the Trigonometric Functions. Graphs of the Sine and Cosine Functions. Graphs of the Tangent, Cotangent, Cosecant, and Secant Functions. Phase Shift; Sinusoidal Curve Fitting.

3. Analytic Trigonometry.

The Inverse Sine, Cosine, and Tangent Functions. The Inverse Trigonometric Functions (Continued). Trigonometric Identities. Sum and Difference Formulas. Double-angle and Half-angle Formulas. Product-to-Sum and Sum-to-Product Formulas. Trigonometric Equations I. Trigonometric Equations II.

4. Applications of Trigonometric Functions.

Right Triangle Trigonometry. The Law of Sines. The Law of Cosines. The Area of a Triangle. Simple Harmonic Motion; Damped Motion; Combining Waves.

5. Polar Coordinates; Vectors.

Polar Coordinates. Polar Equations and Graphs. The Complex Plane; De Moivre's Theorem. Vectors. The Dot Product. Vectors in Space. The Cross Product.

6. Analytic Geometry.

Conics. The Parabola. The Ellipse. The Hyperbola. Rotation of Axes; General Form of a Conic. Polar Equations of Conics. Plane Curves and Parametric Equations.

7. Exponential and Logarithmic Functions.

Exponential Functions. Logarithmic Functions. Properties of Logarithms; Exponential and Logarithmic Models. Logarithmic and Exponential Equations. Compound Interest. Growth and Decay; Newton's Law; Logistic Models. Logarithmic Scales.

Appendix A. Review.

Algebra Review. Geometry Review. Solving Equations. Complex Numbers; Quadratic Equations with a Negative Discriminant. Inequalities. nth Roots; Rational Exponents. Lines. Scatter Diagrams; Lines Curve Fitting.

Appendix B. Graphing Utilities.

The Viewing Rectangle. Using a Graphing Utility to Graph Equations. Using a Graphing Utility to Locate Intercepts and Check for Symmetry. Using a Graphing Utility to Solve Equations. Square Screens. Using a Graphing Utility to Graph a Polar Equation. Using a Graphing Utility to Graph Parametric Equations.

Answers.


Index.

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