Trigonometry: A Unit Circle Approach

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.