Table of Contents

. THE SIX TRIGNONMETRIC FUNCTIONS. Angles, Degrees, and Special Triangles. The Rectangular Coordinate System. Definition I.: Trigonometric Functions. Introduction to Identities. More on Identities. 2. RIGHT ANGLE TRIGONOMETRY. Definition II: Right Triangle Trigonometry. Calculators and Trigonometric Functions of an Acute Angle. Solving Right Triangles. Applications. Vectors: A Geometric Approach. 3. RADIAN MEASURE. Reference Angle. Radians and Degrees. Definition III: Circular Functions. Arc Length and Area of a Sector. Velocities. 4. GRAPHING AND INVERSE FUNCTIONS. Basic Graphs. Amplitude, Reflection, and Period. Vertical Translation and Phase Shift. The Other Trigonometric Functions. Finding an Equation From its Graph. Graphing Combinations of Functions. Inverse Trigonometric Functions. 5. IDENTITIES AND FORMULAS. Proving Identities. Sum and Difference Formulas. Double-Angle Formulas. Half-Angle Formulas. Additional Identities. 6. EQUATIONS. Solving Trigonometric Equations. More on Trigonometric Equations. Trigonometric Equations Involving Multiple Angles. Parametric Equations and Further Graphing. 7. TRIANGLES. The Law of Sines. The Ambiguous Case. The Law of Cosines. The Area of a Triangle. Vectors: An Algebraic Approach. Vectors: The Dot Product. 8. COMPLEX NUMBERS AND POLAR COORDINATES. Complex Numbers. Trigonometric Form for Complex Numbers. Products and Quotients in Trigonometric Form. Roots of a Complex Number. Polar Coordinates. Equations in Polar Coordinates and Their Graphs. Appendix A: Review of Functions. Introduction to Functions. The Inverse of a Function. Appendix B: Exponential and Logarithmic Functions. Exponential Functions. Logarithms Are Exponents. Properties of Logarithms. Common Logarithms and Natural Logarithms. Exponential Equations and Change of Base.