## Table of Contents

1. FUNCTIONS AND GRAPHS.

Coordinate Geometry. Lines. What is a Function? Graphs of Functions. Getting Information from the Graph of a Function. Transformations of Functions. Combining Functions. One-to-One Functions and Their Inverses. Focus on Modeling: Fitting Lines to Data.

2. TRIGONOMETRIC FUNCTIONS: UNIT CIRCLE APPROACH.

The Unit Circle. Trigonometric Functions of Real Numbers. Trigonometric Graphs. More Trigonometric Graphs. Inverse Trigonometric Functions and Their Graphs. Modeling Harmonic Motion. Focus on Modeling: Fitting Sinusoidal Curves to Data.

3. TRIGONOMETRIC FUNCTIONS: RIGHT TRIANGLE APPROACH.

Angle Measure. Trigonometry of Right Triangles. Trigonometric Functions of Angles. Inverse Trigonometric Functions and Triangles. The Law of Sines. The Law of Cosines. Focus on Modeling: Surveying.

4. ANALYTIC TRIGONOMETRY.

Trigonometric Identities. Addition and Subtraction Formulas. Double-Angle, Half-Angle, and Product-Sum Formulas. Basic Trigonometric Equations. More Trigonometric Equations. Focus on Modeling: Traveling and Standing Waves.

5. POLAR COORDINATES AND PARAMETRIC EQUATIONS.

Polar Coordinates. Graphs of Polar Equations. Polar Form of Complex Numbers; DeMoivre's Theorem. Plane Curves and Parametric Equations. Focus on Modeling: The Path of a Projectile.

6. VECTORS IN TWO AND THREE DIMENSIONS.

Vectors in Two Dimensions. The Dot Product. Three-Dimensional Coordinate Geometry. Vectors in Three Dimensions. The Cross Product. Equations of Lines and Planes. Focus on Modeling: Vector Fields.

7. CONIC SECTIONS.

Parabolas. Ellipses. Hyperbolas. Shifted Conics. Rotation of Axes. Polar Equations of Conics. Focus on Modeling: Conics in Architecture.

8. EXPONENTIAL AND LOGARITHMIC FUNCTIONS.

Exponential Functions. The Natural Exponential Function. Logarithmic Functions. Laws of Logarithms. Exponential and Logarithmic Equations. Modeling with Exponential and Logarithmic Functions. Damped Harmonic Motion. Focus on Modeling: Fitting Exponential and Power Curves to Data.

APPENDIX A: Algebra Review.

Real Numbers. Exponents and Radicals. Algebraic Expressions. Equations. Inequalities.

APPENDIX B: Geometry Review.

Congruence and Similarity of Triangles. The Pythagorean Theorem.

APPENDIX C: Graphing Calculators.

Using a Graphing Calculator. Solving Equations and Inequalities Graphically.