Precalculus: A Concise Course – Ron Larson – 2nd Edition

1. FUNCTIONS AND THEIR GRAPHS.
Rectangular Coordinates. Graphs of Equations.
Linear Equations in Two Variables.
Functions.
Analyzing Graphs of Functions.
A Library of Functions.
Transformations of Functions.
Combinations of Functions:
Composite Functions.
Inverse Functions.
Mathematical Modeling and Variation.

2. POLYNOMIAL AND RATIONAL FUNCTIONS.
Quadratic Functions and Models.
Polynomial Functions of Higher Degree.
Polynomial and Synthetic Division.
Complex Numbers.
Zeros of Polynomial Functions.
Rational Functions.
Nonlinear Inequalities.

3. EXPONENTIAL AND LOGARITHMIC FUNCTIONS.
Exponential Functions and Their Graphs.
Logarithmic Functions and Their Graphs.
Properties of Logarithms.
Exponential and Logarithmic Equations.
Exponential and Logarithmic Models.

4. TRIGONOMETRY.
Radian and Degree Measure.
Trigonometric Functions:
The Unit Circle.
Right Triangle Trigonometry.
Trigonometric Functions of Any Angle.
Graphs of Sine and Cosine Functions.
Graphs of Other Trigonometric Functions.
Inverse Trigonometric Functions.
Applications and Models.

5. ANALYTIC TRIGONOMETRY.
Using Fundamental Identities.
Verifying Trigonometric Identities.
Solving Trigonometric Equations.
Sum and Difference Formulas.
Multiple-Angle and Product-to-Sum Formulas.
Law of Sines.
Law of Cosines.

6. TOPICS IN ANALYTIC GEOMETRY.
Lines.
Introduction to Conics: Parabolas. Ellipses. Hyperbolas.
Parametric Equations.
Polar Coordinates.
Graphs of Polar Coordinates.
Polar Equations of Conics.