1 Functions Review

  1.1 Function Basics

  1.2 Graphing Functions

  1.3 Composition

  1.4 Inverse Functions

  1.5 Summary

2 Introduction to Trigonometric Functions

  2.1 The Unit Circle

  2.2 Radians

  2.3 Graphs of Trigonometric Functions

  2.4 Transformations of Trig Functions

  2.5 Inverse Trig Functions

  2.6 Summary

3 Trigonometric Identities

  3.1 Introduction to Trig Identities

  3.2 Sums and Differences of Angles

  3.3 Double and Half Angles 

  3.4 Sum-to-product and Product

  3.5 Problem Solving with Identities

  3.6 Summary

4 Applications to Geometry

  4.1 Right Triangle Trigonometry

  4.2 Law of Cosines

  4.3 Law of Sines

  4.4 More Triangle Relationships

  4.5 Summary

5 Parameterization and Trigonometric Coordinate Systems

  5.1 Parameterization

  5.2 Polar Coordinates

  5.3 Coordinates in Three Dimensions

  5.4 Summary

6 Basics of Complex Numbers

  6.1 Complex Number Arithmetic

  6.2 The Complex Plane

  6.3 Real and Imaginary Parts

  6.4 Nonreal Roots of Polynomials

  6.5 Summary

7 Trigonometry and Complex Numbers

  7.1 Polar Form of Complex Numbers

  7.2 Exponential Form of Complex Numbers

  7.3 Roots of Unity

  7.4 Problems Involving Roots of Unity

  7.5 Summary

8 Geometry of Complex Numbers

  8.1 Transformations of the Complex Plane

  8.2 Parallel and Perpendicular Lines

  8.3 Distance

  8.4 Regular Polygons

  8.5 Classic Theorems

  8.6 Summary

9 Vectors in Two Dimensions

  9.1 What's a Vector

  9.2 The Dot Product

  9.3 Lines and Linear Dependence

  9.4 Projections

  9.5 Summary

10 Matrices in Two Dimensions

  10.1 What is a Matrix?

  10.2 Multiplying Matrices

  10.3 Matrices as Transformations

  10.4 The Determinant

  10.5 Geometric Interpretation of the Determinant

  10.6 Inverting a Matrix

  10.7 Summary

11 Vectors and Matrices in Three Dimensions, Part 1

  11.1 Vectors in Three Dimensions

  11.2 3x3 Matrices.

  11.3 Determinants of 3 X 3 Matrices

  11.4 More Than Just 2x2 and 3x3

  11.5 Summary

12 Vectors and Matrices in Three Dimensions, Part 2 

  12.1 Lines and Planes in Three Dimensions

  12.2 More Planes in Three Dimensions 

  12.3 The Cross Product

  12.4 Geometric Interpretation of the Determinant

  12.5 Inverse of a 3 x 3 Matrix

  12.6 Summary

13 Vector Geometry

  13.1 Introduction

  13.2 Vectors in the Triangle

  13.3 Vectors, Complex Numbers, and Challenging Problems

  13.4 Summary