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