AoPS PreCalculus

Lessons

Module 1: Functions Review, Introduction to Trigonometric Functions, Trigonometric Identities

Function Basics

Graphing Functions

Graphs of Trigonometric Functions

Transformations of Trigonometric Functions

Inverse Trigonometric Functions

Quiz 1 Review

Quiz 1

Introduction to Trigonometric Identities

Sums and Differences of Angles

Double and Half Angles

Sum-to-Product and Product-to-Sum Formulas

Problem Solving with Identities

Module 2: Trigonometric Applications to Geometry, Parameterization and Trigonometric Coordinate Systems, Basics of Complex Numbers

Right Triangle Trigonometry

Law of Cosines

Law of Sines

More Triangle Relationships

Coordinates in Three Dimensions

Quiz 4 Review

Quiz 4

Complex Numbers Arithmetic

The Complex Plane

Real and Imaginary Parts

Nonreal Roots of Polynomials

Module 3: Trigonometry and Complex Numbers, Geometry of Complex Numbers, Vectors in Two Dimensions

Polar Form of Complex Numbers

Exponential Form of Complex Numbers

Roots of Unity

Problems Involving Roots of Unity

Quiz 6 Review

Quiz 6

Transformations of the Complex Plane

Parallel and Perpendicular Lines

Distance

Regular Polygons

Classic Theorems

Definition of a Vector and The Dot Product

Lines and Linear Dependence

Projections

Test 3 Review

Test 3

Module 4: Matrices in Two and Three Dimensions, Vectors in Three Dimensions, and Vector Geometry

Definition of a Matrix

Multiplying Matrices

Matrices as Transformations

The Determinant

Geometric Interpretation of the Determinant

Inverting a Matrix

Quiz 7 Review

Quiz 7

Vectors in Three Dimensions

3x3 Matrices

Determinants of 3x3 Matrices

More than just 2x2 and 3x3 Matrices

Quiz 8 Review

Quiz 8

Lines and Planes in Three Dimensions

More Planes in Three Dimensions

The Cross Product

Geometric Interpretation of the Determinant

Inverse of a 3x3 Matrix

Quiz 9

Quiz 9 Review

Introduction to Vector Geometry

Vectors in the Triangle

Vectors, Complex Numbers, and Challenging Problems

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