 Precalculus Online Math Course
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# Precalculus

Introduction and evaluation of trigonometric functions, trigonometric identities, geometry with trigonometry, parametric equations, special coordinate systems, complex numbers, exponential form of complex numbers, De Moivre's Theorem, roots of unity, geometry with complex numbers, two-dimensional and three-dimensional vectors and matrices, determinants, dot and cross product, applications of vectors and matrices to geometry.

22 weeks

#### Diagnostics

ARE YOU READY? DO YOU NEED THIS?

SYLLABUS
22 weeks

### AoPS Holidays

There are no classes September 5–7, November 23–29, and December 21–January 3.

### Who Should Take?

This class typically follows our Intermediate Algebra course. Students should have completed an honors Algebra 2 or an equivalent course before considering this class. Students who have already taken a standard trigonometry or precalculus class should not simply assume this class is too easy for them. Instead, they should take the diagnostic test above to determine if this class is appropriate for them. Similarly, a student who has completed an honors Algebra 2 course should consider taking our Intermediate Algebra class prior to taking our Precalculus class. Our Intermediate Algebra class includes the non-trigonometric topics of a typical precalculus class, plus a great many interesting topics left out of most standard curricula.

### Lessons

 Lesson 1 Basic Trigonometry Lesson 2 Graphing Trig and Inverse Trig Functions Lesson 3 Trigonometric Identities I Lesson 4 Trigonometric Identities II Lesson 5 Law of Cosines and Law of Sines Lesson 6 More Geometry with Trigonometry Lesson 7 Parametric Equations Lesson 8 Polar, Cylindrical, and Spherical Coordinates Lesson 9 Introduction to Complex Numbers and the Complex Plane Lesson 10 Trigonometry and Complex Numbers Lesson 11 Roots of Unity Lesson 12 Geometry Using Complex Numbers I Lesson 13 Geometry Using Complex Numbers II: Roots of Unity Lesson 14 Vectors in Two Dimensions Lesson 15 Vectors and Matrices in Two Dimensions Lesson 16 Matrices in Two Dimensions Lesson 17 Matrices in Two Dimensions II Lesson 18 Determinants of 2x2 Matrices and Introduction to 3D Vectors Lesson 19 Matrices in Three Dimensions Lesson 20 Lines and Planes in Three Dimensions Lesson 21 Cross Product and Determinant Lesson 22 Applications of Vectors to Euclidean Geometry

### Required Textbook Precalculus By Richard Rusczyk A comprehensive textbook covering precalculus topics. Specific topics covered include trigonometry, complex numbers, vectors, and matrices. Includes many problems from the AIME and USAMO competitions.

The most awesome class ever. It even displaces Geometry, my previous favorite. I absolutely loved it. Sign In