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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

## Schedule

### AoPS Holidays

There are no classes October 31, November 25 ‐ December 1, December 21 ‐ January 3, May 24 ‐ 26, July 4 ‐ 6, and August 29 ‐ September 1, 2025.

### 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

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

Overall a fantastic course! The instructors were very responsive and personable. Absolutely fantastic.