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.

Chapter 1: Functions Review
Definition of functions, graph of functions, composition, and inverse functions
Chapter 2: Introduction to trigonometric functions
Unit Circle, Radians, graphs, transformations of trig functions, and inverse trig
Chapter 3: Trigonometric Identities
Sum and differences, double and half, sum-to-product identities
Chapter 4: Applications to Geometry
Law of cosines, law of sines
Chapter 5: Parameterization and trigonometry coordinate system
Parameterization, polar coordinates
Chapter 6: Basics of Complex Numbers
Arithmetics of complex numbers, complex plane
Chapter 7: Trigonometry and Complex numbers
Trig ratios in exponential form, roots of unity
Chapter 8: Vectors in two dimensions
Definition, dot product, lines and linear dependence
Chapter 9: Vectors and Matrices in Three dimensions
Lines and Planes in three dimensions

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This course is for students who have completed our beginner level math courses.

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AGES 14  - 18
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