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.

Required Text: Precalculus

22 weeks

Diagnostics

ARE YOU READY? DO YOU NEED THIS?

Documents

SYLLABUS

22 weeks ARE YOU READY? DO YOU NEED THIS? SYLLABUS

Schedule

Wednesday Aug 26 - Feb 10	7:30 - 9:00 PM ET Aug 26 - Feb 10 7:30 - 9:00 PM Eastern 6:30 - 8:00 PM Central 5:30 - 7:00 PM Mountain 4:30 - 6:00 PM Pacific Click here to see more time zones	Adam Rumpf	$570 $627 w/books	$570 With Books $627 CLOSED
Wednesday Aug 26 - Feb 10	7:30 - 9:00 PM ET Aug 26 - Feb 10 7:30 - 9:00 PM Eastern 6:30 - 8:00 PM Central 5:30 - 7:00 PM Mountain 4:30 - 6:00 PM Pacific Click here to see more time zones	Olena Blumberg	$570 $627 w/books	$570 With Books $627 CLOSED
Thursday Sep 17 - Mar 4	7:30 - 9:00 PM ET Sep 17 - Mar 4 7:30 - 9:00 PM Eastern 6:30 - 8:00 PM Central 5:30 - 7:00 PM Mountain 4:30 - 6:00 PM Pacific Click here to see more time zones	Kevin Arlin	$570 $627 w/books	$570 With Books $627 ENROLL
Tuesday Nov 3 - Apr 20	7:30 - 9:00 PM ET Nov 3 - Apr 20 7:30 - 9:00 PM Eastern 6:30 - 8:00 PM Central 5:30 - 7:00 PM Mountain 4:30 - 6:00 PM Pacific Click here to see more time zones	Radu Andrei Cebanu	$570 $627 w/books	$570 With Books $627 ENROLL
Monday Dec 7 - May 17	7:30 - 9:00 PM ET Dec 7 - May 17 7:30 - 9:00 PM Eastern 6:30 - 8:00 PM Central 5:30 - 7:00 PM Mountain 4:30 - 6:00 PM Pacific Click here to see more time zones	Kathryn Lesh	$570 $627 w/books	$570 With Books $627 ENROLL
Spring 2021	This course will be offered in Spring 2021. Click here to join our mailing list to be notified when the course schedule is available.

AoPS Holidays

There are no classes October 31, 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	Exponential Form
Lesson 12	Roots of Unity
Lesson 13	Geometry Using Complex Numbers
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.

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