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?

Schedule

Monday Oct 14 - Mar 30	7:30 - 9:00 PM ET Oct 14 - Mar 30 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	Joseph Stahl	$545 $602 w/books	$545 With Books $602 CLOSED
Friday Dec 6 - May 15	7:30 - 9:00 PM ET Dec 6 - May 15 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	Xinke Guo-Xue	$545 $602 w/books	$545 With Books $602 ENROLL 4 spots left
Monday Jan 27 - Jun 29	7:30 - 9:00 PM ET Jan 27 - Jun 29 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	Christian Hokaj	$570 $627 w/books	$570 With Books $627 ENROLL
Thursday Mar 19 - Aug 13	7:30 - 9:00 PM ET Mar 19 - Aug 13 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	Heather Finotti	$570 $627 w/books	$570 With Books $627 ENROLL
Wednesday Apr 22 - Sep 16	7:30 - 9:00 PM ET Apr 22 - Sep 16 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	Jon Joseph	$570 $627 w/books	$570 With Books $627 ENROLL
Summer 2020	This course will be offered in Summer 2020. Click here to join our mailing list to be notified when the course schedule is available.

AoPS Holidays

There are no classes December 21–January 3, May 23–25, July 3–5, and September 5–7.

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.

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