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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?

Documents

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

Schedule

Wednesday
May 29 - Oct 23
7:30 - 9:00
PM ET
May 29 - Oct 23
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
$670 (~$31/week)
$732 w/books
$670 (~$31/week)
With Books $732
CLOSED
Sunday
Jun 9 - Nov 10
7:30 - 9:00
PM ET
Jun 9 - Nov 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
$670 (~$31/week)
$732 w/books
$670 (~$31/week)
With Books $732
WAITLIST
Tuesday
Jun 25 - Nov 19
7:30 - 9:00
PM ET
Jun 25 - Nov 19
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
$670 (~$31/week)
$732 w/books
$670 (~$31/week)
With Books $732
ENROLL
Friday
Aug 9 - Jan 31
7:30 - 9:00
PM ET
Aug 9 - Jan 31
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
$670 (~$31/week)
$732 w/books
$670 (~$31/week)
With Books $732
ENROLL
Thursday
Aug 29 - Feb 20
7:30 - 9:00
PM ET
Aug 29 - Feb 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
$670 (~$31/week)
$732 w/books
$670 (~$31/week)
With Books $732
ENROLL
Sunday
Sep 29 - Mar 16
7:30 - 9:00
PM ET
Sep 29 - Mar 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
$670 (~$31/week)
$732 w/books
$670 (~$31/week)
With Books $732
ENROLL
Monday
Oct 21 - Apr 7
7:30 - 9:00
PM ET
Oct 21 - Apr 7
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
$670 (~$31/week)
$732 w/books
$670 (~$31/week)
With Books $732
ENROLL
Sunday
Nov 10 - Apr 27
7:30 - 9:00
PM ET
Nov 10 - Apr 27
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
$670 (~$31/week)
$732 w/books
$670 (~$31/week)
With Books $732
ENROLL
Tuesday
Dec 10 - May 20
7:30 - 9:00
PM ET
Dec 10 - May 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
$670 (~$31/week)
$732 w/books
$670 (~$31/week)
With Books $732
ENROLL

AoPS Holidays

There are no classes July 4, August 30 ‐ September 2, October 31, November 25 ‐ December 1, and December 21, 2024 ‐ January 3, 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

I have loved all the Art of Problem Solving courses that I've taken in the past, and this one was no exception. The instructor was very knowledgeable and fun to work with, and I learned many new concepts every week. It is a great privilege to take these classes; Art of Problem Solving has truly changed my life.