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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

Sunday
Feb 25 - Jul 28
7:30 - 9:00
PM ET
Feb 25 - Jul 28
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
Saturday
Mar 16 - Aug 17
1:00 - 2:30
PM ET  
Mar 16 - Aug 17
1:00 - 2:30 PM Eastern
12:00 - 1:30 PM Central
11:00 - 12:30 PM Mountain
10:00 - 11:30 AM Pacific
Click here to see more time zones
$670 (~$31/week)
$732 w/books
$670 (~$31/week)
With Books $732
ENROLL
Thursday
Apr 18 - Sep 19
7:30 - 9:00
PM ET
Apr 18 - Sep 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
Monday
May 13 - Oct 21
7:30 - 9:00
PM ET
May 13 - Oct 21
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
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
ENROLL
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
ENROLL
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

AoPS Holidays

There are no classes May 25 ‐ 27, July 4, August 30 ‐ September 2, and November 25 ‐ December 1.

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.
Related course: Precalculus

This was a great class, and I think of all the courses I'm taking at AoPS, it will be the most valuable. All of the material is foundational for the study of higher math, and I feel that I have a strong beginning as I continue on in my studies.