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PrecalculusIntroduction 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, twodimensional and threedimensional vectors and matrices, determinants, dot and cross product, applications of vectors and matrices to geometry. 
22 weeks 
22 weeks ARE YOU READY? DO YOU NEED THIS? SYLLABUS 
Schedule
Sunday
Jun 14  Nov 22 
7:30  9:00
PM ET
Jun 14  Nov 22
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
CLOSED
With Books $627

Sunday
Jun 14  Nov 22 
7:30  9:00
PM ET
Jun 14  Nov 22
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
CLOSED
With Books $627

Monday
Jul 20  Jan 11 
7:30  9:00
PM ET
Jul 20  Jan 11
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 
Andrew Sayler 
$570
$627 w/books

$570
CLOSED
With Books $627

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
ENROLL
With Books $627

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
ENROLL
With Books $627

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
ENROLL
With Books $627

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
ENROLL
With Books $627

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 September 5–7, 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 nontrigonometric 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 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. 