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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, two-dimensional and three-dimensional 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
Sep 21 - Mar 8 |
7:30 - 9:00 PM ET
Sep 21 - Mar 8
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 |
Orianne Luo |
$695
(~$32/lesson)
$757 w/books
|
$695
(~$32/lesson)
CLOSED
With Books $757
|
|
Monday
Oct 20 - Apr 6 |
7:30 - 9:00 PM ET
Oct 20 - Apr 6
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 |
Achilleas Sinefakopoulos |
$695
(~$32/lesson)
$757 w/books
|
$695
(~$32/lesson)
CLOSED
With Books $757
|
|
Sunday
Dec 14 - May 31 |
7:30 - 9:00 PM ET
Dec 14 - May 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 |
Achilleas Sinefakopoulos |
$695
(~$32/lesson)
$757 w/books
|
$695
(~$32/lesson)
ENROLL
With Books $757
|
|
Sunday
Jan 25 - Jun 28 |
7:30 - 9:00 PM ET
Jan 25 - Jun 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 |
Jerry Leung |
$695
(~$32/lesson)
$757 w/books
|
$695
(~$32/lesson)
ENROLL
With Books $757
|
|
Friday
Feb 27 - Jul 31 |
7:30 - 9:00 PM ET
Feb 27 - Jul 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 |
Ben S. |
$695
(~$32/lesson)
$757 w/books
|
$695
(~$32/lesson)
ENROLL
With Books $757
|
|
Tuesday
Mar 17 - Aug 11 |
7:30 - 9:00 PM ET
Mar 17 - Aug 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 |
Marcus Neal |
$695
(~$32/lesson)
$757 w/books
|
$695
(~$32/lesson)
ENROLL
With Books $757
|
|
Sunday
Apr 12 - Sep 27 |
7:30 - 9:00 PM ET
Apr 12 - Sep 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 |
Judy Frank |
$695
(~$32/lesson)
$757 w/books
|
$695
(~$32/lesson)
ENROLL
With Books $757
|
AoPS Holidays
There are no classes November 24 ‐ November 30, December 20 ‐ January 2, May 23 ‐ 25, July 3 ‐ 5, September 5 ‐ 7, and October 31 2026.
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 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. |
