Brilliant has no course called Precalculus. What it has is unusually deep treatment of several precalculus units, spread across seven courses: vectors and matrices above all, then complex numbers and the complex plane, trigonometric functions and their inverses, logarithms as the inverse of exponentiation, and polar coordinates. Eighty Brilliant skills map to the advanced Common Core standards a Precalculus class draws on. Coverage is uneven — this is a set of strong units rather than a single Precalculus course — so it works best alongside a class or textbook.
One scoping note: precalculus is not a single Common Core course, and the standards it draws on are largely the ones marked (+) for advanced work, so this page follows the traditional course sequence most schools use.
Which Brilliant course matches which unit?
| Course | What it covers for Precalculus | Where to start |
|---|---|---|
| Vectors & Matrices (82 lessons) | Vectors as magnitude and direction, component addition and subtraction, linear combinations, unit vectors, velocity, matrix arithmetic, determinants, inverses, matrices as transformations, matrix equations for linear systems | Vectors |
| Complex Plane (50 lessons) | Plotting complex numbers, conjugates, absolute value and distance, polar form, multiplication and division in polar form, powers and principal roots | Plotting Complex Numbers |
| Trigonometric Functions (62 lessons) | Exact values at key angles, symmetry and periodicity, tangent by quadrant, inverse sine and cosine, solving trigonometric equations | Key Angles on the Unit Circle |
| Exponential Functions (63 lessons) | Logarithms as the inverse of exponentiation, exponential and log form, product, quotient, and power rules, change of base, solving log equations | Inverse of Exponentiation |
| Equations & Curves (61 lessons) | Inverse functions through squaring and square roots, graphing an inverse by reflecting across y = x, rational expressions and their zeros | Inverse of Squaring |
| Polar Coordinate Plane (35 lessons) | Converting rectangular coordinates to polar, computing a polar angle with inverse tangent | Computing Polar Coordinates |
| Probability and Chance (31 lessons) | Expected value, expected value across multiple events, comparing strategies | Expected Value |
Where Brilliant is strongest: vectors and matrices
If your Precalculus class has a vectors and matrices unit, this is the best reason to use Brilliant. Vectors & Matrices has 82 lessons and 37 skills mapped to 14 Common Core vector and matrix standards, plus the two on solving linear systems with matrices.
The course builds vectors from shifts on a grid. Vectors teaches representing a point-to-point shift by its components; Component-Wise Addition and Drawing Differences do addition and subtraction both geometrically and numerically. Magnitude and Direction and Finding the Polar Angle handle the polar description, and Unit Vectors scales a vector to a target length. There is also an applied velocity strand, including Relative Velocity and Velocity from Bearing.
The matrix half does something a textbook chapter usually does not. Rather than presenting matrix multiplication as a procedure, it introduces matrices as transformations of the plane — Matrices as Transformations, Transforming Basis Vectors, Rotations and Reflections — and derives the arithmetic from that. Composing by Multiplying makes multiplication mean composition, and Transformed Areas makes the determinant an area scale factor before Determinant of any 2 by 2 Matrix gives the formula. Brilliant teaches solving linear systems with inverse matrices, in Matrices as Systems of Equations and Solving with Inverses.
The scope is two-dimensional throughout — 2×2 matrices, horizontal and vertical components — which is the scope of a Precalculus matrix unit.
Complex numbers and the complex plane
Complex Plane has 50 lessons and 20 skills mapped to the four Common Core standards on complex arithmetic, polar form, geometric interpretation, and distance. It is built around the geometry rather than the algebra. Multiplying by i treats multiplication by i as a 90-degree rotation; Magnitude and Argument sets up polar form, and Multiplying in Polar Form shows why multiplying magnitudes and adding arguments is the same operation. Raising to any Power covers De Moivre’s theorem and The Square Root of i covers principal roots.
Rectangular-form arithmetic is here too: Finding the Complex Conjugate, General Division for dividing by the conjugate, and Complex Separation for distance.
One crossover worth knowing: the angle addition formulas for sine and cosine appear here, derived from complex multiplication, in Sine of a Sum and Cosine of a Sum. They read the formulas off right-triangle diagrams.
Trigonometry, inverses, and logarithms
Trigonometric Functions has 62 lessons, 8 of whose skills map to the advanced standards on this list. Symmetry and periodicity — using even, odd, and period properties to evaluate sine and cosine at any angle — is covered in Cosine and Sine at Negative Angles and Sine and Cosine after 2π. Inverse trigonometric functions are covered in Inverse Cosine and Inverse Sine. Solving trigonometric equations is covered in Solving Equations with Inverse Cosine, which finds all solutions in one rotation, and All Solutions to Trig Equations, which extends that to the infinite solution set.
Inverse functions get their clearest treatment in Equations & Curves, where Inverse of Squaring and Graphing the Inverse build the picture of an inverse as a reflection across the line y = x. For the logarithm as an inverse, Exponential Functions has seven mapped skills, running from Inverse of Exponentiation through The Power Rule, Converting Bases, and The Unknown Inside a Log.
What to supplement
These topics are common in a Precalculus class. For them, use your textbook or teacher:
- Sequences and series. Arithmetic and geometric sequences, recursive and explicit formulas, sigma notation, series sums.
- Conic sections. Parabolas, ellipses, and hyperbolas, their equations, and their focus-directrix definitions.
- Trigonometric identities beyond the basics. Double- and half-angle formulas, and proving identities. The Pythagorean identity is covered in Trigonometric Functions, and angle addition appears in the diagram lessons in Complex Plane.
- Limits, if your class ends with an introduction to calculus. See Does Brilliant cover Calculus?.
Brilliant is a practice and explanation layer alongside your class: interactive problems and step-by-step reasoning for the units it covers. It does not follow your syllabus or assess you.
How this mapping was made
Brilliant’s skills are mapped to standards skill by skill against the live course catalog, and the mapping is reviewed by Brilliant’s curriculum team. The data here was pulled on August 27, 2026. For the full standard-by-standard map, see Common Core math coverage.
Frequently asked questions
Is this enough for AP Precalculus?
No, not on its own. This page maps Brilliant against Common Core standards, not the College Board’s AP Precalculus framework, and Brilliant is not an official AP course. It builds the underlying skills where the two overlap — vectors, matrices, complex numbers in polar form, trigonometric functions — but check your coverage against the official course description and use official practice materials for format and timing.
What order should I take these courses in?
If you are following a class, take the course that matches your current unit. Starting from scratch, a workable order is Trigonometric Functions, Exponential Functions, Vectors & Matrices, then Complex Plane, which leans on polar angles from the first two.
Is Vectors & Matrices a linear algebra course?
Not quite. It works entirely in two dimensions with 2×2 matrices, the scope of a Precalculus matrix unit. It covers determinants, inverses, composition, and solving linear systems, but not eigenvalues, vector spaces, or higher dimensions.
My class calls this Algebra 2 — where should I look?
Schools split this material differently, and logarithms and basic trigonometry often land in Algebra 2. See Does Brilliant cover Algebra 2? for that mapping.
Related resources
- Common Core math coverage: grade-by-grade Brilliant lesson mapping
- Does Brilliant cover Algebra 2?
- Does Brilliant cover Calculus?
- What math does Brilliant cover?
- Explore Brilliant’s courses
Sources
[1] Common Core State Standards Initiative, “Mathematics Standards”. [2] Brilliant, “Common Core math coverage: grade-by-grade Brilliant lesson mapping”, accessed August 2026. [3] Brilliant, “Courses”, accessed August 2026.
