Precalculus & Trigonometry
Functions, full trig identities, laws of sines and cosines, vectors, polar and parametric curves, conics, and a first look at limits.
15 units · 134 topics · 645 questions
Relations that qualify as functions, their domains and ranges, and how shifting, stretching, combining, and inverting a graph works.
What Is a Function · Domain and Range · Evaluating and Building Functions · Piecewise-Defined Functions · +12 more
Quadratics, higher-degree polynomials, their zeros and complex roots, and rational functions with their asymptotes, holes, and inequalities.
Quadratic Functions and Vertex Form · Completing the Square · Power Functions and End Behavior · Polynomial Shape and Degree · +12 more
Growth and decay built from a constant multiplier, the natural base e, and logarithms as the inverse operation that undoes an exponent.
Exponential Growth and Decay · The Natural Base e · Logarithms as Inverses of Exponentials · Graphs of Logarithmic Functions · +7 more
Measuring rotation in degrees and radians, wrapping a circle's own radius along its arc, and the unit circle that grounds every trig function.
Angles in Standard Position · Radian Measure · Converting Between Degrees and Radians · Arc Length · +5 more
The unit circle unrolling into a wave, and how amplitude, period, and phase shift each reshape a sinusoid one parameter at a time.
Unwrapping the Circle into the Sine Wave · The Cosine Graph · Amplitude and Vertical Shift · Period and Frequency of a Sinusoid · +5 more
Restricting sine, cosine, and tangent so they pass the horizontal line test, and using their inverses to solve equations and simplify compositions.
Restricting Domains to Define Inverses · The Inverse Sine Function · The Inverse Cosine and Inverse Tangent Functions · Composing Trig and Inverse Trig Functions · +1 more
The identities that let one trig expression stand in for another, how to prove them, and how to use them to solve equations by hand.
The Pythagorean Identities · Even-Odd and Cofunction Identities · Simplifying Trigonometric Expressions · Proving Trigonometric Identities · +8 more
Solving triangles that aren't right triangles, the ambiguous case where one setup builds two different triangles, and finding area without a height.
The Law of Sines · The Ambiguous Case (SSA) · The Law of Cosines · Choosing Between the Law of Sines and the Law of Cosines · +1 more
Quantities with both size and direction, added tip to tail, broken into components, and combined with the dot product to measure the angle between them.
Vectors, Magnitude, and Direction · Vector Components and Unit Vectors · Vector Addition and Scalar Multiplication · The Dot Product · +2 more
Locating points by distance and angle instead of x and y, polar curves that draw themselves as theta sweeps, and complex numbers plotted in the plane.
The Polar Coordinate System · Converting Between Polar and Rectangular Coordinates · Polar Graphs of Lines and Circles · Polar Roses · +6 more
Tracing a curve as a moving particle with time as its own separate parameter, and switching that motion back into a single x-y equation.
Defining Curves Parametrically · Eliminating the Parameter · Parametrizing Lines and Circles · Parametric Motion and Projectile Paths · +1 more
Circles, parabolas, ellipses, and hyperbolas as slices of a double cone and as loci built from a focus and directrix, in and out of the origin.
Conics as Slices of a Double Cone · The Parabola: Focus and Directrix · The Ellipse: Foci and Eccentricity · The Hyperbola: Foci and Asymptotes · +3 more
Solving several equations at once by elimination and by row-reducing a matrix, and using determinants and inverses to solve systems directly.
Solving Linear Systems by Substitution and Elimination · Systems of Nonlinear Equations · Matrices, Addition, and Scalar Multiplication · Matrix Multiplication · +4 more
Patterns built term by term, the sums of arithmetic and geometric lists, proving a statement true for every integer at once, and expanding a binomial.
Sequences and Recursive Formulas · Arithmetic Sequences · Arithmetic Series · Geometric Sequences · +5 more
The intuitive bridge into calculus: what a function approaches, one-sided limits, continuity, and end behavior far out toward infinity.
The Intuitive Idea of a Limit · Estimating Limits from Graphs and Tables · One-Sided Limits · Limits That Do Not Exist · +2 more