The mathematics of things that repeat. Trigonometric functions come from the unit circle and model periodic phenomena; sinusoidal functions are their transformations. Master the unit circle, sine, cosine, and tangent, inverse trig, solving trig equations, and graphing in the polar plane.
Six ways to master Unit 3 — pick whichever fits how you like to study.
All 15 topics from the College Board CED, in order.
Unit 3 is about periodic behavior — quantities that repeat, like the tides, daylight hours, or a point rotating around a circle. It builds the trigonometric functions from the unit circle: for an angle in standard position, the point where the terminal ray meets the unit circle has coordinates (cos θ, sin θ), and tangent is their ratio. From there you graph sine and cosine and learn the sinusoidal form f(x) = a·sin(b(x − c)) + d, where each parameter controls amplitude, period, phase shift, or midline.
The unit then widens to the tangent and reciprocal functions (secant, cosecant, cotangent), the inverse trigonometric functions with their restricted domains, and solving trigonometric equations — which have infinitely many solutions because of periodicity. It closes with a second coordinate system: polar coordinates (r, θ), converting between polar and rectangular form, graphing polar curves such as circles, roses, and limaçons, and describing how r changes with θ.
This unit is 30–35% of the exam and takes about 35–50 class periods — the longest unit in the course. The three mathematical practices below run through every topic: