Trigonometry
Right triangles, the unit circle, sine waves, and the laws of sines & cosines — with live diagrams.
Trigonometry is the study of triangles — and, surprisingly, of anything that repeats: waves, rotations, seasons. Everything below is live: change any number and watch the results, plots and drawings update.
- 01 Right triangles — SOH CAH TOA In a right triangle, the three sides are related by the Pythagorean theorem, and each acute angle is pinned down by the RATIO of two sides: sin =…
- 02 The unit circle For angles beyond 90° the triangle picture breaks down, so trig moves to the unit circle: a circle of radius 1, where cos(φ) is the x-coordinate and sin(φ) the…
- 03 Sine waves Walk around the circle at constant speed and plot your height over time: that is a sine wave. The amplitude stretches it vertically; the angular frequency ω…
- 04 Any triangle: law of cosines The law of cosines finds the third side from two sides and the angle between them — it is the Pythagorean theorem plus a correction term for the angle not…
- 05 Any triangle: law of sines The law of sines relates each side to the angle opposite it: sin(A)/a = sin(B)/b. Given one matched side-angle pair and one more side, the opposite angle…
next course: Precalculus — Functions →