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Trigonometry
Triangles, circles, and everything that repeats.
Trig starts as a tool for finding unknown sides of triangles — and then turns out to be the mathematics of anything that cycles: sound, light, tides, seasons, heartbeats. Two functions, sine and cosine, carry the whole subject.
Your progress
5 lessons
The big ideas
Ratios that only depend on angle
In a right triangle, the ratio of sides is fixed by the angle alone — big triangle or small. That reliability is what makes sine and cosine functions.
The unit circle
Walk around a circle of radius 1: your height is sine, your horizontal position is cosine. Triangles and waves become one picture.
Everything periodic is sines in disguise
Any repeating signal — a chord, a voice, a tide — can be built from sines added together. That's why trig shows up far from any triangle.
The course — start at lesson one
- 01Sine, cosine & tangentHonest ratios first — SOH-CAH-TOA with meaning.Easy
- 02The unit circleWhere the ratios become coordinates of rotation.Easy
- 03Reading & building wavesAmplitude and period — the anatomy of everything that repeats.Easy
- 04Trig in the wildComponents, inverse angles, and beyond right triangles.Easy
- 05Identities & phaseThe algebra of waves: phase, beats, and the identities that matter.Easy
Out in the world
Sound & music
A note is a sine wave; a chord is a sum of them. Audio engineering is applied trig.
Electricity
AC power is a 50–60 Hz sine wave. Your wall socket runs on trigonometry.
Satellites & surveying
Measuring inaccessible distances by angle — trig's original job, still working.
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