Topic · in development — big ideas below
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.
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.
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.
The planned course
- 01Right-triangle ratiosSine, cosine, tangent — as honest ratios first.soon
- 02The unit circleWhere the ratios become waves.soon
- 03Graphs of sin & cosAmplitude, period, phase — reading a wave's anatomy.soon
- 04Identities that matterThe handful worth knowing, with pictures.soon
- 05Modeling with wavesTides, sound, daylight hours — fitting sines to the world.soon
While you wait — this connects to material that's live now