Trigonometry is the mathematics of triangles and angles — and, through them, of waves, circles and rotation. It begins with a single startling fact: in a right-angled triangle, the ratios of the sides depend only on the angles. Pin down those ratios — sine, cosine and tangent — and you can find any missing side or angle from just a little information.

This course builds from the right-angled triangle out to any triangle (the sine and cosine rules), then beyond triangles altogether to radians and the identities that make trig the language of waves.

Stage 1 — The right-angled triangle

1. Right-Angled Trigonometry (SOH-CAH-TOA)
2. Finding a Side
3. Finding an Angle
4. Exact Values

Stage 2 — Putting it to work

1. Angles of Elevation and Depression
2. Bearings

Stage 3 — Any triangle

1. The Sine Rule
2. The Cosine Rule
3. The Area of a Triangle

Stage 4 — Beyond the triangle

1. Radians
2. Trigonometric Identities
3. Solving Trig Equations
4. Angle Addition Formulae
5. Properties of sin(x)

Let's get started

We begin in the right-angled triangle, naming its sides and meeting the three ratios that unlock everything else.

Let's get started → Right-Angled Trigonometry