Around the Circle

Sine and cosine for every angle

An interactive lesson with 8 steps, about 7 minutes: you predict, drag and solve, with instant feedback on every answer. It runs in your browser and needs JavaScript.

What you’ll learn

• On the unit circle, the point at angle $\theta$ is $(\cos\theta, \sin\theta)$.
• Signs depend on the quarter (quadrant): cosine is negative on the left, sine is negative below.
• $\sin(180° - \theta) = \sin\theta$, and both functions repeat every 360°.

Steps

1. A point on a circle
2. A bigger definition
3. Where the tangent lives
4. Signs
5. Half a turn
6. Same height
7. Find the angle
8. More than a full turn