Labs / Mathematics
Unit Circle Unwrapped
A point rides around a circle of radius one, and its height gets projected out to the right to draw a wave. Drag the point, switch between sine, cosine & tangent, and watch how spinning in a circle and rolling out a wave are secretly the same motion.
θ 30.0°(cos, sin) (0.866, 0.500)sin 0.500cos 0.866tan 0.577
What to try
- Where on the circle is the point when the sine wave hits its very top? What angle is that?
- Switch to cosine. Why does its wave start at 1 instead of 0 — what is the point's x-coordinate at 0°?
- Where does the tangent wave shoot off toward infinity, and what is cosine doing at exactly those angles?
- Flip to radians. How far around the circle is one full wavelength — and why is it 2π?
- Drag the point past 180°. Which of sin, cos & tan go negative, and can you predict it from the (x, y) coordinates?