Interactive unit circle

Drag the angle and see sin(θ), cos(θ) and tan(θ) update in real time — both on the circle and on the wave curves.

The unit circle — radius = 1:

sin(θ) = y · cos(θ) = x · tan(θ) = sin/cos

A point on the unit circle at angle θ has coordinates (cos θ, sin θ).

Angle θ

45°

θ (degrees)

–

θ (radians)

–

sin(θ) = y

–

cos(θ) = x

–

tan(θ) = sin/cos

–

Pythagorean identity

sin²(θ) + cos²(θ) = 1

Important angles to memorise:

θ	Radians	sin	cos	tan
0°	0	0	1	0
30°	π/6	1/2	√3/2	1/√3
45°	π/4	√2/2	√2/2	1
60°	π/3	√3/2	1/2	√3
90°	π/2	1	0	∞

There is geometry in the humming of the strings, there is music in the spacing of the spheres.

— Pythagoras (570–495 f.Kr.)