Unit Circle Explorer

Drag the blue point around one large reference triangle. It snaps to every 30°, 45°, 60°, and quadrantal angle in a single pass.

Explore the circle

Drag counterclockwise for positive angles; cross 0° clockwise to explore negative angles.

Jump to a special angle

Current angle

45° π/4

Quadrant I

Reference angle 45° π/4

Point on the unit circle

(√2/2, √2/2)

x = cos θ y = sin θ

Why it works

On a unit circle the hypotenuse is 1, so the triangle’s horizontal and vertical legs are the cosine and sine.

sin θ√2/2

cos θ√2/2

tan θ1

csc θ√2

sec θ√2

cot θ1