Trigonometry • unit circle intuition

Sine is the unit circle’s y-coordinate, graphed over angle.

Watch one point travel around the unit circle while its vertical height traces the sine curve. This two-pane view makes the connection between circular motion and the graph of y = sin(θ) feel immediate and visible.

Unit circle + sine graph

Pi-labeled angles

Play, pause, scrub

Teacher-friendly visual linkage

Live relationship

sin(0) = 0

Current angle

0° • 0

Current sine value

0.000

Teaching cue

At θ = 0, the point starts on the positive x-axis, so its vertical height is 0.

Unit circle

The rotating point has coordinates (1, 0). The green height is the sine value.

Sine graph

The graph plots the same sine value against angle. Follow the moving point as θ increases.

Green marks the y-coordinate, which is the sine value.

Blue marks the corresponding point on the graph y = sin(θ).

Gold shows the current angle on the circle.