Spinning Out Sine and Cosine

θ

Imagine a point that starts at

(1,0)

and rotates counterclockwise on the unit circle. If

θ

is the length (in radians) of the arc on the circle between

(1,0)

and the point, then as the point moves around the circle its

x

and

y

coordinates are the cosine and sine of

θ

.