## Integral Calculus, Circumference of a Circle

### Circumference of a Circle

Review the definition of sine and cosine.
Recall that an imaginary particle moves around the unit circle counterclockwise,
at constant speed,
and the x and y coordinates define the cosine and sine functions respectively.
Since the speed is always 1, the length traveled is identical to the travel time.
A circuit is completed when t = 2π,
hence the circumference is 2π.
(See arc length for more details.)
Scaling all variables,
the circumference around a circle of radius r is 2πr.