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.