Radians

Imagine a circle. The circumference of the cirlce is 2 times pi times the radius of the circle (2*pi*r).

Now say the radius of the circle is 1. The formula of the circumference of the "unit" circle (a circle with a radius of one) is two times pi. (Since the radius is one, we can eliminate the multiplier "radius" from the equation.

The circumference is 360 degrees. It is also 2pi: 360=2pi. The units are radians. 360 = 2 pi radians. Dividing both sides by 2 results in 180=pi radians. It follows that 90 degrees equals pi/2 radians.

Thus we have a way of describing an angle that relates very directly to the formula for circumference! And how cool is that!