The math way to measure.
A unit of angle measure based on the radius of the circle.
Adopted because it simplifies Calculus formulas. In Calculus, derivatives of trig functions only work cleanly in Radians.
180 degrees = π radians.
In Plain English: Degrees (360) are arbitrary numbers from ancient Babylonians. Radians are physical. One Radian is the angle you get when you wrap the radius along the edge of the circle.
In The Real World: Car tires. When calculating how fast a car moves based on wheel rotation (angular velocity), you must use Radians.
Multiplying by the wrong conversion factor. Remember: You want to cancel out the unit you started with.