Why do we need radians?

Question

Why can't degrees be enough?

Answer 1

The problem is pi can never be accurately determined, when considering relationships involving it, such area, volume, circumference.

Answer 2

Measurements in radians are in fact a pure number. I won't go into why this is so, but anyways -- using them makes it easy to calculate things based on the radius of a circle, and helps avoid rounding errors since you can just carry a pi symbol through all your calculations.