Definition:Angle/Unit

Definition
Angles are usually measured in degrees, denoted by $^\circ$, or in radians, denoted by $\mathrm{rad}$ or without any unit. One full rotation is $360^\circ$ and $2 \pi \ \mathrm{rad}$.

In the context of calculus in particular, it is usual to use radians.

This is because then the derivatives of trigonometric functions, such as, for example:
 * $\dfrac{\mathrm d}{\mathrm d x}\sin x = \cos x$

work out without the necessity of multiplicative constants.

Also see

 * Pi ($\pi$)