Radians Without π

Not every radian measure has π in it. A wheel that turns through 3 radians has turned 3 radius lengths of arc, a little less than a half turn.

To see it in degrees, multiply by $\frac{180^{\circ}}{\pi}$: $\frac{3\cdot 180^{\circ}}{\pi}$ is about 171.9°. Here π does not cancel, so the answer is rounded. The calculator gives $\frac{180}{\pi}$ as about 57.2958, the number of degrees in one radian.

A common calculator mistake is typing a radian angle into a calculator set to degrees, or the other way round. sin 3 in radians is about 0.141; in degrees, sin 3° is about 0.052. Always ask which unit the number is in.