Circular Measure

Radians

One radian is the angle subtended at the centre of a circle by an arc equal in length to the radius. A full turn is $2\pi$ radians, so

$$\pi \text{ rad} = 180^\circ, \qquad 1 \text{ rad} = \frac{180^\circ}{\pi} \approx 57.3^\circ$$

Convert by multiplying: degrees $\to$ radians, multiply by $\tfrac{\pi}{180}$; radians $\to$ degrees, multiply by $\tfrac{180}{\pi}$. Common values: $30^\circ = \tfrac{\pi}{6}$, $45^\circ = \tfrac{\pi}{4}$, $60^\circ = \tfrac{\pi}{3}$, $90^\circ = \tfrac{\pi}{2}$.