4.1 Radians and Degrees

Notes

A radian measures an angle by arc length on a unit circle. A full turn is $2\pi$ radians, so $180^\circ = \pi$ radians.

• Degrees to radians: multiply by $\displaystyle \frac{\pi}{180}$. Radians to degrees: multiply by $\displaystyle \frac{180}{\pi}$.
• Common angles: $\displaystyle 30^\circ = \frac{\pi}{6}$, $\displaystyle 45^\circ = \frac{\pi}{4}$, $\displaystyle 60^\circ = \frac{\pi}{3}$, $\displaystyle 90^\circ = \frac{\pi}{2}$.
• Arc length $s = r\theta$ (with $\theta$ in radians).
• Example: $\displaystyle 135^\circ = 135 \cdot \frac{\pi}{180} = \frac{3\pi}{4}$.