5.1 Radians and Degrees

Notes

A radian measures an angle by arc length on the unit circle: one 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: $\displaystyle 30^\circ = \frac{\pi}{6}$, $\displaystyle 45^\circ = \frac{\pi}{4}$, $\displaystyle 60^\circ = \frac{\pi}{3}$, $\displaystyle 90^\circ = \frac{\pi}{2}$.
• Example: $\displaystyle \frac{5\pi}{6} \cdot \frac{180}{\pi} = 150^\circ$.
• Coterminal angles differ by a full turn ($360^\circ$ or $2\pi$) and end at the same place.