# Reference Angle If the [[Coterminal|Coterminal Angle]] of $\theta$ is in: - Quadrant $\mathrm{I}$: - $0 \leq \theta \leq \frac{\pi}{2}$ - $Reference ~ Angle = \theta$ - $0\degree \leq ~\theta\degree \leq 90\degree$ - $Reference ~ Angle\degree = \theta\degree$ - Quadrant $\mathrm{II}$: - $\frac{\pi}{2} \leq \theta \leq \pi$ - $Reference ~ Angle = \pi - \theta$ - $90\degree \leq ~\theta\degree \leq 180\degree$ - $Reference ~ Angle\degree = 180\degree - \theta\degree$ - Quadrant $\mathrm{III}$: - $\pi \leq \theta \leq \frac{3\pi}{2}$ - $Reference ~ Angle = \theta - \pi$ - $180\degree \leq ~\theta\degree \leq 270\degree$ - $Reference ~ Angle = \theta\degree - 180\degree$ - Quadrant $\mathrm{IV}$: - $\frac{3\pi}{2} \leq \theta \leq 2\pi$ - $Reference ~ Angle = 2\pi - \theta$ - $270\degree \leq ~\theta\degree \leq 360\degree$ - $Reference ~ Angle = 360\degree - \theta\degree$