Question

find the reference angle for $-\frac{19pi}{6}$.

Explanation:

Step1: Make the angle positive

Add \(2\pi\) multiple - times until the angle is positive.
\(-\frac{19\pi}{6}+4\pi=-\frac{19\pi}{6}+\frac{24\pi}{6}=\frac{5\pi}{6}\)

Step2: Determine the quadrant and find the reference angle

The angle \(\frac{5\pi}{6}\) is in the second - quadrant. For an angle \(\theta\) in the second - quadrant, the reference angle \(\theta_{r}=\pi-\theta\).
\(\theta_{r}=\pi - \frac{5\pi}{6}=\frac{\pi}{6}\)

Answer:

\(\frac{\pi}{6}\)