Question

find the reference angle for the angle $\frac{13\pi}{6}$.
the reference angle is
(type your answer in radians. type an integer or a simplified fraction.)

Explanation:

Step1: Reduce the angle by \(2\pi\)

To find the coterminal angle within \(0\) to \(2\pi\), we subtract \(2\pi\) (which is \(\frac{12\pi}{6}\)) from \(\frac{13\pi}{6}\).
\(\frac{13\pi}{6}-2\pi=\frac{13\pi}{6}-\frac{12\pi}{6}=\frac{\pi}{6}\)

Step2: Determine the reference angle

Since \(\frac{\pi}{6}\) is in the first quadrant, the reference angle is the angle itself.

Answer:

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