# What is the reference angle in degrees for (31pi)/6 ?

Mar 18, 2018

$\frac{7 \pi}{6}$

#### Explanation:

A circle is comprised of ${360}^{o}$. In order to find the reference angle, we need to reduce the current angle to an angle that is between ${0}^{o}$ and ${360}^{o}$.

We start with $\frac{31 \setminus \pi}{6}$.

We know that ${0}^{o} = \frac{0 \pi}{6}$ and ${360}^{o} = 2 \pi = \frac{12 \pi}{6}$

Since ${360}^{o} = 2 \pi$ radians, we will subtract of $2 \pi = \frac{12 \pi}{6}$ each iteration:

Iteration 1:
$\frac{31 \pi}{6} - \frac{12 \pi}{6} = \frac{19 \pi}{6}$

Iteration 2:
$\frac{19 \pi}{6} - \frac{12 \pi}{6} = \frac{7 \pi}{6}$

Since $0 \setminus \le q \frac{7 \pi}{6} \setminus \le q \frac{12 \pi}{6}$, we can stop as we have found the reference angle.

The reference angle is $\textcolor{g r e e n}{\frac{7 \pi}{6}}$.