Question

the measure of an angle in standard position is given. find two positive angles and two negative angles that are coterminal with the given angle. (enter your answers as a comma - separated list.)
$\frac{7pi}{6}$
rad

Explanation:

Step1: Recall coterminal - angle formula

Coterminal angles of an angle $\theta$ are given by $\theta + 2k\pi$, where $k\in\mathbb{Z}$.

Step2: Find positive coterminal angles

For $k = 1$:
$\frac{7\pi}{6}+2\pi=\frac{7\pi + 12\pi}{6}=\frac{19\pi}{6}$
For $k = 2$:
$\frac{7\pi}{6}+4\pi=\frac{7\pi+24\pi}{6}=\frac{31\pi}{6}$

Step3: Find negative coterminal angles

For $k=-1$:
$\frac{7\pi}{6}-2\pi=\frac{7\pi - 12\pi}{6}=-\frac{5\pi}{6}$
For $k = - 2$:
$\frac{7\pi}{6}-4\pi=\frac{7\pi-24\pi}{6}=-\frac{17\pi}{6}$

Answer:

$\frac{19\pi}{6},\frac{31\pi}{6},-\frac{5\pi}{6},-\frac{17\pi}{6}$