# How do you find the values of theta given csctheta=2?

Jun 23, 2018

$\frac{\pi}{6} + 2 k \pi$
$\frac{5 \pi}{6} + 2 k \pi$

#### Explanation:

$\csc t = \frac{1}{\sin t} = 2$
$\sin t = \frac{1}{2}$
Trig table and unit circle give 2 solutions for t:
$t = \frac{\pi}{6} + 2 k \pi$ and
$t = \pi - \frac{\pi}{6} = \frac{5 \pi}{6} + 2 k \pi$