# How do you find the exact value of csc((17pi)/6)?

Jan 23, 2018

2

#### Explanation:

First find the angle coterminal to $\frac{17 \pi}{6}$ that falls between $0$ and $2 \pi$: $\frac{17 \pi}{6} - 2 \pi = \frac{5 \pi}{6}$. So we know that $\csc \left(\frac{17 \pi}{6}\right) = \csc \left(\frac{5 \pi}{6}\right)$.

$\csc \left(x\right) = \frac{1}{\sin} \left(x\right)$ and we know that $\sin \left(\frac{5 \pi}{6}\right) = \frac{1}{2}$ because it's from the Unit Circle.

So:

$\csc \left(\frac{17 \pi}{6}\right) = \csc \left(\frac{5 \pi}{6}\right) = \frac{1}{\sin} \left(\frac{5 \pi}{6}\right) = \frac{1}{\frac{1}{2}} = 2$.