# How do you find the exact value without a calculator for cot (arcsin(5/6))?

Sep 6, 2015

$\cot \left(\arcsin \left(\frac{5}{6}\right)\right) = \pm \frac{\sqrt{11}}{5}$

#### Explanation:

If $x = \arcsin \left(\frac{5}{6}\right)$
we have one of the 2 situations pictured below:

$\cot \left(\arcsin \left(\frac{5}{6}\right)\right) = \cot \left(x\right)$

$\textcolor{w h i t e}{\text{XXXXXX}} = \pm \frac{\sqrt{11}}{5}$ (based on definition of $\cot$)