# What is  tan(arcsin( 5/6))?

Jul 23, 2015

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

#### Explanation:

If $x = \arcsin \left(\frac{5}{6}\right)$
$\textcolor{w h i t e}{\text{XXXX}}$then $\sin \left(x\right) = \frac{5}{6}$
and $x$ is one of the 2 possible angles indicated below
(arcsin is restricted to $\left[0 , \pi\right]$):

The third side ($\pm \sqrt{11}$) can be derived using the Pythagorean theorem.

From the diagram:
$\textcolor{w h i t e}{\text{XXXX}}$$\tan \left(x\right) = \pm \frac{5}{\sqrt{11}}$