# How do you evaluate cot (arcsin(5/6))?

Sep 4, 2015

$\frac{\sqrt{11}}{5}$

#### Explanation:

Let arc $\sin \left(\frac{5}{6}\right) = \theta$

$\sin \theta = \frac{5}{6}$, that means $\csc \theta = \frac{6}{5}$

${\cot}^{2} \theta = {\csc}^{2} \theta - 1 = \frac{11}{25}$

$\cot \theta = \frac{\sqrt{11}}{5}$, that means $\theta = a r c \cot \left(\frac{\sqrt{11}}{5}\right)$

Hence $\cot a r c \sin \left(\frac{5}{6}\right) = \cot a r c \cot \left(\frac{\sqrt{11}}{5}\right) = \frac{\sqrt{11}}{5}$