# How do you find the exact value of csc^-1 2?

##### 1 Answer
Jun 30, 2018

${\csc}^{- 1} 2 = {30}^{\circ}$

#### Explanation:

${\csc}^{- 1} 2$ represent the angle $\alpha$ whose cosecant ratio is $2$ i.e. $\csc \alpha = 2$

or $\sin \alpha = \frac{1}{\csc} \alpha = \frac{1}{2}$

As $\sin {30}^{\circ} = \frac{1}{2}$, $\alpha = {30}^{\circ}$

i.e. ${\csc}^{- 1} 2 = {30}^{\circ}$