Question

How do you find the exact value of ${\sin }^{-1}0$?

Answer 1

Find the value.

Given trigonometric function :${\sin }^{-1}0$

Since the domain and range of the sine function is defined as
Domain: $[-1,1]$ and Range: $\left[-{\displaystyle \frac{\pi }{2}},{\displaystyle \frac{\pi }{2}}\right]$

${\sin }^{-1}0={\sin }^{-1}(\sin n\mathrm{\pi })\left[\because \sin n\mathrm{\pi }=0\right]$, where $n$is an integer.

$=n\mathrm{\pi }$

Therefore, ${\sin }^{-1}0=n\mathrm{\pi }$ , where $n$is an integer.

Hence, the exact value of ${\sin }^{-1}0$ is $n\mathrm{\pi }$, , where $n$is an integer.