Question

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

Answer 1

Solve for the required value.

Given inverse trigonometric function : ${\sin }^{-1}(-1)$

Let $x={\sin }^{-1}\left(-1\right)$

So, $\sin x=-1$

We know that, $\sin \left(-\frac{\mathrm{\pi }}{2}\right)=-1$

Therefore, $\sin x=\sin \left(-\frac{\mathrm{\pi }}{2}\right)$

$\Rightarrow x=-\frac{\mathrm{\pi }}{2}$

Hence, the exact value of${\sin }^{-1}(-1)$ is $-\frac{\mathrm{\pi }}{2}$.