Question

The principal value of ${\sin }^{-1}(-1)$ is

• A. $\frac{\pi }{2}$
• B. $\frac{3\pi }{2}$
• C. $-\frac{\pi }{2}$
• D. $\frac{5\pi }{2}$

Answer 1

The correct option is C $-\frac{\pi }{2}$

Let ${\sin }^{-1}(-1)=x$
$\Rightarrow \sin x=-1$
$\Rightarrow \sin x=\sin (-\frac{\pi }{2})$
We know that range of principal value branch of ${\sin }^{-1}$ is $[-\frac{\pi }{2},\frac{\pi }{2}]$ and $\sin (-\frac{\pi }{2})=-1$
$\therefore$ Principal value of ${\sin }^{-1}(-1)$ is $-\frac{\pi }{2}.$