Question

The principal value of ${\sin }^{-1}(-\frac{\sqrt{3}}{2})$ is

• A. $\frac{\pi }{3}$
• B. $-\frac{\pi }{3}$
• C. $\frac{\pi }{6}$
• D. $-\frac{\pi }{6}$

Answer 1

The correct option is B $-\frac{\pi }{3}$

Let the principal value be $y$
$y={\sin }^{-1}(-\frac{\sqrt{3}}{2}),y\in [-\frac{\pi }{2},\frac{\pi }{2}]\Rightarrow \sin y=-\frac{\sqrt{3}}{2}\Rightarrow \sin y=\sin (-\frac{\pi }{3})\Rightarrow y=-\frac{\pi }{3}$