Question

Find the principal value $si{n}^{-1}\left(\frac{1}{\sqrt{2}}\right)$

• A. $\frac{\pi }{4}$
• B. $\frac{\pi }{3}$
• C. $\frac{\pi }{6}$
• D. $\frac{\pi }{2}$

Answer 1

Answer: (A)

Let $si{n}^{-1}\left(\frac{1}{\sqrt{2}}\right)=\theta$
$\Rightarrow sin\theta =\frac{1}{\sqrt{2}}$
$=sin\frac{\pi }{4}$
$\Rightarrow \theta =\frac{\pi }{4}\in \left[\frac{-\pi }{2},\frac{\pi }{2}\right]$
$\therefore$ Principal value of $si{n}^{-1}\left(\frac{1}{\sqrt{2}}\right)$ is $\frac{\pi }{4}$