Question

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

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

Answer 1

Answer: (A)

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