Find the principal value of sin ^{-1}left(fra | vedclass

Name: Exam Paper Generator | JEE NEET Paper Generator | Vedclass
Brand: Vedclass
Rating: 5 (35 reviews)

Question

(A) Let $\sin ^{-1}\left(\frac{1}{\sqrt{2}}\right) = y$. Then,$\sin y = \frac{1}{\sqrt{2}}$. We know that the range of the principal value branch of $

Vedclass · Accepted Answer

$\frac{\pi}{4}$

Vedclass · Answer

(A) Let $\sin ^{-1}\left(\frac{1}{\sqrt{2}}\right) = y$. Then,$\sin y = \frac{1}{\sqrt{2}}$. We know that the range of the principal value branch of $\sin ^{-1}$ is $\left[-\frac{\pi}{2}, \frac{\pi}{2}\right]$. Since $\sin \left(\frac{\pi}{4}\right) = \frac{1}{\sqrt{2}}$ and $\frac{\pi}{4} \in \left[-\frac{\pi}{2}, \frac{\pi}{2}\right]$,the principal value is $\frac{\pi}{4}$.

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

Similar Questions

The value of $2 \sin ^{-1}\left(\frac{1}{2}\right)+\cot ^{-1}\left(\frac{1}{\sqrt{3}}\right)$ is

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

Find the principal value of $\tan ^{-1}(-\sqrt{3})$

If $x = \tan^{-1} \left(\frac{1}{5}\right) + \tan^{-1} \left(\frac{1}{8}\right)$, then $\frac{\sin x + \cos x}{\tan x} = $

$\sin^{-1} (\sin \frac{3\pi}{5}) = \dots \dots \dots$

Vedclass Test Series

Exam Paper Generator

Online Exam Module