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

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

Question

(C) We know that the range of the principal value branch of $\sin^{-1} x$ is $[-\frac{\pi}{2}, \frac{\pi}{2}]$.Given expression is $\sin^{-1} \left( \

Vedclass · Accepted Answer

$-\frac{\pi}{3}$

Vedclass · Answer

(C) We know that the range of the principal value branch of $\sin^{-1} x$ is $[-\frac{\pi}{2}, \frac{\pi}{2}]$.Given expression is $\sin^{-1} \left( \sin \frac{5\pi}{3} \right)$.First,simplify the argument: $\sin \frac{5\pi}{3} = \sin \left( 2\pi - \frac{\pi}{3} \right) = -\sin \frac{\pi}{3} = -\frac{\sqrt{3}}{2}$.Now,$\sin^{-1} \left( -\frac{\sqrt{3}}{2} \right) = -\sin^{-1} \left( \frac{\sqrt{3}}{2} \right) = -\frac{\pi}{3}$.Since $-\frac{\pi}{3} \in [-\frac{\pi}{2}, \frac{\pi}{2}]$,the principal value is $-\frac{\pi}{3}$.

The principal value of $\sin^{-1} \left( \sin \frac{5\pi}{3} \right)$ is

Similar Questions

If $4 \sin ^{-1} x + 6 \cos ^{-1} x = 3 \pi$,where $-1 \leq x \leq 1$,then $x =$

$\sin^{-1}(\sin \frac{7\pi}{6}) = $

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

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

$2 \tanh^{-1} \frac{1}{2}$ is equal to

Vedclass Test Series

Exam Paper Generator

Online Exam Module