The principal value of is \(sin^{-1}\left(\frac{-1}{2}\right)\)A. \(

1.	The principal value of is \(sin^{-1}\left(\frac{-1}{2}\right)\)A. \(-\frac{\pi}{6}\)B. \(\frac{5\pi}{6}\)C. \(\frac{7\pi}{6}\)D. none of these
Answer» Correct Answer is \(-\frac{\pi}{4}\) Let the principle value be given by x Now, let x = \(sin^{-1}\left(\frac{-1}{2}\right)\) ⇒sin x = \(\frac{-1}{2}\) ⇒sin x= - sin( \(\frac{\pi}{6}\)) ( \(\because sin\left(\frac{\pi}{6}\right)\))= \(\frac{1}{2}\)) ⇒sin x=sin( \(\frac{\pi}{6}\)) ( \(\because -sin(\theta)=sin(-\theta\))) ⇒x =\(-\frac{\pi}{4}\)

The principal value of is \(sin^{-1}\left(\frac{-1}{2}\right)\)A. \(-\frac{\pi}{6}\)B. \(\frac{5\pi}{6}\)C. \(\frac{7\pi}{6}\)D. none of these

Answer»

Correct Answer is \(-\frac{\pi}{4}\)

Let the principle value be given by x

Now, let x = \(sin^{-1}\left(\frac{-1}{2}\right)\)

⇒sin x = \(\frac{-1}{2}\)

⇒sin x= - sin( \(\frac{\pi}{6}\)) ( \(\because sin\left(\frac{\pi}{6}\right)\))= \(\frac{1}{2}\))

⇒sin x=sin( \(\frac{\pi}{6}\)) ( \(\because -sin(\theta)=sin(-\theta\)))

⇒x =\(-\frac{\pi}{4}\)