The principal value of \(cos^{-1}\left(\frac{-1}{2}\right)\)isA. \(\f

1.	The principal value of \(cos^{-1}\left(\frac{-1}{2}\right)\)isA. \(\frac{-\pi}{3}\)B. \(\frac{2\pi}{3}\) C. \(\frac{4\pi}{3}\) D. \(\frac{\pi}{3}\)
Answer» Correct Answer is \(\frac{2\pi}{3}\) Let the principle value be given by x Now, let x = \(cos^{-1}\left(\frac{-1}{2}\right)\) ⇒ cos x = \(\frac{-1}{2}\) ⇒ cos x= - cos( \(\frac{\pi}{3}\)) ( \(\because cos\)(\(\frac{\pi}{3}\))= \(\frac{1}{2}\)) ⇒ cos x=cos( \(\pi-\frac{\pi}{3}\)) ( \(\because -cos(\theta)=cos(\pi-\theta\))) ⇒ x =\(\frac{2\pi}{3}\)

The principal value of \(cos^{-1}\left(\frac{-1}{2}\right)\)isA. \(\frac{-\pi}{3}\)B. \(\frac{2\pi}{3}\) C. \(\frac{4\pi}{3}\) D. \(\frac{\pi}{3}\)

Answer»

Correct Answer is \(\frac{2\pi}{3}\)

Let the principle value be given by x

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

⇒ cos x = \(\frac{-1}{2}\)

⇒ cos x= - cos( \(\frac{\pi}{3}\)) ( \(\because cos\)(\(\frac{\pi}{3}\))= \(\frac{1}{2}\))

⇒ cos x=cos( \(\pi-\frac{\pi}{3}\)) ( \(\because -cos(\theta)=cos(\pi-\theta\)))

⇒ x =\(\frac{2\pi}{3}\)