Find the principal value of cos ^{-1}left(-fr | vedclass

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(C) Let $\cos ^{-1}\left(-\frac{1}{2}\right) = y$.Then,$\cos y = -\frac{1}{2}$.Since $\cos \left(\frac{\pi}{3}\right) = \frac{1}{2}$,we have $\cos y =

Vedclass · Accepted Answer

$\frac{2 \pi}{3}$

Vedclass · Answer

(C) Let $\cos ^{-1}\left(-\frac{1}{2}ight) = y$.Then,$\cos y = -\frac{1}{2}$.Since $\cos \left(\frac{\pi}{3}ight) = \frac{1}{2}$,we have $\cos y = -\cos \left(\frac{\pi}{3}ight)$.Using the identity $\cos(\pi - 	heta) = -\cos 	heta$,we get $\cos y = \cos \left(\pi - \frac{\pi}{3}ight) = \cos \left(\frac{2 \pi}{3}ight)$.The range of the principal value branch of $\cos ^{-1}$ is $[0, \pi]$.Since $\frac{2 \pi}{3} \in [0, \pi]$,the principal value of $\cos ^{-1}\left(-\frac{1}{2}ight)$ is $\frac{2 \pi}{3}$.

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

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