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Fill in the blanks The principle value of \cos ^{-1}\left ( -\frac{1}{2} \right ) is ___________.

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The principal value of \cos^{-1}\left ( -\frac{1}{2} \right ) is \frac{2\pi}{3}.

Principal value cos-1 x is [0,\pi]

Let, \cos^{-1}\left ( -1 \right )=\theta

\Rightarrow \cos \theta=-\frac{1}{2}

As, \cos \frac{2\pi}{3} =-\frac{1}{2}

So, \theta= \frac{2\pi}{3}

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