Find the principal values of the following:

    5. \cos^{-1}\left(-\frac{1}{2} \right )

Answers (1)

Let us assume that  \cos^{-1}\left(-\frac{1}{2} \right ) =y then,

Easily we have; \cos y = \left ( \frac{-1}{2} \right ) or we can write it as: 

-\cos \left ( \frac{\pi}{3} \right ) = \cos \left ( \pi - \frac{\pi}{3} \right ) = \cos \left ( \frac{2\pi}{3} \right ).

as we know that the range of the principal values of \cos^{-1}  is \left [ 0,\pi \right ].

Hence \frac{2\pi}{3} lies in the range it is a principal solution.

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