Find the principal values of the following:

    2. \cos^{-1}\left(\frac{\sqrt3}{2} \right )

Answers (1)

So, let us assume that \cos^{-1}\left(\frac{\sqrt3}{2} \right ) = x  then,

Taking inverse both sides we get;

cos\ x = (\frac{\sqrt{3}}{2}),  or   cos (\frac{\pi}{6}) = (\frac{\sqrt{3}}{2})         

and as we know that the principal values of cos^{-1} is from [0,\pi],

Hence cos\ x = (\frac{\sqrt{3}}{2})     when x = \frac{\pi}{6} . 

Therefore, the principal value for \cos^{-1}\left(\frac{\sqrt3}{2} \right )is   \frac{\pi}{6}.

 

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