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  • Fill in the blanks The value of cos inverse in to bracket cos 12\pi divided 3 is

The value of \cos^{-1}\left ( \cos \frac{14\pi}{3} \right )

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The value of \cos^{-1}\left ( \cos \frac{14\pi}{3} \right ) is \frac{2\pi}{3}

We needd, \cos^{-1}\left ( \cos \frac{14\pi}{3} \right )

Principal value of cos-1 x is [0,π]

Also, cos (2nπ + θ) = cos θ for all n ? N

\cos \frac{14\pi}{3}=\cos \left ( 4\pi+\frac{2\pi}{3} \right )

\Rightarrow \cos \frac{14\pi}{3}=\cos \frac{2\pi}{3}

So, \cos^{-1} \left (\cos \frac{14\pi}{3} \right )=\cos^{-1}\left (\cos \frac{2\pi}{3} \right )

\Rightarrow \cos^{-1} \left (\cos \frac{14\pi}{3} \right )=\frac{2\pi}{3}

 

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