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Value of cos^{-1}(\cos \frac{4\pi}{3}) is

Option: 1

\frac{4\pi}{3}


Option: 2

\frac{\pi}{3}


Option: 3

\frac{2\pi}{3}


Option: 4

None of these


Answers (1)

best_answer

As we have learnt

\cos ^{-1}(\cos (\theta))=\theta \quad \text { for all } \theta \in[0, \pi]

 

Now,

\\cos^{-1}(\cos \frac{4\pi}{3}) \text{ will not equal}\,\, \frac{4\pi}{3} \,\,as \,\,\frac{4\pi}{3} \text{ does not lie in} [0,\pi]\\\\ We\,\,can\,\,write\,\,it\,\,as\,\,cos^{-1}(\cos (2 \pi -\frac{2\pi}{3})) \\ =cos^{-1}(\cos \frac{2\pi}{3})\\ =\frac{2\pi}{3} \,\,(As\,\,\frac{2\pi}{3} \text{ does lies in} [0,\pi])

Posted by

Ritika Harsh

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