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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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