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Evaluate \cos^{-1}(\sin \frac{33\pi}{5}) 

Option: 1

\frac{\pi}{5}


Option: 2

\frac{3\pi}{10}


Option: 3

\frac{\pi}{10}


Option: 4

None of these


Answers (1)

best_answer

Let us first reduce the angle and convert sin term to cos

\\\cos^{-1}(\sin \frac{33\pi}{5})\\ = \cos^{-1}(\sin (6\pi+\frac{3\pi}{5}))\\ =\cos^{-1}(\sin \frac{3\pi}{5})\\ = \cos^{-1}(\cos(\frac{\pi}{2}- \frac{3\pi}{5})\\ =\cos^{-1}(\cos(- \frac{\pi}{10}))

Now, looking at the graph, as -\pi<-\frac{\pi}{10}< 0, and in this interval

cos-1(cos(x)) = -x

So, \cos^{-1}(\cos(- \frac{\pi}{10})) = \frac{\pi}{10}

Posted by

Pankaj Sanodiya

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