How do you find the exact value of $cos(arcsin(5/13))$ ?

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Answer 1 · 2016-12-26T11:04:24

The answer is $=12/13$

We need

$cos^2theta+sin^2theta=1$

Let $y=arcsin(5/13)$

So,

$siny=5/13$

$cos^2y=1-sin^2y=1-25/169=144/169$

$cosy=12/13$

Therefore,

$cos(arcsin(5/13))=12/13$

How do you find the exact value of cos(arcsin(5/13))cos(arcsin(5/13))?