Question

EVALUATE cos(sin^-1(-5/13)) . answer using slash bar or fraction sign.

Answer 1

EVALUATE cos(sin^-1(-5/13)) =12 / 13
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Answer 2

Answer:

Step-by-step explanation:

$cos(sin^{-1}(-5/13))$

lets say

$sin^{-1}(-5/13) =\alpha$

so it means

$sin\alpha =\frac{-5}{13}$

and we need $cos\alpha = ?$

Now use he pythagorean

$cos^2\alpha +sin^2\alpha =1$

$cos^2\alpha +(\frac{-5}{13})^2  =1$

$cos^2\alpha=1-\frac{25}{169}$

$cos^2\alpha =\frac{144}{169}$

Take sqrt on both sides we get

$cos\alpha =12/13$

Hence

$cos(sin^{-1}(-5/13)) = \frac{12}{13}$