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