Question

find cos(sin^-1 5/7)

Answer 1

\(\bf cos\left[sin^{-1}\left(\frac{5}{7}\right)\right]\\ \quad \\ \quad \\
sin^{-1}\left(\cfrac{5}{7}\right)\implies \cfrac{opposite}{hypotenuse}\implies \cfrac{b}{c}\)

Answer 2

use pythagorean theorem to get the missing side
once you have that, the "adjacent side" that is, use it to find cosine, recall that http://www.mathwarehouse.com/trigonometry/images/sohcohtoa/sohcahtoa-all.png