Question

Find the exact value of the expression. a) cos(arcsin(8/17)) b) sin^-1(tan(pi/4))

Answer 1

there is the picture of an angle whose sine is \(\frac{8}{17}\)
to find the cosine of that angle, you need the other side of the triangle
by pythagoras you get
\[a=\sqrt{17^2-8^2}=15\]

Answer 2

now you can see that \(\cos(\theta))=\cos(\sin^{-1}(\frac{8}{17}))=\frac{15}{17}\)