Chapter 6.2, Problem 73AYU

In Problems 67-78, $f\left(x\right)=\sin x$, $-\frac{\pi }{2}\le x\le \frac{\pi }{2}$, $g\left(x\right)=\cos x$, $0\le x\le \pi$, and $h\left(x\right)=\tan x$, $-\frac{\pi }{2}<x<\frac{\pi }{2}$. Find the exact value of each composite function.

$g\left(h^{-1}\left(\frac{12}{5}\right)\right)$