Trigonometry

For \(0^\circ\le x<360^\circ\), let
\[\mathrm{F}(x)=(3\sin x+4\cos x)^2-6(3\sin x+4\cos x)+11.\]

1. Find the exact minimum and maximum values of \(\mathrm{F}(x)\).

2. Find all values of \(x\) at which each occurs.