Question

The range of $f\left(x\right)={\sin }^{2}x-3\sin x+2$ is [$0$,a] Find a

Answer 1

$f\left(x\right)={\sin }^{2}x-3\sin x+2$
$={(\sin x-3/2)}^2+2-9/4$
$={(\sin x-3/2)}^2-1/4$
Now $-1\le \sin x\le 1$
or $-5/2\le \sin x-3/2\le -1/2$
or $1/4\le {(\sin x-3/2)}^2\le 25/4$
or $0\le {(\sin x-3/2)}^2-1/4\le 6$
Therefore, $a=6$
Ans: 6