Example

$\theta$	${16\sin \theta ( \cos \theta +1)}$	$A(\theta )$
$0$	$16\sin 0\left( \cos 0+1\right) =0$	$0$
$\dfrac{\pi }{3}$	$\begin{eqnarray} 16&\sin \dfrac{\pi }{3}\left( \cos \dfrac{\pi }{3} +1\right) \\ &= 16\left(\dfrac{\sqrt{3}}{2}\right) \left(\dfrac{1}{2}+1\right) \\ &= 16\left( \dfrac{3\sqrt{3}}{4}\right) =12\sqrt{3} \end{eqnarray}$	$\approx\!20.8$	$\longleftarrow$ absolute maximum value
$\dfrac{\pi }{2}$	$\begin{eqnarray} 16&\sin \dfrac{\pi }{2}\left(\cos \dfrac{\pi }{2}+1\right) \\ &=16( 1) (0+1) =16 \end{eqnarray}$	$16$