#### Answer

$F(\frac{\pi}{2})=\frac{1}{2}$
This means that half of the moon's face illuminated by the sun.

#### Work Step by Step

$F(t)=\frac{1}{2}(1-\cos t)$
For $F(\frac{\pi}{2})$, the phase angle $t=\frac{\pi}{2}$. Substituting $t=\frac{\pi}{2}$ in the equation,
$F(\frac{\pi}{2})=\frac{1}{2}(1-\cos \frac{\pi}{2})$
$F(\frac{\pi}{2})=\frac{1}{2}(1-0)$
$F(\frac{\pi}{2})=\frac{1}{2}(1)$
$F(\frac{\pi}{2})=\frac{1}{2}$
This means that half of the moon's face illuminated by the sun.