Answer
$\dfrac{1}{2}$
Work Step by Step
Let us consider:
$f(\theta)=\sin \theta$ and $\theta=60^{\circ}$
We wish to find:
$f(\dfrac{\theta}{2})$
When $\theta=60^{\circ}$, then $\dfrac{\theta}{2}=\dfrac{60^{\circ}}{2}=30^{\circ}$
We know from the unit circle that
$\sin (30^{\circ})=\sin (\dfrac{\pi}{6})=\dfrac{1}{2}$
Thus, we have: $f(\dfrac{\theta}{2})=\sin (30^{\circ})
\\=\sin (\dfrac{\pi}{6}) \\ =\dfrac{1}{2}$