Answer
$\dfrac{\sqrt 3}{2}$
Work Step by Step
Let us consider:
$g(\theta)=\cos \theta$ and $\theta=60^{\circ}$
We wish to find:
$g(\dfrac{\theta}{2})$
When $\theta=60^{\circ}$, then $\dfrac{\theta}{2}=\dfrac{60^{\circ}}{2}=30^{\circ}$
We know from the unit circle that
$\cos (30^{\circ})=\cos (\dfrac{\pi}{6})=\dfrac{\sqrt 3}{2}$
Thus, we have: $g(\dfrac{\theta}{2})=\cos (30^{\circ}) \\=\cos (\dfrac{\pi}{6}) \\=\dfrac{\sqrt 3}{2}$
