Answer
$\dfrac{1}{2}$
Work Step by Step
Let us consider:
$g(\theta)=\cos \theta$
We are given that $\theta=60^{\circ}$
We know form the unit circle that $\cos (60^{\circ})=\cos (\dfrac{\pi}{3})=\dfrac{1}{2}$
Thus, we have: $g(\theta)=cos(60^{\circ})
\\=cos\dfrac{\pi}{3} \\ =\dfrac{1}{2}$