Answer
$\dfrac{\sqrt 3}{4}$
Work Step by Step
Recall the identity: $(f \cdot g) (x)=f(x) \cdot g(x)$
Let us consider that $f(x)=\sin x $ and $g(x)=\cos x$
We know from the unit circle that $\sin (\dfrac{4 \pi}{3}) =\dfrac{-\sqrt {3}}{2}$ and $\cos (\dfrac{4 \pi}{3})=\dfrac{-1}{2}$
Thus, we have: $(f \cdot g) (\dfrac{4 \pi}{3}) =\sin (\dfrac{4 \pi}{3}) \cdot \cos (\dfrac{4\pi}{3}) \\=\dfrac{-\sqrt {3}}{2} \cdot (\dfrac{-1}{2}) \\=\dfrac{\sqrt 3}{4}$
