Answer
$\dfrac{1}{2}$
Work Step by Step
$\dfrac{5\pi}{3}$ is an angle in Quadrant IV.
The reference angle of an angle in Quadrant IV can be found using the formula $2\pi-\theta$.
Thus, the reference angle of $\dfrac{5\pi}{3}$ is:
$2\pi - \dfrac{5\pi}{3}=\dfrac{6\pi}{3}- \dfrac{5\pi}{3} = \dfrac{\pi}{3}$
$\dfrac{\pi}{3}$ is a special angle whose cosine value is $\dfrac{1}{2}$. $\dfrac{5\pi}{3}$ is in Quadrant IV where cosine is positive.
Thus,
$\cos{(\frac{5\pi}{3})}=\frac{1}{2}$
