Answer
$\frac{1}{2}$
Work Step by Step
$\frac{5\pi}{6}$ radians= $\frac{5\times180}{3}^{\circ}=300^{\circ}$
$300^{\circ}$ is in the fourth quadrant and cosine function is positive in the fourth quadrant.
As $\theta$ is in quadrant IV, the reference angle is
$\theta'=
360^{\circ}-\theta=360^{\circ}-300^{\circ}=60^{\circ}$
$\cos\frac{5\pi}{3}=\cos300^{\circ}=+\cos60^{\circ}=\frac{1}{2}$
