Answer
$-\sqrt3$
Work Step by Step
Convert the angle measure to degrees to obtain:
$=\frac{5\pi}{3} \cdot \frac{180^o}{\pi} = 5(60^o)=300^0$
Thus,
$\tan{(\frac{5\pi}{3})}
\\= \tan{300^o}$
300 degrees is in Quadrant IV so :
(i) its reference angle is $360^o-300^o=60^o$
(ii) its tangent is negative
From Section 2.1 (page 50) , we learned that:
$\tan{60^o} = \sqrt3$
This means that:
$\tan{300^o} = -\tan{60^o} = -\sqrt3$.
