Answer
$\dfrac{\sqrt3}{3}$
Work Step by Step
Convert the angle measure to degrees to obtain:
$=-\frac{2\pi}{3} \cdot \frac{180^o}{\pi} = -2(60^o)=-120^o$
Thus,
$\cot{(-\frac{2\pi}{3})} = \cot{(-120^o)}$
$-120^o$ is co-terminal with $-120^o+360^o=240^o$.
$240^o$ is in Quadrant III so its reference angle is $=240^o-180^o=60^o$.
Note that the cotangent function is positive in Quadrant III.
From Section 2.1 (page 50) , we learned that:
$\cot{60^o} = \dfrac{\sqrt3}{3}$
This means that:
$\cot{(-\frac{2\pi}{3})}
\\=\cot{(-120^o)}
\\=\cot{60^o}
\\= \dfrac{\sqrt3}{3}$
