Answer
$-\sqrt 3$.
Work Step by Step
The reference angle of an angle $0 \leq \theta \lt 2\pi $ based on its position can be computed by using the following steps:
a) Quadrant- I: $\theta $
b) Quadrant -II: $(\pi-\theta)$
c) Quadrant- III: $(\theta - \pi)$
d) Quadrant - IV: $(2\pi - \theta)$
First, we make the angle positive:
$-210^{\circ}+360^{\circ}=150^{\circ}$
We are in quadrant 2, so the reference angle is:
$180^{\circ}-150^{\circ}=30^{\circ}$
Thus, we have $ \cot 30^{\circ}=-\sqrt 3$
The answer is negative because cotangent is negative in the second quadrant.
