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: $180^{\circ}-\theta $
c) Quadrant -III: $\theta - 180^o $
d) Quadrant -IV: $360^{\circ}-\theta $
Reference angle is equal to
$ =\dfrac{19 \pi}{6}-3 \pi=\dfrac{\pi}{6}$
Since, $\cot (\dfrac{\pi}{6})=\sqrt 3$
So, $\cot \dfrac{19\pi}{6}=\sqrt 3$; Because $\theta $ lies in Quadrant-III.
