You can put this solution on YOUR website! As the angle is 11pi/6, then its reference angle is 2pi-11pi/6= pi/6
Further, as the reference angle lies in IV quadrant, hence
cot(11pi/6)= -cot(pi/6) = -cos(pi/6)/sin(pi/6)
-((sqrt3)/2)/(1/2)
-(sqrt3/2)*(2/1)
-(sqrt3)