Finding the $\cot\left(\sin^{-1}\left(-\frac12\right)\right)$ How can I calculate this value?

$$\cot\left(\sin^{-1}\left(-\frac12\right)\right)$$
Draw a right triangle (in the x>0,y&lt;0 quadrant) with opposite edge -1 and hypotenuse 2.  Then the adjacent side is $\sqrt{2^2-1^2}=\sqrt{3}$.  cotangent is the ratio of adjacent side over opposite side.
Let arcsin(-1/2)=  x
Implies sinx=-1/2
Implies x= 120 degree
Now u need to find value of cot x
So  cot x= - underroot 3