csc(x)=3 and pi/2 less than (x) less than 3pi/2, find cot(x).

Answer 1

Then sin x = 1/3 and x is in quadrants II

I sketched a diagram, made my hypotenuse 3 and the opposite 1.
then the adjacent is √8, using Pythagoras

tan x = -1/√8
= -1/(2√2) or -√2/4 if rationalized.