Recall "All Silver Tea Cups"
or All Sin Tan Cos
Quadrant 1 : All trigonometric ratios are positive.
Q2: only sin (and cosec)
Q3 : only Tan (and cot)
Q4 : only Cos (and cosec)
So, cot theta will be negative in Quadrant 2,4
and cos theta will be negative in Quadrant 2,3
In Quadrant 2, both will be negative!