Question

In which quadrant is θ located if cosθ is positive and cotθ is negative?

Answer 1

Cos θ  is positive, where x values are positive, so
cos θ  is positive in 1st and 4th quadrants.

cot θ  = cos θ / sin θ 
For cot θ be negative, sin θ  should be negative, because cos θ  is positive.
 sin θ  is negative, where y values is negative. (3d and 4t quadrants).

So, cos θ  is positive and cot θ  is negative in 4th quadrant.