If cot θ = 12/5, then tan θ = 5/12.
If sec θ = -13/5, then cos θ = -5/13
For tan θ to be positive while cos θ is negative, the quadrant is 3.
The figure below shows θ graphed as a reference angle in quadrant 3.
Answer:
The statement that θ is in quadrant 4 is FALSE.
