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

Solution:

Given, cos θ is positive and cotθ is negative.

We have to find the quadrant in which θ is located.

We observe that cosθ is positive in I and IV quadrants.

We know, cotθ = cosθ/sinθ

Since cosθ is positive, sinθ must be negative.

We observe that sinθ is negative in III and IV quadrants.

Therefore, θ lies in the IV quadrant.

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

Summary:

θ is located in the IV quadrant if cosθ is positive and cotθ is negative.