Find cot θ if csc θ = square root of seventeen divided by four and tan θ > 0

We know that cosecant theta is hypotenus over opposite of a triangle. We are given that this value is equal to (√17) / 4 so 4 is the opposite side of theta. Cotangent theta is the adjacent over opposite. We use the pythagorean theorem to find for the adjacent side.

a = √17 - 4^2

a = 1

Therefore, cotangent of theta is equal to 1/4.