Answer: cot θ ≈ -3.4470190
Step-by-step explanation:
We are given csc θ = 3.5891420
That means sin theta = 1/(csc theta) = 0.278618121
Using the arcsin function on a calculator, we get θ = 0.282354953 radians.
But the terminal side of central angle theta lies in Quadrant II, so 0.282354953 radians is really θ', the reference angle in Quadrant II.
That means that actually θ= (π - 0.282354953) = 2.8592377
tan θ = -0.290105737
cot θ = 1/tan θ ≈ -3.4470190
cot θ ≈ -3.4470190
I hope this was helpful.