Question

Find sin θ if cot θ = - 4 and cos θ < 0

Answer 1

cos theta is negative in the 2nd and 3rd quadrants but cot theta is negative in the 2nd quadrant so our angle is in the 2nd.

Answer 2

It has to be in quadrant 2 because that is the only quadrant where tan/cot are negative and cos/sec are negative

Answer 3

now cot θ = 1/tanθ

and tanθ = opposite/adjacent