cot(θ) = cos(θ)/sin(θ)
So if both cot(θ) and cos(θ) are negative, that means sin(θ) must be positive.
Recall that
cot²(θ) + 1 = csc²(θ) = 1/sin²(θ)
so that
sin²(θ) = 1/(cot²(θ) + 1)
sin(θ) = 1 / √(cot²(θ) + 1)
Plug in cot(θ) = -2 and solve for sin(θ) :
sin(θ) = 1 / √((-2)² + 1)
sin(θ) = 1/√(5)
