Question

Find sin θ if cot θ = -2 and cos θ < 0

Answer 1

??

Answer 2

cos(t) / sin(t) = -2
cos(t) = -2sin(t)

using sin(t) = sqrt(1-cos^2(t)) we get

cos(t) = -2sqrt(1-cos^2(t))
square both sides :

cos^2(t) = 4(1-cos^2(t))
5cos^2(t) = 4
cos(t) = +\- sqrt(4/5)

you know that cos(t) < 0
so cos(t) = - sqrt(4/5)

Answer 3

okay. so