tanx = sinx/cosx ===> sinx = -sqrt(15)*cosx
cosx^2 + sinx^2 = 1
cosx^2 + (-sqrt(15)*cosx)^2 = 1
cosx^2 + 15*cosx^2 = 1
16*cosx^2 = 1
cosx^2 = 1/16
cosx = sqrt(1/16) = 1/4
From this, you obtain sinx by "sinx^2 = 1 - cosx^2"
Edit:
As 90 < x < 180, cosx should be negative, so cosx = -1/4, not 1/4...