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

Given was cotθ = - 21 and cot is the reciprocal of tan

therefore

tanθ = 1 - 2

solve for the hypotenuse c since t he opposite side a=1 and the adjacent sides b=-2 were already given. that is,

c2 = a2 + b2

c = √ (1) 2 + (-2) 2

c = √5

Solving for sinθ

sinθ = oppositesides hypoteνse = ab

sinθ = 1 √5 need to rationalize

sinθ = (1 √5) * √5 √5

sinθ = √5 5

Note that the adjacent side of the angle is - 2 so the angle

θ is found in the 2nd quadrant.