if cos θ = -1/6 and sin θ = y/r and θ is in quadrant III, find y

Answer 1

cos(theta)^2 + sin(theta)^2 = 1

1/36 + sin(theta)^2 = 1

sin(theta)^2 = 35/36

sin(theta) = -sqrt(35)/6 because in 3rd quadrant

y = sqrt(35)

Answer 2

r = 6 = hypotenuse

opposite side^2 = 6^2 -1^2 = 35

opposite side = sqr35

sin(theta) = opposite side/hypotenuse = sqr35/6 = y/r. y = sqr35