Verified answer

sin(θ) = (√5)/4

sin^2(θ) + cos^2(θ) = 1

[(√5)/4]^2 + cos^2(θ) = 1

cos^2(θ) = 1 - 5/16

cos(θ) = ±√(11/16)

cos(θ) = ±(√11)/4

cosΘ = ±√[1 – sin²Θ]

cosΘ = ±√[1 – 5/16] = ±√(11)/4

The sign depends on which quadrant Θ is in.