Question

Question
Find cosθ
if the y-coordinate of the point where the terminal side of θ
intersects the unit circle is 2√2
, given that θ
is an acute angle and in the first quadrant.(1 point)

Answer 1

That value is impossible as written: points on the unit circle have y between −1 and 1, but 2√2 ≈ 2.828 > 1. Please check the problem.

If you meant y = 2√2/4 = √2/2 (a common value), then since y = sin θ and θ is acute (first quadrant) we have
cos θ = √(1 − sin^2 θ) = √(1 − (√2/2)^2) = √(1 − 1/2) = √(1/2) = √2/2.