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)
Since the point lies on the unit circle, its distance from the origin is 1. Therefore, the x-coordinate of the point is given by x = sqrt(1^2 - (2√2)^2) = sqrt(1 - 8) = sqrt(-7).
However, since θ is in the first quadrant and x is negative, the actual x-coordinate will be -sqrt(-7) = -i√7.
The cosine of θ is given by the x-coordinate, so cosθ = -√7.