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.

Answer 1

In the first quadrant, the x-coordinate of the point where the terminal side intersects the unit circle is positive and the y-coordinate is positive.

Given that the y-coordinate is √2/2, we can find the x-coordinate using the Pythagorean theorem:

x^2 + (√2/2)^2 = 1
x^2 + 1/2 = 1
x^2 = 1 - 1/2
x^2 = 1/2
x = ±√(1/2)

Since x is positive in the first quadrant, x = √(1/2) = √2/2.

Therefore, the coordinates of the point where the terminal side intersects the unit circle are ( √2/2, √2/2).

Since cosine is the x-coordinate of the point on the unit circle, cosθ = √2/2.