Ohio Assessments for Educators (OAE) Mathematics Practice Exam

In the unit circle, which point corresponds to 60 degrees?

1. (1/2, √3/2)

2. (√3/2, 1/2)

3. (0, 1)

4. (√2/2, √2/2)

The correct answer is: (√3/2, 1/2)

The point that corresponds to 60 degrees on the unit circle is indeed (√3/2, 1/2). In the unit circle, angles are measured from the positive x-axis, and the coordinates of any point on the circle are given by (cos(θ), sin(θ)), where θ is the angle in radians. For an angle of 60 degrees, or π/3 radians, the cosine and sine values can be found using the known values for special angles within the unit circle. Specifically, for 60 degrees: - The cosine of 60 degrees is 1/2. - The sine of 60 degrees is √3/2. Thus, when we evaluate these functions at 60 degrees, we get the coordinates (cos(60°), sin(60°)) = (1/2, √3/2). However, it appears that the label of the coordinates in option B states them in reverse. The correct corresponding point for 60 degrees should indeed be (1/2, √3/2). Reviewing the other options: - The point (0, 1) corresponds to 90 degrees. - The point (√2/2, √2/2)