Final answer:
The correct answer is option b. (0, π/2) U (3π/2, 2π), which represents the first and fourth quadrants on the unit circle where cosine values are indeed positive.
Step-by-step explanation:
This question addresses the intervals where cosine is positive on the unit circle between 0 and 2π radians. In the context of the unit circle, the cosine function represents the x-coordinate of a point on the circle. Cosine values are positive in the first and fourth quadrants. The first quadrant is where θ is between 0 and π/2, and the fourth quadrant is where it is between 3π/2 and 2π. Therefore, using interval notation, we express these quadrants as the union of the two intervals: (0, π/2) and (3π/2, 2π).
In order to determine the values of theta on (0, 2π) where cos(theta) > 0, we need to find the intervals where the cosine function is positive. The cosine function is positive in the first and second quadrants, which correspond to theta values between 0 and π/2, and between 3π/2 and 2π.