What is the smallest positive angle theta in radians that satisfies sin(theta) = 1/2 for theta in [0, 2π)?

• A. π/6
• B. 5π/6
• C. π/3
• D. π/2

Answer: (A)

This question tests finding where the sine value matches a given number on the unit circle and picking the smallest angle in the specified interval. Sine corresponds to the y-coordinate on the unit circle. The value 1/2 occurs at a 30-degree angle, which is π/6 radians, where the y-coordinate is 1/2. In the interval from 0 to 2π, this is the first time you hit sin θ = 1/2 as you move forward. There is another angle in the interval, 5π/6, where sine is also 1/2, but it’s larger than π/6. The other options give different sine values: π/3 yields √3/2, and π/2 yields 1. So the smallest positive angle is π/6.