Solve sin θ = 1/2 for θ in [0, π].

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Multiple Choice

Solve sin θ = 1/2 for θ in [0, π].

Explanation:
The value 1/2 for sine occurs at angles whose reference angle is π/6, since sin(π/6) = 1/2. In the interval from 0 to π, sine is positive in both the first and second quadrants. That gives two possibilities: θ = π/6 in the first quadrant, and θ = π − π/6 = 5π/6 in the second quadrant. Other angles listed don’t give sine equal to 1/2 (π/4 and π/3 give larger values, and 7π/6 is in the third quadrant with sine negative). So the solutions in [0, π] are θ = π/6 and θ = 5π/6.

The value 1/2 for sine occurs at angles whose reference angle is π/6, since sin(π/6) = 1/2. In the interval from 0 to π, sine is positive in both the first and second quadrants. That gives two possibilities: θ = π/6 in the first quadrant, and θ = π − π/6 = 5π/6 in the second quadrant. Other angles listed don’t give sine equal to 1/2 (π/4 and π/3 give larger values, and 7π/6 is in the third quadrant with sine negative). So the solutions in [0, π] are θ = π/6 and θ = 5π/6.

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