If sin θ = 1/2 and θ ∈ [0, π/2], which angle satisfies?

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Prepare for the AMSOC 26-003 Module A Test. Utilize flashcards and multiple choice questions with hints and explanations. Ace your exam!

Multiple Choice

If sin θ = 1/2 and θ ∈ [0, π/2], which angle satisfies?

Explanation:
In the interval from 0 to π/2, sine increases as θ grows, so there is a unique angle whose sine is 1/2. The standard value with sin equals 1/2 in that first quadrant is 30 degrees, which is π/6. Therefore θ = π/6 satisfies the condition sin θ = 1/2. The other angles don’t fit: π/3 has sin equal to √3/2, π/2 has sin equal to 1, and 2π/3 is in the second quadrant with sin equal to √3/2, which is outside the allowed interval.

In the interval from 0 to π/2, sine increases as θ grows, so there is a unique angle whose sine is 1/2. The standard value with sin equals 1/2 in that first quadrant is 30 degrees, which is π/6. Therefore θ = π/6 satisfies the condition sin θ = 1/2.

The other angles don’t fit: π/3 has sin equal to √3/2, π/2 has sin equal to 1, and 2π/3 is in the second quadrant with sin equal to √3/2, which is outside the allowed interval.

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