This question is designed to be answered without a calculator.How many solutions does the equation (2 sin x + 1)(sin x – 1) = 0 have over the interval 0 ≤ x < 2π?

Set each factor equal to zero: 2 sin x + 1 = 0 gives sin x = −1/2, and sin x − 1 = 0 gives sin x = 1. In 0 ≤ x < 2π, sin x = −1/2 at 7π/6 and 11π/6, while sin x = 1 at π/2. That makes 3 solutions, so the correct choice is C) 3.

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