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    Question

    Solve for 0° ≤ θ ≤ 360°: 2 sin²θ + 3

    sinθ − 2 = 0
    A 20°, 110° Correct Answer Incorrect Answer
    B 30°, 170° Correct Answer Incorrect Answer
    C 30°, 150° Correct Answer Incorrect Answer
    D 70°, 150° Correct Answer Incorrect Answer

    Solution

    Let x = sinθ. 2x² + 3x − 2 = 0 Solve quadratic: Discriminant D = 3² − 4×2×(−2) = 9 + 16 = 25 x = [−3 ± 5]/(2×2) x₁ = (−3 + 5)/4 = 2/4 = 1/2 x₂ = (−3 − 5)/4 = −8/4 = −2 (not possible, since |sinθ| ≤ 1) So sinθ = 1/2 In [0°, 360°], sinθ = 1/2 at: θ = 30°, 150° Answer: θ = 30°, 150°.

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