Which are solutions to 3sin^2 θ - 2sin θ = 0, 90°≤θ≤90°

The solutions of the equation are -41.8° , 0.0° , 41.8°

Step-by-step explanation:

∵ 3 sin²Ф - 2 sinФ = 0 is a quadratic function

∵ The domain of the function is -90° ≤ Ф ≤ 90°

- Lets take sinФ as a common factor

∴ sinФ (3 sinФ - 2) = 0

- Two terms multiplied by each other = 0

∴ One of them must be equal zero

∴ sinФ = 0 or 3 sinФ - 2 = 0

- If sinФ = 0 ⇒ Ф = 0.0°

- If 3 sinФ - 2 = 0 ⇒ 3 sinФ = 2 ⇒ sin Ф = 2/3

∵ sinФ 2/3

∴ Ф = 41.8° ⇒ Ф ≤ 90° (in first quadrant)

∵ -90° ≤ Ф ≤ 90°

∴ Ф = -41.8° ⇒ Ф ≥ -90° (in fourth quadrant)

∴ The solutions of the equation are -41.8° , 0.0° , 41.8°

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