SOLUTION: Solve the equation for θ if 0° ≤ θ < 360°. (Enter your answers as a comma-separated list.)
2 sin θ + 1 = csc θ
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-> SOLUTION: Solve the equation for θ if 0° ≤ θ < 360°. (Enter your answers as a comma-separated list.)
2 sin θ + 1 = csc θ
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2 sin θ + 1 = csc θ
2 sin θ + 1 = 1/sin θ
Multiply by sin θ and get
2 sin^2 θ + sin θ = 1
2 sin^2 θ + sin θ - 1 = 0
Now factor and solve
(2 sin θ - 1)(sin θ + 1) = 0
so that
sin θ = 1/2 and θ = 30 and 150 degrees
AND
sin θ = -1 and θ = 270 degrees
