Quadratic Trig Equations Help

Question

Find all angles, 0° ≤ Θ ≤ 360°, that satisfy the equation below, to the nearest tenth of a degree.

9sin^2 Θ - 4 = 0

Answer 1

You solve the equation as if sin²(θ) = x²

9x² = 4 x = ±4/9

Therefore, θ = sin^-1(±4/9) This corresponds to a principal angle in the first quadrant of 26.39º. the rest of the angles with the same or negative sines are 180 - θ, 180 + θ, and 360 - θ.

Hope that helped.