Find all solutions in the interval 0° ≤ θ < 360° where θ1 < θ2 < θ3 < θ4 < θ5 < θ6. sin (3θ − 45°) = −√3/2

Answer 1

sin(x) = -√3/2 at 4π/3 and 5π/3

45º = π/4

Thus, we solve 3x - π/4 = 4π/3, 5π/3. 4π/3 + 2π, 5π/3 + 2π, 4π/3 + 2π, 5π/3 + 2π, or

3x = 19π/12, 23π/12, 43π/12, 47π/12, 67π/12, 71π/12

x = 19π/36, 23π/36, 43π/36, 47π/36, 67π/36, 71π/36