Find all angles, 0^{\circ}\le\theta<360^{\circ}0 ∘ ≤θ<360 ∘ , that satisfy the equation below, to the nearest 10th of a degree.

Question

3tanxsinx+2sinx=0

Answer 1

3tan(x)sin(x) + 2sin(x) = 0

sin(x)[3tan(x) + 2] = 0

So, either sin(x) = 0 or 3tan(x) + 2 = 0

For sin(x) = 0, x = 0° and x = 180°

For 3tan(x) + 2 = 0, tan(x) = -2/3. Plugging tan^-1(-2/3) into a calculator gives x = -33,7° however that is not in the domain of 0° to 360° so add 360: x = 360° - 33.7° = 326.3°. But tangent repeats every 180° so we also will get the same value at 326.3° - 180° = 146.3°

So x = 0°, x = 146.3°, x = 180°, and x = 326.3°