Question

3sinx + 3 = 2/sinx

Answer 1

Solve 3sin x + 3 = 2/sin x
3sin^2 x + 3sin x -2 = 0. Call sin x = x. Solve this quadratic equation.
3x^2 + 3x - 2 = 0.
D = b^2 - 4ac = 9 + 24 = 33. -> VD = 5.74
Two real roots.
x1 = -3/6+ 5.74/6 = 2.74/6 = 0.45
x2 = -3/6 -5.74/6 = -8.74/6 = 1.45 rejected since > 1
sin x = x1 = 0.45 = sin 26.74 deg, and sin x = sin (180 - 26.74) = sin 153.26
a) sin x = sin 26.74 -> x = 26.74
b) sin x = sin 153.26 -> x = 153.26.