Question

12sin^2(theta)-6sin(theta)=4

Answer 1

Call sin x = x -> quadratic equation:
6x^2 - 3x - 2 = 0.
Solve by the formula : D = b^2 - 4ac = 57 ->VD = V57= 7.55
x1 = 3/12 + (7.55)/12 = 10.55/12 = 0.875
x2 = 3/12 - (7.55)/12 = -4.55/12 = -0/38.
a) Solve sin x = x = 0.875 = sin (61.04) and sin (180 - 61.04) = sin(118.96)
Answers: x = 61.04 and x = 118.96
b) Solve sin x = x = -.0.38 = sin (202.33) and sin (360 - 22.33) = sin (337.67)

Answer 2

b) Final answers:
x = 61,04, and 118.96.
x = 202.33, and x = 337.67
You can check these answers by replacing these values of x into the original equation.