Solve using a calculator finding all solutions in 0 2 pi Rou

Solve using a calculator, finding all solutions in [0, 2 pi). Round to the nearest hundredth. sin x+ sin 3x= - cos x A. 1.57, 1.83, 2.88, 4.71, 6.02 B. 1.57, 1.83, 2.88, 4.71, 4.97, 6.02 C. 0.26, 1.31, 1.57, 3.40, 4.45, 4.71 D. 2.18, 5.32

Solution

sin x + sin 3x = -cos x

Now sin A + sin B = 2*sin(A+B)/2* cos(A-B)/2

2*sin2x* cosx = -cos x

2*sin2x = -1

sin2x = -1/2

2x = 3.665, 5.76

x = 1.83, 2.88