Can someone please explain solving trigonometric equations? Here is an example problem:

Question

anonymous · Answer

Solve the equation 6 sin 2x = 5 for$$0\le x <2\pi$$. Give answers to the nearest hundredth of a radian.

anonymous · Answer

One method is the following:
6 sin 2x = 5
sin 2x = 5/6
2x = 0.99, 2.16, 7.27, 8.44
x = 0.49, 1.08, 3.63, 4.22

How?

anonymous · Answer

I'm confused as to how the 4 solutions were obtained. I understand how you get 0.99, but not the rest.

anonymous · Answer

So, after you get the initial x-value (0.4926) you're supposed to subtract it from pi/2 to get the second solution (1.0782)?

anonymous · Answer

it is really just because of the period that you are analyzing. when you solve for 2x, what you are asking is what angle 2x has a sin that is = to 5/6, I actually got that it is around 56 degrees which is some odd radians. The point is that 2pi is 360 degrees and from however many radians 56 degrees is, you still have four more values in between that and 2pi which will give you the same answer because the trig functions are cyclical. So that is why you have four answers. Then once you divide the 2 out you get the same four answers all divided by 2.