Finding the x of a sine equation!

20 = 8sin((pi/6)(x+2))+16 ........... subtract 16

4 = 8sin(pi/6x+pi/3) ................ divide by 8

1/2 = sin(pi/6x+pi/3) ..............arcsin1/2 to get rid of sin and get pi/6

pi/6 = pi/6x+pi/3 .......... subtract pi/3

-pi/6 = pi/6x ....... divide by pi/6 to get x

-1 = x

My question is: Is there any way to find out the other value of 1/2 sine except looking at the unit circle, which is 5pi/6?

1/2 = sin(pi/6x+pi/3) .. arcsin1/2 to get rid of sin and get 5pi/6

5pi/6 = pi/6x+pi/3 ... subtract pi/3

pi/2 = pi/6x ....... divide by pi/6 to get x

3 = x

And, how would I do it if the y value is 10?

10 = 8sin((pi/6)(x+2))+16

I don't know how to go through the steps to find the one of the values for sine -3/4 (after you go through the steps)

The only one I found was 8.3803207 for x.

By tracing the sine graph on my calculator, I was able to get the answers 5.6196793 and 8.3803207