Trig help, please!

[ayane]

Solve 2sin(x/2)=1 between 0 and 2pi.

I have to do this trig problem, and the answer to a similar problem in my book (with the sin(x/2), which is what concerns me) is "no solution." Does the problem I'm trying to do have no solution too? If there are solutions, how many?

[tesspi]

First treat your sin (x/2) as a variable and divide both sides by 2.
Then you have sin(x/2)=1/2
Now, this says that there is some angle that has sine equal to 1/2.
So, this occurs at pi/3 and 2pi/3.
Now you have two equations ... x/2=pi/3 and x/2=2pi/3.
Multiply both sides by 2 and you have your answers. :)

[Sinsane]

That is right.
There are also other shorter methods to figure it out.
I'm not quite sure how to explain though, my teach was explaining once and I didnt pay much attention.