For angles ranging from 0 to 360,
Sin(angle) may be viewed as the y co-ordinate of a point on a unit circle,
of radius 1.
If 2x is the angle,
where is the y co-ordinate -1 ?
answer: at 270 degrees, or
Sin(270 degrees)= -1.
So 2x is 270 degrees or 270+n(360) degrees, n=0,1,2,3........
The second result is obtained for 2x=270+360 degrees,
as x<360 degrees.