Ok, lets go back to yr 11 stuff for clarification.
Do you remember how you learnt All Stations To Central?
Because Cos is positive at 1st and 4th quadrant, if you are given the domain of 0 ~ 2pi, then you must include two angles, because both those angles give 1/2.
Taking an example, if you were told to do it in degrees, you'd realise that cos 60 = 1/2. Then you would do 360-60, which would give you 300 degrees. Now, that when you convert into radians, it becomes pi/3 and (5pi)/3.
But, really you shouldn't need to think in angles, because it's easier to picture up the general solutions in your head, or just the graph of it and see how much radians you went clockwise, or anticlockwise, depending on the domain.