Subject: trig problem
The period of a periodic function, which is the "shortest repeating interval", is sometimes difficult to identify if all you have is a diagram. I expect that in this situation the period is what I have marked in the diagram below.
If the point indicated by the black dot has coordinates (pi,2) then the red dots are approximately evenly spaced, about pi/3 units apart. Thus the period is 4/3 pi.