What exactly does the period tell you in a trig graph?

Homework Statement

i understand how to find the period of a trig equation... (either 2pi/|b| for sin and cos or pi/|b| for tan etc. but i do not understand what information the period tells me..

Homework Equations

alright for example.. if my problem is y= 4sin2x

The Attempt at a Solution

the period in the above solution would be pi... correct? so what does that tell me?????