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

[mathkillsme]

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?

 

[Tedjn]

If you graph it, you will find that 4sin(2x) repeats itself after every multiple of pi. To be precise, the period of a function f(x) is the smallest number T such, for all x, f(x) = f(x + T). In this case, you will notice that pi is the smallest number such that, for all x, 4sin(2x) = 4sin(2(x + pi)) = 4sin(2x + 2pi).