how to solve a periodic function

Hello student,
A periodic function is defined to be the function that repeats itself after a specific period.
Frist of all, you should be clear with the various properties of periodic functions.
Eg. for a periodic function f(x) with period a, f(x+a) = f(x).
Moreover, if you are well-versed with the drawing of graphs, then you can easily judge from the graph itself whether a function is periodic or not.
There are several cocnepts associated to periodic functions like amplitude of periodic function, graphing of periodic function etc. For a detailed study, you can visit the website.
The formula of the period of trigonometric function is , P = 2πK, where K is multiple of x.
We are illustrating here two eaxmples of periodic functions:
Example 1: Find the value of sin 13π/6.
Sol: We know that sine is a periodic function with period 2π.
So, sin(x + 2π) = sin x
Therefore sin 13π/6 = sin(2π + π/6)
This means sin π/6 = 1/2.
This gives sin 13π/6 = 1/2.
Example2: Find the period of the function cos(x/3).
Sol: Let y = cos(x/3)
The formula of the period of trigonometric function, P = 2π/S, where S is multiple of x.
So, P = 2π/(1/3)
Note: For the sin function the period is always (2pi)/b
where "b" fits into the form y = a sin(bx+c)+d