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how to solve a periodic function

how to solve a periodic function

Grade:12

3 Answers

Latika Leekha
askIITians Faculty 165 Points
8 years ago
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
AUREA
61 Points
8 years ago
do you mean how to find the period of periodic function?
AUREA
61 Points
8 years ago
Let f(x) be a periodic functon having period T. then solve the equation
f(x+T)=f(x)
the smallest such value of T is the fundamental period of f and Tshould be  positive and independent of x
let us take an example:to find the period of sin x
sin(x+T)=sin x
i.e x+T = nπ+(-1)nx
putting n=0 gives T=0
n=1 does not give a value of T independent of x
n=2 gives T=2π and so on
thus least value +ve value of T independent of x is 2π.
there are vsome properties of periodic functions mostly trigonometric which are useful:-
modulus of trignometric functions(sin, cos, tan, cot, sec, cosec) have fund. period π
sinnx, cosnx, cosecnx, secnx have period 2π if n=odd & π if n is even
if f(x) has period T , then kf(ax+b) is periodic having period T/IaI
             e.g. period of sin(9x+3)=2π/9
There are more other propreties of perioic functions.


 

 
 

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