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how to solve a periodic function

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5 years ago Latika Leekha
165 Points
```							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 xTherefore 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)/bwhere "b" fits into the form y = a sin(bx+c)+d
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5 years ago
```							do you mean how to find the period of periodic function?
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5 years ago
```							Let f(x) be a periodic functon having period T. then solve the equationf(x+T)=f(x)the smallest such value of T is the fundamental period of f and Tshould be  positive and independent of xlet us take an example:to find the period of sin xsin(x+T)=sin xi.e x+T = nπ+(-1)nxputting n=0 gives T=0n=1 does not give a value of T independent of xn=2 gives T=2π and so onthus 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 πsinnx, cosnx, cosecnx, secnx have period 2π if n=odd & π if n is evenif f(x) has period T , then kf(ax+b) is periodic having period T/IaI             e.g. period of sin(9x+3)=2π/9There are more other propreties of perioic functions.
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5 years ago
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