How to identify odd and even functions from graph(fourier series)

let us say, we are given a curve..

i will describe everything from figure…

u should know that this is the least found thing on internet..so it is valuable…

the above kind of figure are always odd…because y=sinx is odd…and most of them are similar behaviour fxns….so they are odd…

 

 

and there is next way called “rotational symmetry” to identify if it is odd.

first rotate the y=sinx figure into Y

then into X

and finally if the same curve continues, then it is odd…

it is equal when seen through origin..

so it is odd.

(LOGIC behind this:

from algebra, if f(x)=-f(-x)…then the function can be seen like this

f(x)=f(-x)…..f(x) is reflected through Y

f(-x)=g(x) (say)

and g(x)=-f(-x)…f(-x) is again reflected so -f(-x) i.e opposite is produced….180 degree rotation)

i know that all of you have spent most time in searching…how to determine whether it is odd or even functions…now i am sure, that you got the thing…

this is used in fourier series in electric circuit theory( probably in other things also).

if it is neither odd nor even , then it is called NEITHER.

(the process of finding odd is called “rotational symmeter”…”origin symmetry”)

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