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Is there a continuous periodic function which is not trigonometric. if yes, what?

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- Thread starter geniusprahar_21
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- #1

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Is there a continuous periodic function which is not trigonometric. if yes, what?

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lurflurf

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Yes there are very many. Define a continuous function on [a,b] where f(a)=f(b) then define f outside of [a,b] so that f(x+(b-a))=f(x). A simple example that is not trigonometric (even though it looks like it is) is Arccos(cos(x)).geniusprahar_21 said:Is there a continuous periodic function which is not trigonometric. if yes, what?

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quasar987

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HallsofIvy

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I don't know any functions that aren't "man-made"!

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...f(x) = Arccos(cos(x)) = x...

No, the inverse cosine function returns values in a specific interval (which I can't remember atm), so you can't have arccos(cos(x)) = x for all x.

- #6

lurflurf

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That is right Arccos(cos(x))=x on [0,pi], it is also periodic with period pi, so it repeats all those values. I use Arccos with the capital A to make clear that I am using the principle value of Arccos not just any value that gives the needed value. This is a general way to write periodic functions. let f(x) be diffined and continuous on [a,b] with f(a)=f(b) thenMuzza said:No, the inverse cosine function returns values in a specific interval (which I can't remember atm), so you can't have arccos(cos(x)) = x for all x.

g(x)=f(a+(b-a)(1+(1/pi)Arccos(cos(pi(x-a)/(b-a)))))

is a periodic extension of f that is f=g on [a,b] and g(x+2n(b-a))=g(x)

when n is an integer.

remenber the definition of a periodic function is a function is periodic with period p if

f(x+p)=f(x) for all x.

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Alkatran

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For example, there is:

e^(2+x*i)

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quasar987

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Every function is man-made. Not every function is "man-made".HallsofIvy said:I don't know any functions that aren't "man-made"!

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f(x)=x-2n for x belonging to [2n, 2n+1) where n is any integer

= (2n+2)-x for x belonging to [2n+1, 2n+2]

check this out...if i havent made any silly mistakes...it shud come out 2 be continuous and periodic...ive modelled it on the sin graph + on the [x] graph..lol...cudnt think of a better example sorry....cheers! ;)

- #10

Galileo

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Constant functions.

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