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Is there a continuous periodic function which is not trigonometric. if yes, what?
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?
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....f(x) = Arccos(cos(x)) = x...
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.
Every function is man-made. Not every function is "man-made".HallsofIvy said:I don't know any functions that aren't "man-made"!