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Trignometry

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31 Jul 2008 18:51:12 IST

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Periodicity

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Prove : Sin (x²) is a non periodic function

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edison

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Joined: 19 Oct 2006

Posts: 7537

31 Jul 2008 21:53:40 IST

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The Sin (x²) is definitely a non periodic function, it is oscillatory between +1 and -1 with continuously reducing period as'x' progresses.

Proof of its non periodicity.

Let us assume that Sin (x²) is a periodic function with period T

Thus Sin ((x + T)²) = Sin (x²)

or Sin (x² + 2T + T²) = Sin (x²)

Which means that the periodicity of the function is 2T + T², but we have assumed that it is T

so 2T + T² = T

or T + T² = 0

or T = 0 or -1, which is not possible.

Thus our assumption that the function Sin (x²) is periodic is false

Rejaul Makshud

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Joined: 1 Aug 2008

Posts: 96

5 Aug 2008 20:59:34 IST

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u should know abot the basic of periodicity.

If f(x) be a non periodic function and g(x) be a periodic function then f(g(x)) be a non periodic function.

Here , consider f(x) = x²and g(x) = sin x .

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