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Topic: Nonperiodic Trigonometric functions
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Posts: 3
From: New Jersey
Registered: 11/22/11
Nonperiodic Trigonometric functions
Posted: Nov 22, 2011 9:16 AM
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Is the function
f(x)=sin(sqrt(2)x)cos(sqrt(3)x) periodic?

If yes, what is the period?

If not, how to prove it?

In general, if a and b are irrational numbers so that ab is not rational, is
f(x)=sin(ax)cos(bx) periodic?

If yes, what is the period?

If not, how to prove it?

My suggested 'proof' involves using successive decimal approximations for a and b, so the period grows larger as the denominator of the decimal approximation grows larger, thus the period 'goes to infinity'.
But I can't find a reference for this type of reasoning.

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