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Batu
Posts:
3
From:
New Jersey
Registered:
11/22/11


Nonperiodic Trigonometric functions
Posted:
Nov 22, 2011 9:16 AM


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.



