Demonstrate Period of trigonometric functions?

Apr 2013
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0
doral, florida
[h=1]Demonstrate Period of trigonometric functions?[/h] Prove that if f and g are periodic with period p, then f/g is also periodic,
but its period could be smaller than p.

Help me, Ido not know how complete this exercise, what I should do here, can someone please explain?
 

HallsofIvy

MHF Helper
Apr 2005
20,249
7,909
You know the definition of "periodic" don't you? If f is periodic with period p, then f(x+ p)= f(x) for all x. If g is periodic with periodic p, then g(x+ p)= g(x) for all x.

So what can you say about \(\displaystyle \frac{f}{g}(x+ p)= \frac{f(x+ p)}{g(x+ p)}\)?
 
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