Thread: Demonstrate Period of trigonometric functions?

Demonstrate Period of trigonometric functions?

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?

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 $\displaystyle \frac{f}{g}(x+ p)= \frac{f(x+ p)}{g(x+ p)}$?