What non-polynomial functions can be "factored"?

[MAGNIBORO]

hi, and thanks for come in, sorry for bad english

I was watching a proof of euler to the basilean problem, and a part of the proof he did this

sin(x) = x ( x + π ) ( x - π ) ( x + 2π ) ( x - 2π ) ( x + 3π ) ( x - 3π) ...

i understand why, but i wanted to know what not polynomial functions they have this property and how
"factored" this functions.

also wanted to know if all periodic functions have this property.

by last
this is true?

cos(x) = ( x + π/2 ) ( x - π/2 ) ( x + π3/2 ) ( x - π3/2 ) ( x + π5/2) ( x - π5/2 ) ...

thanks.

 

[micromass]

https://en.wikipedia.org/wiki/Weierstrass_factorization_theorem

 

[MAGNIBORO]

https://en.wikipedia.org/wiki/Weierstrass_factorization_theorem

I 'll have to study more for entender this ;(
thank you for the answer =D