my teacher wrote that from symmetry considerations we could say that:
F(x)=Sin((n/L)*Pi*x) is an even function for odd n's around X=L/2, and odd for even n's.
could somebody please explain why is that so?
I tried to test it:
x=L/2 => f=Sin(2*Pi*n) and this function is zero at X=L/2 for every n I use. odd or even...!