Given the series
and that f(x) = f(pi - x), what can one say about the coefficients an and bn? I know that due to orthogonality an=0 for odd functions and bn=0 for even functions, but I'm not sure what symmetry the function f(x) = f(pi-x) has.
Given the series
and that f(x) = f(pi - x), what can one say about the coefficients an and bn? I know that due to orthogonality an=0 for odd functions and bn=0 for even functions, but I'm not sure what symmetry the function f(x) = f(pi-x) has.
Here are a few hints:
First the function is symmetric across the line $\displaystyle x=\frac{\pi}{2}$
Also since the inside of your trig function is of the form
$\displaystyle nx$ The generic form is $\displaystyle \displaystyle \frac{n \pi x}{L}$ This gives the function must be $\displaystyle 2L$ peroidic.
Using this try to figure out if the function is odd or even!