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.
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
Also since the inside of your trig function is of the form
The generic form is This gives the function must be peroidic.
Using this try to figure out if the function is odd or even!
Here are a few hints:
First the function is symmetric across the line
Also since the inside of your trig function is of the form
The generic form is This gives the function must be peroidic.
Using this try to figure out if the function is odd or even!
So the function f is even about the point x=pi/2. This means that a(n) will be 0 when cos(nx) is odd about x=pi/2 and b(n)=0 when sin(nx) is odd about x=pi/2.
A similar argument for cos gives a(2n+1) = b(2n) = 0. Is this the best way to tackle the problem?