17. Write g : [0, T] → R for the Sin function, i.e. g(x) = sin(x). We can try and write g in terms of Cosine functions! Calculate the coefficient in Fourier's Cosine series ELo ak cos(kx) for g. Why...

Extracted text: 17. Write g : [0, T] → R for the Sin function, i.e. g(x) = sin(x). We can try and write g in terms of Cosine functions! Calculate the coefficient in Fourier's Cosine series ELo ak cos(kx) for g. Why can you be sure that the series converges to g? Calculate your expression for g at the point x = T/2 to obtain an infinite series for r.