Consider the following non-periodic function:

f(x)= π-x

0

4(a) Write down the odd periodic extension, p(x), of the non-periodic function f(x), with a

period T = 2π. If appropriate, write this in piecewise form.

4(b) Sketch p(x), from 4(a), over the interval [-3π,3π]. Label both axes, as well any intercepts

on either axis.

4(c) Determine the Fourier coefficients for p(x).

4(d) Write down the first three non-zero terms of the Fourier series representing p(x). If a, is

non-zero, then count this as the first non-zero term of the Fourier series. (2 marks)