A function is defined over (0, 2) by f (20 ) = - a 0

A function is defined over ((), 2) by O < c and c < 1 1 < c and c < 2 We then extend it to an odd periodic function of period 4 and its graph is displayed below. 0.4 -0.4 The function may be approximated by the Fourier series =ao+E00 ( nnm f@) n=l an cos where L is the half-period of the function. nqrc + bn sin Use the fact that f@) and f@) cos are odd functions, enter the value of an in the box below. an = , for n Hence the Fourier series made up entirely of sines. Calculate the following coefficients of the Fourier series and enter them below in Maple syntax.