Find the Fourier coefficients of the functions given in what follows. All are supposed to be periodic with period 2π. Sketch the graph of the function.
a. f(x) = x, -π < x < π;
b. f(x) = |x|, -π < x < π;
c. f(x) = {0, -π < x < 0,
1, 0 < x < π;
d. f(x) = |sin x|.