1. The problem statement, all variables and given/known data Find the Fourier series defined in the interval (-π,π) and sketch its sum over several periods. i) f(x) = 0 (-π < x < 1/2π) f(x) = 1 (1/2π < x < π) 2. Relevant equations ao/2 + ∑(ancos(nx) + bnsin(nx)) a0= 1/π∫f(x)dx an = 1/π ∫f(x)cos(nx) dx bn = 1/π ∫f(x) sin(nx) 3. The attempt at a solution I've worked out the a0 by splitting the limits and integrating individually for -π < x < 1/2π and 1/2π < x < π. When I did this i got a0 = ½ for an = 1/π ∫(upper limit π, lower limit 1/2π) cos(nx) dx = 1/π[1/n sin(nx)] = 1/π ((1/n. sin(πn) - 1/n.sin(πn/2)) = 1/nπ(0- sin(πn/2) Here is where i get stuck as sin(πn/2) is 0 for even values of n and alternates between 1, -1 for odd values. Can i leave this written in sin form of the Fourier series as every other example i've changed the value of sin/cos to either 0 or (-1)n. Thanks for any help!