%%Plots for pproblem B
%%PLOT SIN SERIES FOR f(t) = t ON [0,1]
hold on
T = linspace(-1, 2, 300);

ff = T;
plot(T,ff);
%ylim([-.2 1.5]);

sapprox = zeros(1, 300);

N = 8;
for k = 1:N
    
    sapprox = sapprox + 2*(-1)^(k+1) *  sin(pi* k*T)/(k*pi);
    plot(T, sapprox);
   %ylim([-.2 1.5]);
end  
hold off


%plot the cosine approx
figure
plot(T,ff);
ylim([-.2 1.5]);

hold on
capprox = (1/2)*ones(1,300);
N = 5;

for j = 1:N
    k = 2*j - 1;
    capprox = capprox - (4/pi^2) *  cos(pi * k*T)/k^2;
    plot(T, capprox);
   ylim([-.2 1.5]);  
end  
hold off