x=-2*pi:0.01:2*pi
y=x.*0+1
y1=cos(x)
y2=sin(x)
y3=cos(2.*x)
y4=sin(2.*x)
y5=cos(3.*x)
y6=sin(3.*x)
y7=cos(4.*x)
y8=sin(4.*x)
y9=cos(5.*x)
y10=sin(5.*x)
y11=cos(6.*x)
y12=sin(6.*x)
y13=cos(7.*x)
y14=sin(7.*x)
y15=cos(8.*x)
y16=sin(8.*x)
y17=cos(9.*x)
y18=sin(9.*x)
y19=cos(10.*x)
y20=sin(10.*x)
figure(1)
plot(x,y,x,y1,x,y3,x,y5,x,y7,x,y9,x,y11,x,y13,x,y15,x,y17,x,y19)
axis([-7,7,-1.5,1.5])
legend('cos(0)','cos(x)','cos(2x)','cos(3x)','cos(4x)','cos(5x)','cos(6x)','cos(7x)','cos(8x)','cos(9x)','cos(10x)')
figure(2)
plot(x,y2,x,y4,x,y6,x,y8,x,y10,x,y12,x,y14,x,y16,x,y18,x,y20)
legend('sin(x)','sin(2x)','sin(3x)','sin(4x)','sin(5x)','sin(6x)','sin(7x)','sin(8x)','sin(9x)','sin(10x)')
axis([-7,7,-1.5,1.5])
%%
theta=-2*pi:0.01:2*pi
sum23=0.5
sum29=0.5
sum211=0.5
for i=1:3
    sum23=sum23+-1/(pi*i)*(1-(-1).^i)*sin(i*theta)
end
for i=1:9
    sum29=sum29+-1/(pi*i)*(1-(-1).^i)*sin(i*theta)
end
for i=1:11
    sum211=sum211+-1/(pi*i)*(1-(-1).^i)*sin(i*theta)
end
figure(3)
plot(theta,sum23,theta,sum29,theta,sum211)
legend('N=3','N=9','N=11')
%%
sum33=pi
sum39=pi
sum311=pi
for i=1:3
    sum33=sum33+-2/i*sin(i*theta)
end
for i=1:9
    sum39=sum39+-2/i*sin(i*theta)
end
for i=1:11
    sum311=sum311+-2/i*sin(i*theta)
end
figure(4)
plot(theta,sum33,theta,sum39,theta,sum311)
legend('N=3','N=9','N=11')