DCT - approximate a function using DCT.

Hi Guys I have task I dont know how to do it. I must write a function using DCT( Discrete Cosine Transform) that make a approximation of math function like sin(x). I read a Wiki about that.I stay in one point for long time I dont know what I did wrong becouse It doesnt work I think.

function [] = DCT(a,b,N)
x = linspace(a,b,N);
y = zeros(1,N);

y = sin(2*pi*x);
plot(x,y,'g');
grid on;hold on;
K = N;

for k = 1:N
G=0;
for m = 1:K
    if k==1
        G = G + (1/sqrt(N))*y(m);
    else
        G = G + (sqrt(2)/sqrt(N))*y(m)*cos((pi*k*(2*m-1))/(2*N));
    end
    
end
G(k)=G;
end