clear all;close all;clc


n = 2;

numIter = 1000000;

C = zeros(1,numIter);
S = zeros(1,numIter);
for iter=1:1:numIter

    theta = 2.*pi.*rand(1, n);

    C(iter) = sum(cos(theta));

    S(iter) = sum(sin(theta));

end

figure;
plot(C,S,'.');
title('(C,S)')




clear C S
C = zeros(1,numIter);
S = zeros(1,numIter);
for iter=1:1:numIter

    theta = 2.*pi.*rand(1, 1);

    C(iter) = 1 + (cos(theta));

    S(iter) = (sin(theta));

end


figure;
plot(C,S,'.');
title('(1,0) + (cos(U),sin(U))')