phase plot no giving the correct plot

%clc;
%clear all;
%close all;
N=6;
n=0:N-1;
x=sin(2*pi*n/6);
for k=0:N-1
    sum=0;
    for n=0:N-1
        A=exp(-j*k*((2*pi)/N)*n);
        B=A*x(n+1);
        sum=sum+B;
    end
    a(k+1)=sum/N;
end
a
mag=abs(a);
phase=angle(a);
k=0:N-1
subplot(2,1,1);
stem(k,mag);
title('magnitude plot 73020')
grid on;
subplot(2,1,2);
stem(k,phase);
title('phase plot 73020')
grid on;

the figure shows the output but the phase plot is not correct.

Answer 1

[dpb]

Don't forget floating point precision...

>> real(a)
ans =
   1.0e-15 *
    0.0555    0.1665    0.0555    0.0185   -0.1295   -0.9899
>> imag(a)
ans =
         0   -0.5000    0.0000    0.0000    0.0000    0.5000
>> real(a)<3*eps
ans =
  1×6 logical array
   1   1   1   1   1   1
>>

Perhaps what you were expecting was on the order of...

>> angle(complex(zeros(size(a)),imag(a)))
ans =
         0   -1.5708    1.5708    1.5708    1.5708    1.5708
>> 

But, the plot is correct given the input; as is the result of angle -- just not the same as the analytic solution.