MATLAB: The sums of cos(x) over 2*pi range not zero

Question

when evaluating the following codes:

t = linspace(-pi,pi,128); s = sin(t); c = cos(t); sum(s), sum(c)

ans =

     6.811558403281303e-15

ans =

-0.999999999999978

Q: should not both be zero?

and try

 sum(c(2:end))

ans =

   2.5313e-14

also quad(@cos,-pi,pi)

ans =

   4.0143e-09

Q: Why the discrepancy?

Thank you for your input.

Thanks J

Answer 1

T = fundamental period

N = number of samples

dt = T/N sampling interval

f0 = 1/T fundamental frequency

(n-1)*f0 harmonics 1<=n <= N

Orthogonality interval

t = t0:dt:t0+T-dt;

t = t0+[0:dt:T-dt];

t = t0+dt*[0:N-1];

help fft

doc fft

Hope this helps

Greg