Hello Khaled, If you have t=0 as the first element of a uniform time array, then calculating y from that and taking the fft will give two peaks per frequency. For a given frequency w, assuming your normalization is correct, the left complex amplitude [C exp(i phi)] is the positive freq. contribution, to be multiplied by exp(iwt), and the right complex amplitude [C exp(-i phi)] is the negative freq. contribution, to be multiplied by exp(-iwt). Adding these you get the result 2C cos(wt + phi). It's most often stated in terms of cos but of course it is also 2C sin(wt + phi + pi/2).
This all assumes you have fft'd a real function as in your example.
