# Why are there two phases for one dominant frequency?

I was playing with a set of time history, trying to extract its phases corresponding to the each distinguishable dominant frequency.

Just look at the figures: I got one of the dominant frequency in Fig.1, but in Fig. 2 there are two different phases close to the dominant frequency (f=0.05). Here I am confused; I do not understand why there are two phases near the dominant frequency.

Edit: it seems when I increase the threshold of masking noises, the negative phase disappeared.

Appendix: the code I used for phase extraction

    %     figure;plot(f,P1);
%     xlabel 'Frequency (Hz)';xlim([0 2.5])
%     ylabel 'A' %ylabel 'degrees' %
%     grid

Yb=fft(y);
ly = length(Yb);
fb = (0:ly-1)/ly*Fs;

%     X3=Yb;
%     threshold = max(abs(Yb))/2; %tolerance threshold
%     %X3(abs(Yb)<threshold) = 0; %maskout values that are below the threshold
%     phs = unwrap(angle(X3));
%     %phs = (angle(X3));
%     figure;plot(fb,phs*180/pi)
%     %figure;plot(fb,(mod(phs*180/pi,360)))
%     xlabel 'Frequency (Hz)';xlim([0 2.5])
%     ylabel 'Phase (degrees)' %ylabel 'degrees' %
%     grid

X1=Yb;%store the FFT results in another array
%detect noise (very small numbers (eps)) and ignore them
[maxYb, maxin]=max((abs(Yb))/ly);
threshold = max((abs(Yb)))/2; %tolerance threshold
X1(abs(Yb)<threshold) = 0; %maskout values that are below the threshold
phase=atan2(imag(X1),real(X1))*180/pi; %phase information

%     figure;plot(fb,phase); %phase vs frequencies
%     %disp(['at ',num2str(),])
%     xlabel 'Frequency (Hz)';xlim([0 2.5])
%     ylabel 'Phase (degrees)' %ylabel 'degrees' %

disp(['Amax=',num2str(maxYb)])
fmax=fb(maxin);disp(['f for Amax=',num2str(fmax)])
phsmax=phase(maxin);disp(['phs for Amax=',num2str(phsmax)])
phs=phsmax;

%inverse fft test
%     X1i=ifft(X1);
%     figure;     plot(t,X1i)
%     hold on;    plot(t, y)