Bug
The bug was a sampling rate that was too low. Ts = 0.07s while the frequency of the sinusoid was 13Hz. Therefore the period of the sinusoid is 1/13 = 0.077 s. With the sampling rate being roughly the same as the period it is little wonder that most of the signal was not captured.
Modified code
F0 = 13;
T0 = 1/F0;
Ts = 0.001;
t = 0:Ts:13*T0;
x = real(exp(j*(2*pi*F0*t-pi/2)));
plot(t,x)
Wanted waveform
