Phase angle is producing an error

Hi, I am getting a phase error on my waveform it is not quite reaching +pi or -pi in some cases(not everytime which I find strange). I think its leading to significant problems in other modules of my code. I have pin point the error to display quite nicely below. What is causing that?

clear all

% -- Controls --
f=5
Fs =100*f;    
Ts = 1/Fs;      
dt = 0 : Ts : 10/f;

% -- Waveform --
waveform =  exp(1*i*((2*pi .* f .* dt) ))  ;
waveform = waveform';

% -- Inspect Phase --
for a=1:length(waveform)
    waveform_phase(a) =  angle(waveform(a)); %radians 
end

plot shows theres an error in phase, it is sometimes off the correct value of +pi or -pi

The below code has hline and vline - remove them if you don't have them but its more difficult to see the error

figure(1);cla;clf;
ax=gca; set(gca,'Fontsize',7)

yyaxis left
plot(dt,waveform_phase,'b','displayname','input phase','MarkerSize',4)
set(gca,'YTick',-pi:pi/2:pi) 
set(gca,'YTickLabel',{'-\pi',' ','0',' ','\pi'})
ylabel('Phase (Radians)','Fontsize',7);
hline(pi,'--b')
hline(-pi,'--b')

yyaxis right
hold on
plot(dt,waveform,'r','displayname','input waveform')
set(gca) 
ylim([min(real(waveform)) max(real(waveform))])
ylabel('Amplitude (V)','Fontsize',7);
hline(min(real(waveform)),'--r')
hline(max(real(waveform)),'--r')

legend('show','Location','southeast')

xlim([0 dt(end)/2])
xlabel('Time ','Fontsize',7);

Also If I increase sampling frequency its not noticeable by eye on the plot and the error is small, but still has effects in my overall code. I cant be having a sampling frequency 10000 above the max frequency to just measure phase?

[Adam]

When I plot that I am not seeing a problem. For every trough the phase is either +pi or -pi. It is true it is not consistent as to which it is, but since they are the same thing is that a problem?

[Nathan Kennedy]

I've attached an image showing it from the script I uploaded. I added arrows in windows paint to show.. cant be just me?

I changed the marking style to a single line instead of stars, the error can be seen clearly?

Also If I increase sampling frequency its not noticeable by eye on the plot and the error is small, but still has effects in my overall code. I cant be having a sampling frequency 10000 above the max frequency to just measure phase?

[Adam]

Yes, I get that also, but the value for that point is at precisely -pi which is the same thing as +pi as an angle. As you can see, you have placed exactly one arrow per trough, because each has its result at either +pi or -pi, which is what I said in my previous comment. It is not consistent, probably down to the vagueries of the fact that it is a discrete signal and in floating point accuracy so flips between -pi and +pi can happen in the same way you sometimes see things like -0 as well as 0.

If you unwrap the phase then it would be perfectly consistent.

[Nathan Kennedy]

Hi I tried using the unwrap function and it was not giving me a smooth plot. how isit implemented with my code?