Why does the length of the tangent line keep changing?

I'm new to Matlab, and I am making a code to animate the tangent line of sine as it moves along the graph. I am not sure why the length of the line keeps changing as it moves along the curve or how to fix the error I keep getting an error message in line 34 (the one that reads "an.XData = x2;") that states "Invalid or deleted object." Thanks in advance!

Here is my code:

n = 1000;
x = linspace(0,2*pi,n+1);
r = false;

hold on
y = sin(x);
plot(x,y)
hold off

xlim([0 2*pi])
ylim([-1.1 1.1])

x0 = 0;
y0 = sin(x0); 
len = 0.7;
m = cos(x0);
theta = atan(m);
x2 = [(x0 + len*cos(theta)), (x0 - len*cos(theta))];
y2 = [(y0 + len*sin(theta)), (y0 - len*sin(theta))]; 

an = line(x2,y2);
c = an.Color;
an.Color = '#4DBEEE';

i = 1;

while (i <= n)  
    x0 = (i/n)*2*pi;
    y0 = sin(x0);
    m = cos(x0);
    theta = atan(m);
    x2 = [(x0 + len*cos(theta)), (x0 - len*cos(theta))];
    y2 = [(y0 + len*sin(theta)), (y0 - len*sin(theta))]; 
    an.XData = x2;
    an.YData = y2;
    
    hold on
    drawnow
    
    if ~r
        i = i + 1;
        if i == n
            r = true;
        end
    else 
        i = i - 1;
        if i == 0
            r = false;
        end
    end     
end

hold off

Answer 1

[Adam Danz]

"Why does the length of the tangent line keep changing?"

The length is not changing. The reason it appears to change is because the aspect ratio between the x and y axes are not equal so as the line becomes more vertical it is stretched along the y axis since the y axis itself is streched relative to the x axis. To fix that, add this line below before your while-loop.

axis equal

"I keep getting an error message in line 34 (the one that reads "an.XData = x2;") that states "Invalid or deleted object."

That error doesn't occur unless you close your figure while the while-loop is running. The object is deleted when you delete the figure so the an.XData no longer exists.

To prevent that error, add a condition in the while-loop that requires the figure to exist. That will require a few changes:

% 1) at the top of your code
fh = figure();  % you need the figure handle (fh)

% 2) The while-loop should require that the figure exists
while (i <= n) && isvalid(fh)
   
% 3) Require that the figure exists just before accessing the figure
%    Put this just before an.XData = x2; 
    if ~isvalid(fh)
        continue
    end
    
% 4) The 'hold on' should be moved out of the loop, just prior to the loop

% 5) The 'hold off' at the end will create a new, empty figure or will change 
%    the hold state of the next existing figure.  Just get rid of it.  If you 
%    need it, add another condition after the while-loop that checks if the 
%    figure (fh) exists. 

[Pauline Wang]

Thank you so much for your help! The code worked perfectly with your suggestions.

[Adam Danz]

Great! Glad I could help!