How can i plot this graph?

I am trying to plot the graphs of y=-x mod 1 and y=-0.5*cos(2*pi*-x) mod 1. There are two issues here, for some reason there are points for eg x=0.25 where the y value should be 1 but instead theres a line between 0.25 to the next x value. Secondly MATLAB is plotting and straight line on x=0 for the line y=-x mod 1 which doesnt make sense. any help would be appreciated.

clear
clc
clf
syms x y

f1 = y == mod(-0.5*cos(2*pi*-x),1);
f2 = y == mod(-x,1);
%f3 = y == mod(-0.5*cos(2*pi*(-y)),1);
p1 = fimplicit(f1,[-0.5 1.8 0 1]);
hold on
p2 = fimplicit(f2,[-0.5 1.8 0 1]);
%p3= fimplicit(f3,[-2 2 0 1]);
hold off
fsize=15;
title('Intersection of curves','FontSize',fsize)
xlabel('x(t)','FontSize',fsize)
ylabel('y(t)','FontSize',fsize) 
%s=vpasolve(mod(y+0.5*cos(2*pi*y),1),mod(x+y,1),[1.7,0.5]);
%s.x
%s.y
% End of Program 05a.

Answer 1

[Walter Roberson]

symbolic mod() does not mean what you think it means. When you pass an expression, it takes the mod of each subexpression, leaving any variables untouched, and drops the mod. For example, mod(5*x,3) is 2*x and not mod(2*x,3)

You have to replace your mod() operations with remainder operations such as

mod(A,B) --> A - floor(A/B)*B

(You might need a different expression for negative values of B)

[ak]

Thanks for your reply. But replacing mod with floor produces the exact same graph.

[Walter Roberson]

syms x y
Mod = @(A,B) A - floor(A/B)*B;
f1 = y == Mod(-0.5*cos(2*pi*-x),1);
f2 = y == Mod(-x,1);
%f3 = y == mod(-0.5*cos(2*pi*(-y)),1);
p1 = fimplicit(f1,[-0.5 1.8 0 1]);
hold on
p2 = fimplicit(f2,[-0.5 1.8 0 1]);
%p3= fimplicit(f3,[-2 2 0 1]);
hold off
fsize=15;
title('Intersection of curves','FontSize',fsize)
xlabel('x(t)','FontSize',fsize)
ylabel('y(t)','FontSize',fsize) 

This does not produce the same graph as before for me.

[ak]

Ah, I see what you meant now...

It worked!! Thank you so much. You are an absolute HERO

Answer 2

[Marcel Kreuzberg]

clear
clc
clf
x = -0.5:0.001:1.8;
f2=mod(x,1);
f1=mod(-0.5*cos(2*pi*-x),1);
plot(x,f1,'.');
hold on
plot(x,f2,'.');
hold off
fsize=15;
title('Intersection of curves','FontSize',fsize)
xlabel('x(t)','FontSize',fsize)
ylabel('y(t)','FontSize',fsize)