MATLAB: How can i plot this graph

modular arithmeticplot

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.

Best Answer

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)
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