Write a Matlab program called iterate.m which plots the curves y=x and y=cos(x)

Question

Write a Matlab program called iterate.m which plots the curves y=x and y=cos(x) on the same plot for x values between 0 and 1.5, then uses iteration to find the solution with x>0 to the equation

x = cos(x)

For the iteration loop, you will need to choose an appropriate initial value of x and an appropriate number of iteration steps.

For this problem, upload the file iterate.m

Ihave plotted them, but when it comes to the iteration i do not get the right answer. This is my program,

x-values

x= 0:.01:1.5;

% equations of curves

y1 = x;

y2 = cos(x);

%plotting for both curves

plot(x,y1,'r');

hold on

plot(x,y2,'g');

for x=(0.1:0.001:2);

   x=cos(x);

end

disp(x)

Explanation / Answer

clc

clear

x= 0:.01:1.5;

% equations of curves

y1 = x;

y2 = cos(x);

%plotting for both curves

plot(x,y1,'r');

hold on

plot(x,y2,'g');

xlabel('x')

ylabel('y')

legend('y = x','y = cos(x)')

x0 = 0.5; %initial value of x

err = 1; %error term. Value of err = 1 is assigned just to initialize the loop,

%later the error will be calculated after each iteration

while err>10^(-5) %loop will work untill the error is less than 0.00001

x1 = x0;

x0 = cos(x0);

err = abs(x1-x0);

end

a = sprintf('solution of x=cos(x) is at x = %1.5f ',x0);

disp(a)

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