Question

Using MATLAB and bisection

Find the first 10 roots of the function y(x) = cos(5x).

Note you will need to have a script file that steps along the x-axis and calls bisect when a root bracket is found.

Answer 1

`Hey,

Note: If you have any queries related the answer please do comment. I would be very happy to resolve all your queries.

clc%clears screen
clear all%clears history
close all%closes all files
format long
f=@(x) cos(5*x);
findroots(0:0.1:6,f,1e-5)
function R=findroots(x,f,tol)

R=[];
a=x(1);
count=1;
for kk=1:length(x)
if(f(a)*f(x(kk))<0)
b=x(kk);
iter = 0;
  
if f(a)*f(b)>=0

disp('No Root')

else

prev = (a+b)/2;
p=a;
while (abs(f(p))>tol)
prev=p;

iter =iter+ 1;

p = (a+b)/2;

if f(p) == 0
  
break;

end

if f(a)*f(p)<0

b = p;

else

a = p;

end
if(iter==100)
disp('the required accuracy is not reached in 50 iterations');
end
end

end
R(count)=p;
count=count+1;
a=x(kk);
else
a=x(kk);
end

end
end

Kindly revert for any queries

Thanks.