Not sure how to solve equations using newton-Raphson method

Can anyone help me solve these two equation using newton-raphson method

5/2*cos(x(1))+3*cos(x(1)+x(2))-5

5/2*sin(x(1))+3*sin(x(1)+x(2))-2

[Sulaymon Eshkabilov]

Could you pl., show what you have done so far?

[KSSV]

Hints: https://de.mathworks.com/matlabcentral/answers/459048-finding-the-roots-of-equation-by-newton-raphson-method

[Matthew Worker]

iter = 0;

x = input('Enter intiial value ');

Dx = [10; 10];

C=[5; 2];

disp('Iter DC Jacobian matrix Dx x');

while max(abs(Dx)) >= 0.0001 & iter <10

iter=iter+1;

f = [5/2*cos(x(1))+3*cos(x(1)+x(2)); 5/2*sin(x(1))+3*sin(x(1)+x(2))];

DC = C -f;

J = [-5/2*sin(x(1)) -3*sin(x(1)+x(2))

5/2*cos(x(1)) 3*cos(x(1)+x(2))]

Dx=J\DC

x=x+Dx

end

Answer 1

[Monisha Nalluru]

From my understanding you are trying to solve the multi variable equations. The equation followed is

As a example

X0=[1;1]; %inital guess
toleX=1e-4; %tolerance

X = X0;
Xold = X0;

while true
    [f,j]=systemequ(X);
    X = X - inv(j)*f;
    err = abs(X-Xold);
    Xold = X;
    if(err < toleX) %checking the error and tolerance
        break
    end    
end

function [fval,jac]= systemequ(X) %funtion return f(Xn) and jacobian value

x=X(1);
y=X(2);

fval(1,1)=5/2*cos(x)+3*cos(x+y)-5;
fval(2,1)=5/2*sin(x)+3*sin(x+y)-2;

jac=[-5/2*sin(x) -sin(x+y);
    5/2* cos(x) 3*cos(x+y)];
end