Roots of a function

I have two equations:

y1 = 2sinx1;

y2 = 2cos^2(x1) + 3sin(2x2+3);

here y1 = 0 while y2 = 1.

Can anyone please tell me which approach would be the best to find out the values of x1 and x2.

Thank you.

[Torsten]

x1=0
x2=(asin(-1/3)-3)/2

Best wishes

Torsten.

Answer 1

[Torsten]

Try this:

function driver
y=zeros(1,2);
y(1)=0;
y(2)=1;
x0=zeros(1,2);
x=fsolve(@(x)HW1(x,y),x0)

function res = HW1(x,y)
res(1)=y(1)-2*sin(x(1));
res(2)=y(2)-(2*cos(x(1))^2 + 3*sin(2*x(2) + 3));

Best wishes

Torsten.

[Muhammad Umar Farooq]

Thanks a lot. It works perfectly well. I am really thankful to you.

I am new to Matlab. Can you tell me which optimization will let me find the unique values of x1 and x2 for the given values of y1 and y2. If I change the interval from [0 0] to [2 2] it finds the zeros between this interval.

[Torsten]

Your equations don't have a unique solution. So - depending on the starting guess x0 - you'll get different solutions for x. Do you have any condition on x that could make the solution unique ?

Best wishes

Torsten.

Answer 2

[Vlad Miloserdov]

if you still need this

A=solve('0 = 2*sin(x1)','1 = 2*cos(x1)^2 + 3*sin(2*x2+3)','x1','x2');
% first ans
A.x1(1)
A.x2(1)
% second ans
A.x1(2)
A.x2(2)

[Muhammad Umar Farooq]

Thank you for your answer.

Yes, It solves the equation but I want to do this using optimization. Maybe fzero or something. I made a function but when I use fzero or some other optimization method it gives the error of not enough input arguments.

Thank you.

[Torsten]

You have two equations - thus you will need MATLAB's "fsolve".

Best wishes

Torsten.

[Muhammad Umar Farooq]

Yes, Thank you.

I have tried to use fsolve when I input the function, I get an error of not enough input arguments and the optimization stops.

[Torsten]

Please show your code.

Best wishes

Torsten.

[Muhammad Umar Farooq]

function [y1,y2] = HW1(x1,x2)

y1 = 2*sin(x1);

y2 = 2*cos(x1)^2 + 3*sin(2*x2 + 3);

end

I call this function HW1 from optimization tool box and it stops after giving error of not enough input arguments.

Thank you for your help. I am stuck for two days with this error.