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Two equations of two unknown angles

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If I have:
A = 87; B = 65; C = 73; D = 92;
And the two equations are:
D*sin(200)+A*sin(x)+B*sin(y)=0;73+D*cos(200)+A*cos(x)+B*cos(y)=0
How do I write a code to find x and y?
What is the solution to this error?
  2 Comments
Ravichandar Nalukurthy
Ravichandar Nalukurthy on 23 Feb 2021
Thank you, however I still get the invalid expression error.

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Accepted Answer

John D'Errico
John D'Errico on 23 Feb 2021
Edited: John D'Errico on 23 Feb 2021
First, I would recognize that you PROBABLY intended 200 to be a number in DEGREES, not radians. (200 radians would seem to make little sense.) Therefore, you need to use sind and cosd, not sin and cos.
Since you know how to use solve, (sort of) I'll do it that way.
syms x y
A = 87; B = 65; C = 73; D = 92;
E1 = D*sind(200)+A*sind(x)+B*sind(y) == 0
E1 = 
E2 = 73+D*cosd(200)+A*cosd(x)+B*cosd(y) == 0
E2 = 
As you can see, sind and cosd convert the problem internally into one in radians. The x and y solutions will still be in the form of degrees though.
[xsol,ysol] = solve(E1,E2,x,y)
xsol = 
ysol = 
vpa(xsol)
ans = 
vpa(ysol)
ans = 
These will be angles in degrees, since I used sind and cosd. There are two primary solutions, but there are infinitely many solutions. We could add integer multiples of 360 degrees to those solutions.

More Answers (1)

David Hill
David Hill on 23 Feb 2021
fun = @solution;
x0 = [0,0];
I = fsolve(fun,x0);%solution
function f = solution(x)
A=87;B=65;D=92;
f(1)=D*sin(200)+A*sin(x(1))+B*sin(x(2));
f(2)=73+D*cos(200)+A*cos(x(1))+B*cos(x(2));
end

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