# Thread: solving a system of transcendental equations

1. ## solving a system of transcendental equations

hi,
I want to solve the system of three transcendental equations for A, B & C.

0.97*cos(B)*cos(C)-0.18*cos(B)*sin(C)+ 0.01*sin(B)=0.6304

0.97*(-cos(A)*sin(C)-sin(A)*sin(B)*cos(C))-0.18*cos(A)*cos(C)+sin(A)*sin(B)*sin(C))-0.01*(sin(A)*cos(B))=0.7235

0.97*(sin(A)*sin(C)+cos(A)*sin(B)*cos(C)-0.18*-sin(A)*cos(C)+cos(A)*sin(B)*sin(A))-0.01*(cos(A)*cos(B))= -0.2981

Kindly suggest any analytical or numerical way of solving it. I have already tried the symbolic toolbox in matlab and it gives incomprehensible solutions.
I also tried eliminating A from equations ----2 and ----3 and solving the resultant two equations. This approach results in 0=0 kind of problem.

Yours Truely
Ganesh

2. Originally Posted by ganesh_lg
hi,
I want to solve the system of three transcendental equations for A, B & C.

0.97*cos(B)*cos(C)-0.18*cos(B)*sin(C)+ 0.01*sin(B)=0.6304

0.97*(-cos(A)*sin(C)-sin(A)*sin(B)*cos(C))-0.18*cos(A)*cos(C)+sin(A)*sin(B)*sin(C))-0.01*(sin(A)*cos(B))=0.7235

0.97*(sin(A)*sin(C)+cos(A)*sin(B)*cos(C)-0.18*-sin(A)*cos(C)+cos(A)*sin(B)*sin(A))-0.01*(cos(A)*cos(B))= -0.2981

Kindly suggest any analytical or numerical way of solving it. I have already tried the symbolic toolbox in matlab and it gives incomprehensible solutions.
I also tried eliminating A from equations ----2 and ----3 and solving the resultant two equations. This approach results in 0=0 kind of problem.

Yours Truely
Ganesh
This is not the most elegant method of doing this, but is certainly the fastest.

Rewrite your equations in the form:

$f_1(A,B,C)=0$
$f_2(A,B,C)=0$
$f_3(A,B,C)=0$

Form the objective function:

$
O(A,B,C) =f_1(A,B,C)^2+f_2(A,B,C)^2+f_3(A,B,C)^2
$

Then use the Excel solver to minimise $O$. One result of this are:

$A\approx3.46,\ B\approx -3.07,\ C\approx 2.08$

However I doubt that if this is an approximation to an exact solution that the exact solution is unique. (to the machine prescission this is a solution and to the same prescission it is not unique).

An approximate solution with all variables in the range $\pm \pi$ is:

$A\approx 0.092,\ B \approx -0.370,\ C\approx -0.994$

CB