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## How to Solve a Nonlinear System of Equations with Sine and Cosine?

Hey everyone, I have a system of equations that is kind of complex, and would like to create a generic solution for it, but I am not sure if this is possible. I have 6 equations, and only 4 unknowns. These equations are describing a physical system, so there is a solution to the problem, and will always be a solution given the imputs from the physical system. All of the equations are of the form: A+B*Sin(theta1)+C*Sin(theta2)+D*Cos(theta1)+E*Cos(theta2)+F*Sin(theta1)*Sin(theta2)+G*Cos(theta1)*Cos(theta2)+H*Sin(theta1)*Cos(theta2)+I*Cos(theta1)*Sin(theta2)=J+K*Sin(theta3)+L*Sin(theta4)+M*Cos(theta3)+N*Cos(theta4)+O*Sin(theta3)*Sin(theta4)+P*Cos(theta3)*Cos(theta4)+Q*Sin(theta3)*Cos(theta4)+R*Cos(theta3)*Sin(theta4) All 6 equations are in this form, with different coeeficients A through R. I have the equations for all the coefficients, and am only looking for theta1 through theta4. All the thetas should be between 0 and 2pi(). I would have what the angles actually are +/- 20 degrees. If I leave the system unconstrained in Maple, it crunches for a long time, but never finishes, when I give it the starting point +/- 20 degrees it can find it almost instantly. The problem I have is that I need a way to solve it without using any of the built in solve functions. I need to port this problem into C++ code, written by myself (can't be a library to solve nonlinear equations) because it will then be converted into machine code, and I can't include a library in that. Any ideas on where I should go with this? John Vickers

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