# Solve a system of equations in polar coordinate?

GROUPS:
 My system contains 6 equations and 6 unknowns in polar coordinate and I wrote them in Cartesian coordinates and now 3 of the unknowns are the radii and 3 of them are angels. But I am not sure if I write the angles in the correct format. This code runs but solutions are not correct since by changing the initial values the answers stay the same. Here is my code: ClearAll; s1 = 0.067; theta1 = -152 Degree; s2 = 0.015; theta2 = -130 Degree; s3 = 0.0078; theta3 = -165 Degree; exp1 = ExpandAll[ s1*Cos[theta1 Degree] - s1*s*Cos[theta1 Degree + thetas Degree + 180 Degree] - d*Cos[thetad Degree] + d*s*Cos[thetad Degree + thetas Degree + 180 Degree] == 1 - r*Cos[thetar Degree + 180 Degree]]; exp2 = ExpandAll[ s2*Cos[theta2 Degree] - (0.3)*s2*s* Cos[theta2 Degree + thetas Degree + 180 Degree] - d*Cos[thetad Degree] + (0.3)*d*s* Cos[thetad Degree + thetas Degree + 180 Degree] == (0.3) - (0.3)*r* Cos[thetar Degree + 180 Degree]]; exp3 = ExpandAll[ s3*Cos[theta3 Degree] - (0.0001)*s3*s* Cos[theta3 Degree + thetas Degree] - d*Cos[thetad Degree] + (0.0001)*d*s* Cos[thetad Degree + thetas Degree] == (0.0001) - (0.0001)*r* Cos[thetar Degree]]; exp4 = ExpandAll[ s1*Sin[theta1 Degree] - s1*s*Sin[theta1 Degree + thetas Degree + 180 Degree] - d*Sin[thetad Degree] + d*s*Sin[thetad Degree + thetas Degree + 180 Degree] == 1 - r*Sin[thetar Degree + 180 Degree]]; exp5 = ExpandAll[ s2*Sin[theta2 Degree] - (0.3)*s2*s* Sin[theta2 Degree + thetas Degree + 180 Degree] - d*Sin[thetad Degree] + (0.3)*d*s* Sin[thetad Degree + thetas Degree + 180 Degree] == (0.3) - (0.3)*r* Sin[thetar Degree + 180 Degree]]; exp6 = ExpandAll[ s3*Sin[theta3 Degree] - (0.0001)*s3*s* Sin[theta3 Degree + thetas Degree] - d*Sin[thetad Degree] + (0.0001)*d*s* Sin[thetad Degree + thetas Degree] == (0.0001) - (0.0001)*r* Sin[thetar Degree]]; v = Total[{exp1, exp2, exp3, exp4, exp5, exp6} /. Equal[l_, r_] -> Norm[1 - (r)]]; NMinimize[v, {s, thetas, r, thetar, d, thetad}, MaxIterations -> 10^3]