I have these two equation and I am trying to solve for theta 1 and theta 2, can someone explain why there are 2 solution for each theta?
syms th1 th2 px py eq1 = px == cos(th1+th2)+cos(th1)eq2 = py == sin(th1+th2)+sin(th1)sol = solve(eq1,eq2,th1,th2)syms th1 th2 px py eq1 = px == cos(th1+th2)+cos(th1)eq2 = py == sin(th1+th2)+sin(th1)sol = solve(eq1,eq2,th1,th2)th1 = simplify(sol.th1)th2 = simplify(sol.th2)
th1 =
2*atan((2*py + (- px^4 – 2*px^2*py^2 + 4*px^2 – py^4 + 4*py^2)^(1/2))/(px^2 + 2*px + py^2))
2*atan((2*py – (- px^4 – 2*px^2*py^2 + 4*px^2 – py^4 + 4*py^2)^(1/2))/(px^2 + 2*px + py^2))
th2 =
-2*atan((-(px^2 + py^2)*(px^2 + py^2 – 4))^(1/2)/(px^2 + py^2))
2*atan((-(px^2 + py^2)*(px^2 + py^2 – 4))^(1/2)/(px^2 + py^2))
Best Answer