I have the following 2 equations with the unknowns: $S$ and $C$.
$v_1 = \displaystyle \frac{v}{2}\left(x_{1}S-x_{2}\sqrt{1-S^2}+x_{3}C-x_{4}\sqrt{1-C^2}\right)$
$v_2 = \displaystyle \frac{v}{2}\left(y_{1}S-y_{2}\sqrt{1-S^2}+y_{3}C-y_{4}\sqrt{1-C^2}\right)$
Initial I had 2 equations written using $\cos$ and $\sin$ functions, but I managed to rewrite them and bringing them to this algebraic form. Any idea or solution to find out $S$ and $C$ is very welcoming.