Simplify a set of equations

Question

I have:

$A=-R_2\sin{t_0}$

$B=R_2\cos{t_0}$

$C=R_1\cos{t_0}$

$D=R_1\sin{t_0}$

So on the right side I have three variables ($R_1, R_2, t_0$) but on the left-side I have four variables. Is it correct to assume that it should be possible to have three variables on the left side as well? If so, how?

Answer 1

You can use substitution to eliminate one of the variables. From last equation you can extract $R_1=D/\sin t_0$. By plugging the result on the third one $$A=-R_2\sin{t_0}\\ B=R_2\cos{t_0}\\ D=C\tan t_0$$ you get three variables on the left $\{A,B,D\}$ and three on the right $\{R_2,t_0,C\}$