Solve for r (complex solution)
\left\{\begin{matrix}r=\frac{1-y}{\sin(x)}\text{, }&\nexists n_{1}\in \mathrm{Z}\text{ : }x=\pi n_{1}\\r\in \mathrm{C}\text{, }&y=1\text{ and }\exists n_{1}\in \mathrm{Z}\text{ : }x=\pi n_{1}\end{matrix}\right.
Solve for r
\left\{\begin{matrix}r=\frac{1-y}{\sin(x)}\text{, }&\nexists n_{1}\in \mathrm{Z}\text{ : }x=\pi n_{1}\\r\in \mathrm{R}\text{, }&y=1\text{ and }\exists n_{1}\in \mathrm{Z}\text{ : }x=\pi n_{1}\end{matrix}\right.
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1-r\sin(x)=y
Swap sides so that all variable terms are on the left hand side.
-r\sin(x)=y-1
Subtract 1 from both sides.
\left(-\sin(x)\right)r=y-1
The equation is in standard form.
\frac{\left(-\sin(x)\right)r}{-\sin(x)}=\frac{y-1}{-\sin(x)}
Divide both sides by -\sin(x).
r=\frac{y-1}{-\sin(x)}
Dividing by -\sin(x) undoes the multiplication by -\sin(x).
r=-\frac{y-1}{\sin(x)}
Divide y-1 by -\sin(x).
1-r\sin(x)=y
Swap sides so that all variable terms are on the left hand side.
-r\sin(x)=y-1
Subtract 1 from both sides.
\left(-\sin(x)\right)r=y-1
The equation is in standard form.
\frac{\left(-\sin(x)\right)r}{-\sin(x)}=\frac{y-1}{-\sin(x)}
Divide both sides by -\sin(x).
r=\frac{y-1}{-\sin(x)}
Dividing by -\sin(x) undoes the multiplication by -\sin(x).
r=-\frac{y-1}{\sin(x)}
Divide y-1 by -\sin(x).
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