Solve for x
\left\{\begin{matrix}x=y\cot(ϕ)\text{, }&\exists n_{3}\in \mathrm{Z}\text{ : }\left(ϕ>\frac{\pi n_{3}}{2}\text{ and }ϕ<\frac{\pi n_{3}}{2}+\frac{\pi }{2}\right)\\x\in \mathrm{R}\text{, }&y=0\text{ and }\exists n_{2}\in \mathrm{Z}\text{ : }ϕ=\pi n_{2}\text{ and }\nexists n_{1}\in \mathrm{Z}\text{ : }ϕ=\pi n_{1}+\frac{\pi }{2}\end{matrix}\right.
Solve for y
y=x\tan(ϕ)
\nexists n_{1}\in \mathrm{Z}\text{ : }ϕ=\pi n_{1}+\frac{\pi }{2}
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x\tan(ϕ)=y
Swap sides so that all variable terms are on the left hand side.
\tan(ϕ)x=y
The equation is in standard form.
\frac{\tan(ϕ)x}{\tan(ϕ)}=\frac{y}{\tan(ϕ)}
Divide both sides by \tan(ϕ).
x=\frac{y}{\tan(ϕ)}
Dividing by \tan(ϕ) undoes the multiplication by \tan(ϕ).
x=y\cot(ϕ)
Divide y by \tan(ϕ).
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