Solve Tg(varphi)=Q/P

$$T g ( \varphi ) = \frac { Q } { P }$$

Solve for P

$$\left\{\begin{matrix}P=Q\cot(\phi )\text{, }&\exists n_{2}\in \mathrm{Z}\text{ : }\left(\phi >\frac{\pi n_{2}}{2}\text{ and }\phi <\frac{\pi n_{2}}{2}+\frac{\pi }{2}\right)\text{ and }Q\neq 0\\P\neq 0\text{, }&\exists n_{1}\in \mathrm{Z}\text{ : }\phi =\pi n_{1}\text{ and }Q=0\end{matrix}\right.$$

Steps for Solving Linear Equation

Variable P cannot be equal to 0 since division by zero is not defined. Multiply both sides of the equation by P.

$$P\tan(\phi )=Q$$

The equation is in standard form.

$$\tan(\phi )P=Q$$

Divide both sides by \tan(\phi ).

$$\frac{\tan(\phi )P}{\tan(\phi )}=\frac{Q}{\tan(\phi )}$$

Dividing by \tan(\phi ) undoes the multiplication by \tan(\phi ).

$$P=\frac{Q}{\tan(\phi )}$$

Divide Q by \tan(\phi ).

$$P=Q\cot(\phi )$$

Variable P cannot be equal to 0.

$$P=Q\cot(\phi )\text{, }P\neq 0$$

Solve for Q

$$Q=P\tan(\phi )$$

$$\nexists n_{1}\in \mathrm{Z}\text{ : }\phi =\pi n_{1}+\frac{\pi }{2}\text{ and }P\neq 0$$