Solve tanalpha=b/a

$$\tan \alpha = \frac { b } { a }$$

Solve for a

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

Steps for Solving Linear Equation

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

$$a\tan(\alpha )=b$$

The equation is in standard form.

$$\tan(\alpha )a=b$$

Divide both sides by \tan(\alpha ).

$$\frac{\tan(\alpha )a}{\tan(\alpha )}=\frac{b}{\tan(\alpha )}$$

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

$$a=\frac{b}{\tan(\alpha )}$$

Divide b by \tan(\alpha ).

$$a=b\cot(\alpha )$$

Variable a cannot be equal to 0.

$$a=b\cot(\alpha )\text{, }a\neq 0$$

Solve for b

$$b=a\tan(\alpha )$$

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