Solve cosalpha=a/b

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

Solve for b

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

Steps for Solving Linear Equation

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

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

The equation is in standard form.

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

Divide both sides by \cos(\alpha ).

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

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

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

Variable b cannot be equal to 0.

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

Solve for a

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

$$b\neq 0$$