Solve varepsilon=4operatorname{acos}θ

$$\varepsilon = 4 \operatorname { acos } \theta$$

Solve for a

$$\left\{\begin{matrix}a=\frac{\epsilon }{4\cos(\theta )}\text{, }&\nexists n_{1}\in \mathrm{Z}\text{ : }\theta =\pi n_{1}+\frac{\pi }{2}\\a\in \mathrm{R}\text{, }&\epsilon =0\text{ and }\exists n_{1}\in \mathrm{Z}\text{ : }\theta =\pi n_{1}+\frac{\pi }{2}\end{matrix}\right.$$

Steps for Solving Linear Equation

Swap sides so that all variable terms are on the left hand side.

$$4a\cos(\theta )=\epsilon$$

The equation is in standard form.

$$4\cos(\theta )a=\epsilon$$

Divide both sides by 4\cos(\theta ).

$$\frac{4\cos(\theta )a}{4\cos(\theta )}=\frac{\epsilon }{4\cos(\theta )}$$

Dividing by 4\cos(\theta ) undoes the multiplication by 4\cos(\theta ).

$$a=\frac{\epsilon }{4\cos(\theta )}$$

Solve for ε

$$\epsilon =4a\cos(\theta )$$