Solve cosx/4=c/n

$$\cos \frac { x } { 4 } = \frac { c } { n }$$

Solve for n

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

Steps for Solving Linear Equation

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

$$n\cos(\frac{x}{4})=c$$

The equation is in standard form.

$$\cos(\frac{x}{4})n=c$$

Divide both sides by \cos(\frac{1}{4}x).

$$\frac{\cos(\frac{x}{4})n}{\cos(\frac{x}{4})}=\frac{c}{\cos(\frac{x}{4})}$$

Dividing by \cos(\frac{1}{4}x) undoes the multiplication by \cos(\frac{1}{4}x).

$$n=\frac{c}{\cos(\frac{x}{4})}$$

Variable n cannot be equal to 0.

$$n=\frac{c}{\cos(\frac{x}{4})}\text{, }n\neq 0$$

Solve for c

$$c=n\cos(\frac{x}{4})$$

$$n\neq 0$$