Solve y=rcosθ

$$y = r \cos \theta$$

Solve for r

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

Steps for Solving Linear Equation

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

$$r\cos(\theta )=y$$

The equation is in standard form.

$$\cos(\theta )r=y$$

Divide both sides by \cos(\theta ).

$$\frac{\cos(\theta )r}{\cos(\theta )}=\frac{y}{\cos(\theta )}$$

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

$$r=\frac{y}{\cos(\theta )}$$

Solve for y

$$y=r\cos(\theta )$$