Solve cosθ=rsinθ

$$\cos \theta = r \sin \theta$$

Solve for r

$$r=\cot(\theta )$$

$$\nexists n_{1}\in \mathrm{Z}\text{ : }\theta =\pi n_{1}$$

Steps for Solving Linear Equation

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

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

The equation is in standard form.

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

Divide both sides by \sin(\theta ).

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

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

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

Divide \cos(\theta ) by \sin(\theta ).

$$r=\cot(\theta )$$