Solve r=a(1quadsinθ)

$$r = a ( 1 \quad \sin \theta )$$

Solve for a

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

Steps for Solving Linear Equation

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

$$a\times 1\sin(\theta )=r$$

The equation is in standard form.

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

Divide both sides by \sin(\theta ).

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

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

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

Solve for r

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