Solve r=a(3-sinθ)

$$r = a ( 3 - \sin \theta )$$

Solve for a

$$a=-\frac{r}{\sin(\theta )-3}$$

Steps for Solving Linear Equation

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

$$a\left(3-\sin(\theta )\right)=r$$

Use the distributive property to multiply a by 3-\sin(\theta ).

$$3a-a\sin(\theta )=r$$

Combine all terms containing a.

$$\left(3-\sin(\theta )\right)a=r$$

The equation is in standard form.

$$\left(-\sin(\theta )+3\right)a=r$$

Divide both sides by 3-\sin(\theta ).

$$\frac{\left(-\sin(\theta )+3\right)a}{-\sin(\theta )+3}=\frac{r}{-\sin(\theta )+3}$$

Dividing by 3-\sin(\theta ) undoes the multiplication by 3-\sin(\theta ).

$$a=\frac{r}{-\sin(\theta )+3}$$

Solve for r

$$r=-a\left(\sin(\theta )-3\right)$$