Solve r=a(sinθ+1)

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

Solve for a

$$\left\{\begin{matrix}a=\frac{r}{\sin(\theta )+1}\text{, }&\nexists n_{1}\in \mathrm{Z}\text{ : }\theta =2\pi n_{1}+\frac{3\pi }{2}\\a\in \mathrm{R}\text{, }&r=0\text{ and }\exists n_{1}\in \mathrm{Z}\text{ : }\theta =2\pi n_{1}+\frac{3\pi }{2}\end{matrix}\right.$$

Steps for Solving Linear Equation

Use the distributive property to multiply a by \sin(\theta )+1.

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

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

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

Combine all terms containing a.

$$\left(\sin(\theta )+1\right)a=r$$

Divide both sides by \sin(\theta )+1.

$$\frac{\left(\sin(\theta )+1\right)a}{\sin(\theta )+1}=\frac{r}{\sin(\theta )+1}$$

Dividing by \sin(\theta )+1 undoes the multiplication by \sin(\theta )+1.

$$a=\frac{r}{\sin(\theta )+1}$$

Solve for r

$$r=a\left(\sin(\theta )+1\right)$$