Solve r=a(1-sine)

$$r = a ( 1 - \sin e )$$

Solve for a

$$a=-\frac{r}{\sin(e)-1}$$

Steps for Solving Linear Equation

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

$$a\left(1-\sin(e)\right)=r$$

Use the distributive property to multiply a by 1-\sin(e).

$$a-a\sin(e)=r$$

Combine all terms containing a.

$$\left(1-\sin(e)\right)a=r$$

The equation is in standard form.

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

Divide both sides by 1-\sin(e).

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

Dividing by 1-\sin(e) undoes the multiplication by 1-\sin(e).

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

Solve for r

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