Solve r=Q(1-sinθ)

$$r = Q ( 1 - \sin \theta )$$

Solve for Q

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

Steps for Solving Linear Equation

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

$$Q\left(1-\sin(\theta )\right)=r$$

Use the distributive property to multiply Q by 1-\sin(\theta ).

$$Q-Q\sin(\theta )=r$$

Combine all terms containing Q.

$$\left(1-\sin(\theta )\right)Q=r$$

The equation is in standard form.

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

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

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

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

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

Solve for r

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