Solve r=2asin^2θ

$$r = 2 a \sin ^ { 2 } \theta$$

Solve for a

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

Steps for Solving Linear Equation

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

$$2a\left(\sin(\theta )\right)^{2}=r$$

The equation is in standard form.

$$2\left(\sin(\theta )\right)^{2}a=r$$

Divide both sides by 2\left(\sin(\theta )\right)^{2}.

$$\frac{2\left(\sin(\theta )\right)^{2}a}{2\left(\sin(\theta )\right)^{2}}=\frac{r}{2\left(\sin(\theta )\right)^{2}}$$

Dividing by 2\left(\sin(\theta )\right)^{2} undoes the multiplication by 2\left(\sin(\theta )\right)^{2}.

$$a=\frac{r}{2\left(\sin(\theta )\right)^{2}}$$

Solve for r

$$r=2a\left(\sin(\theta )\right)^{2}$$