Solve r=sqrt{1-2θ}

$$r = \sqrt { 1 - 2 \theta }$$

Solve for θ

$$\theta =\frac{1-r^{2}}{2}$$

$$r\geq 0$$

Steps for Solving Radical Equations

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

$$\sqrt{1-2\theta }=r$$

Square both sides of the equation.

$$-2\theta +1=r^{2}$$

Subtract 1 from both sides of the equation.

$$-2\theta +1-1=r^{2}-1$$

Subtracting 1 from itself leaves 0.

$$-2\theta =r^{2}-1$$

Divide both sides by -2.

$$\frac{-2\theta }{-2}=\frac{r^{2}-1}{-2}$$

Dividing by -2 undoes the multiplication by -2.

$$\theta =\frac{r^{2}-1}{-2}$$

Divide r^{2}-1 by -2.

$$\theta =\frac{1-r^{2}}{2}$$

Solve for θ (complex solution)

$$\theta =\frac{1-r^{2}}{2}$$

$$arg(r)<\pi \text{ or }r=0$$

Solve for r

$$r=\sqrt{1-2\theta }$$

$$\theta \leq \frac{1}{2}$$