Convert to Rectangular r=1/(1-cos(x))

$r = \frac{1}{1 - \cos (x)}$

Step 1

Multiply both sides by $r$ .

$r \cdot r = r \frac{1}{1 - \cos (x)}$

Simplify the left side.

Multiply $r$ by $r$ .

$r^{2} = r \frac{1}{1 - \cos (x)}$

Simplify the right side.

Combine $r$ and $\frac{1}{1 - \cos (x)}$ .

$r^{2} = \frac{r}{1 - \cos (x)}$

Step 2

Since $r^{2} = x^{2} + y^{2}$ , replace $r^{2}$ with $x^{2} + y^{2}$ and $r$ with $\sqrt{x^{2} + y^{2}}$ .

$x^{2} + y^{2} = \frac{\sqrt{x^{2} + y^{2}}}{1 - \cos (x)}$