# Polar/Rectangular Equation Calculator

## Convert equations between polar and rectangular coordinates step by step

The calculator will convert the polar equation to rectangular (Cartesian) and vice versa, with steps shown.

Related calculator: Polar/Rectangular Coordinates Calculator

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Convert $\left(x - 1\right)^{2} + \left(y - 1\right)^{2} = 2$ to polar coordinates.

### Solution

In polar coordinates, $x = r \cos{\left(\theta \right)}$ and $y = r \sin{\left(\theta \right)}$.

Thus, the input can be rewritten as $\left(r \sin{\left(\theta \right)} - 1\right)^{2} + \left(r \cos{\left(\theta \right)} - 1\right)^{2} = 2$.

Simplify: the input now takes the form $r \left(r - 2 \sqrt{2} \sin{\left(\theta + \frac{\pi}{4} \right)}\right) = 0$.

Thus, $r = 2 \sqrt{2} \sin{\left(\theta + \frac{\pi}{4} \right)}$.

$\left(x - 1\right)^{2} + \left(y - 1\right)^{2} = 2$A in polar coordinates is $r = 2 \sqrt{2} \sin{\left(\theta + \frac{\pi}{4} \right)}$A.