# 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

### Your Input

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

### Answer

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