Polar/Rectangular Equation Calculator
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, $$$r = 2 \sqrt{2} \sin{\left(\theta + \frac{\pi}{4} \right)}$$$.