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.