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

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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.