Is it possible to change the pole and/or the polar axis in a polar coordinate system? Citing Wikipedia's article on polar coordinates... > In mathematics, the polar coordinate system is a two-dimensional coordinate system in which each point on a plane is determined by a distance from a fixed point [pole] and an angle from a fixed direction [polar axis]. $x = r\cos{φ}$ $y = r\sin{φ}$ $r = \sqrt{x^2 + y^2}$ $φ = \arctan2{(y, x)}$ The article expounds further in the below image, with $O$ being the pole and $L$ being the polar axis. !enter image description here Is it possible to change the coordinate system's pole and/or polar axis (e.g., setting $-L$ as the polar axis)?

Yes this is possible, and is in fact done all the time. If you want the pole to be at $(x_0,y_0)$ you just make the following substitutions in your equations.

$$ x \rightarrow x-x_0$$ $$ y \rightarrow y-y_0$$

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**Edit:** To answer the question about changing the polar-axis.

One way this can be done is by rotating the coordinates so that the $x-axis$ is at an angle to what it used to be. To rotate the coordinates by and angle $\theta$ apply the transformation,

$$ x' = x \cos(\theta) - y \sin(\theta) $$ $$ y' = x \sin(\theta) + y \sin(\theta) $$

In that case what you would want to substitute into the polar coordinate equations is,

$$ x\rightarrow (x-x_0) \cos(\theta) - (y-y_0) \sin(\theta) $$ $$ y \rightarrow (x-x_0) \sin(\theta) + (y-y_0) \sin(\theta) $$