Confusion about how the transition between Cartesian and polar coordinates is done

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So right now, I'm really confused with polar coordinates. Being really familiar with the ordinary Cartesian coordinate, I do not get how the transition between Cartesian to polar coordinate is done.

So I've been reading various resources, and in one source, they mentioned about shifting the origin to the centre of a square and then calculate the polar coordinates, and in other source, they didn't mention anything about shifting the origin to the centre and calculate the polar coordinates right off the bat. So I'm confused which is which?

Do I shift the origin to the centre and calculate the polar coordinates then or perform the calculation without doing so?