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Can polar co-ordinate system only be defined in a "background" Cartesian co-ordinate system?

What I'm confused about is this: the definition of the polar unit vectors or the polar basis is in terms of the parameter theta. Now, before we go about defining our basis we need to define this theta in reference to some axes. So we already need to have some co-ordinate system defined and only then can we define a polar co-ordinate system w.r.t to this previously defined co-ordinate system. We cannot define it like an independent Cartesian system. Is this correct?

What I'm confused about is this: the definition of the polar unit vectors or the polar basis is in terms of the parameter theta. Now, before we go about defining our basis we need to define this theta in reference to some axes. So we already need to have some co-ordinate system defined and only then can we define a polar co-ordinate system w.r.t to this previously defined co-ordinate system. We cannot define it like an independent Cartesian system. Is this correct?

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