Part of the rules for transposition is to change the axis of the cylinder by:

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When performing a transposition in the context of cylindrical coordinates, changing the axis of the cylinder by 90 degrees is significant because it aligns with the mathematical principle of rotating the coordinate system. This rotation allows for a more straightforward transformation of the coordinates from one system to another, especially when translating three-dimensional shapes into two-dimensional representations or vice versa.

In practical applications, rotating by 90 degrees effectively reorients the point of interest in relation to the origin and can simplify calculations related to angles and distances within the system. This is particularly relevant in fields like optics or architecture, where understanding light paths or structural designs requires a solid grasp of orientation in cylindrical systems.

Other angles, such as 45, 180, or 270 degrees, would not appropriately facilitate the standard transposition process as they affect the coordinate system in less intuitive ways, complicating the analysis and potentially leading to misinterpretations of shape or position in practical applications. Therefore, the method of rotating 90 degrees stands out as the correct choice for transposition.

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