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Functions in coordinate systems

  1. Dec 24, 2012 #1
    Hi all. What does it mean that a function in polar coordinates may not be a function in Cartesian coordinates?

    For example, [itex] r(\theta) = 1 + \sin\theta [/itex] is a function because each [itex]\theta[/itex] corresponds to a single value of [itex]r[/itex]. However, in Cartesian coordinates, the graph of this function most clearly fails the vertical line test.

    Therefore, functionality depends on the coordinate system?
     
  2. jcsd
  3. Dec 24, 2012 #2

    mfb

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    2016 Award

    Staff: Mentor

    It depends on the type of function you want.
    • If you want a function y(x), you cannot get the same graph as your equation gives.
    • You can find a function R->R2 with (x,y)(t), however, which gives one point (x,y) for each value of t, and has the same graph as your function.
    • You can find a function R2->R, f(x,y) where your graph corresponds to all points where f(x,y)=0.
    • ...
     
  4. Dec 24, 2012 #3

    Stephen Tashi

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    I wouldn't call the property of being a function "functionality", but, yes, a set of ordered pairs representing certain information may be a function and when the same information is represented in a different way as a different set of ordered pairs, that other set of ordered pairs may fail to be a function.
     
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