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Non-trigonometric parametric equation of a circle

  1. Oct 2, 2012 #1
    I wish to write this equation:


    as a parametric equation but WITHOUT the use of sine and cosine.

    Is this possible?
  2. jcsd
  3. Oct 2, 2012 #2
    I don't think so. You could use the maclauren series for sine and cosine, but you'd need an infinite sum for it to be completely correct.

    Edit: A generic circle can be drawn in the complex plane without sine/cosine, but it wouldn't be whatsoever equivalent to the formula you gave.
  4. Oct 2, 2012 #3

    I like Serena

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    There is another parametrization:
    $$x={1-t^2 \over 1+t^2}$$
    $$y={2t \over 1+t^2}$$
  5. Oct 3, 2012 #4


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    Almost - this is a semicircle. -1<t<1.
  6. Oct 3, 2012 #5

    I like Serena

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    It's a little more with ##t \in \mathbb R##, or even better with ##t \in \mathbb R \cup \{\infty\}##.
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