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Why is there this pattern in the polar curves cos[at] U sin[at]

  1. Jun 22, 2011 #1
    1. The problem statement, all variables and given/known data

    Polar plot the following

    sin[t] U cos[t]
    sin[2t] U cos[2t]
    sin[3t] U cos[3t]
    sin[4t] U cos[4t]
    sin[5t] U cos[5t]

    Notice that cos[t] and sin[t] are the same graph rotated 90 degrees only? Interesting! Just like the cartesian graph.

    Now here is something more interesting

    The number of loops follow as

    1t U 1 loop
    2t U 4 loops
    3t U 3 loops
    4t U 8 loops
    5t U 5 loop

    Notice how the odd number stays the same and the even doubles? Why is there this pattern?
     
  2. jcsd
  3. Jun 22, 2011 #2

    LCKurtz

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    They actually have the same number of loops. When you use the odd multiple of t the graph is plotted twice. Try going from 0 to pi.
     
  4. Jun 23, 2011 #3
    But you can't see it! So it is halved.
     
  5. Jun 23, 2011 #4

    LCKurtz

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    Believe whatever you want to.
     
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