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Is tan|x| periodic?

  1. Aug 31, 2011 #1
    Is tan|x| periodic and if not, why not?


    I just found in my book that tan|x| isn't periodic, and how do we make up a rule how to seek periodicity of functions.

    I.e.

    ln(sin(x)), e^sin(x)... etc
     
  2. jcsd
  3. Aug 31, 2011 #2

    disregardthat

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    Find a constant a such that f(x+a) = f(x). So basically you can solve for a function a(x) here, and make sure its a constant function.
     
  4. Aug 31, 2011 #3

    jambaugh

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    Plot the graph. Notice that if you erase the coordinate axes you can still see where the origin must lie.
     
  5. Sep 1, 2011 #4
    I did plot the graph, thats why i got confused. I saw a lot of functions, resembling tan(x). I got the feeling that it was periodic, but actually tan|x| isn't.
     
  6. Sep 2, 2011 #5

    jambaugh

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    Look at the graph closely. It should have a mirror symmetry around x=0. But notice it is not mirror symmetric around any other point. So you can't shift the graph through a period so it looks exactly the same.
     
  7. Sep 2, 2011 #6
    Thank you I understand now. I had bad view of what it means to be periodic.
     
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