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End behavior

  1. Mar 27, 2006 #1
    is y=sin(x) the end behavior of y=sin(x/2)?
     
  2. jcsd
  3. Mar 27, 2006 #2

    benorin

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    Yep, oscillatory. the function oscillates between -1 and 1.
     
  4. Mar 27, 2006 #3
    I wish i knew what that looks like? is there a picture anywhere? sorry if thats too much trouble.
     
  5. Mar 27, 2006 #4
    and why is it oscillatory?
     
  6. Mar 27, 2006 #5

    benorin

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    sin(x/2) looks just like sin(x), only its squished along the x-axis by a factor of 2.
     
  7. Mar 27, 2006 #6
    also, are there any interesting points in the graph of sin(x/2)...my last question.
     
  8. Mar 27, 2006 #7

    J77

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    :eek:

    The behaviour of trig fns like sine is fundamental!!!

    Have a look on mathworld or such.

    (btw: in answer to your last question - zero at 0, 2n\pi, \pi\in\mathbb{Z}, diff to find extrema etc...)
     
  9. Mar 27, 2006 #8

    benorin

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    [tex]sin\left( \frac{x}{2}\right) =0\mbox{ if }x=2n\pi,n\in\mathbb{Z}[/tex]

    J77, double click on the equations to see how to typeset in here (we don't use $..$)
     
  10. Mar 27, 2006 #9
    thank you very much guys..appreciate your help...
     
  11. Mar 27, 2006 #10

    benorin

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    And no, there are no other points of interest.
     
  12. Mar 27, 2006 #11

    J77

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    :biggrin:

    Thanks for the latex thing, benorin.
     
  13. Mar 27, 2006 #12

    benorin

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  14. Mar 27, 2006 #13

    Tom Mattson

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    The question doesn't even make any sense. But I would hesitate before saying, "yep". Yes, they do both oscillate between the same 2 fixed numbers, but the former oscillates twice as rapidly as the latter.

    No, it is stretched out by a factor of 2. The period of [itex]\sin(x/2)[/itex] is [itex]4\pi[/itex], which is twice as long as the period of [itex]\sin(x)[/itex].
     
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