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Math Help - 1-exp(i.theta), please help

  1. #1
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    1-exp(i.theta), please help

    hello,
    can you give some hints to prove the following:
    |1-exp(i theta)|>=2|theta|/pi whenever -pi<=theta<=pi

    thank you in advance
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  2. #2
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    i had read some latex tutors on this forum and this is the inequality above:

      \forall -\pi\leq\theta\leq\pi : |1-\exp(i \theta)|\geq \frac{2 |\theta|}{\pi}
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  3. #3
    MHF Contributor Also sprach Zarathustra's Avatar
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    Recall Euler's formula:

    e^{i\theta}=cos(\theta)+isin(\theta)

    And:
     |1- cos(\theta)-isin(\theta)|= (1-cos(\theta))^2+sin^2(\theta)
    Last edited by Also sprach Zarathustra; July 18th 2010 at 10:02 AM.
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  4. #4
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    ok, i could arrive at:
    |1-e^{i\theta}|=2|sin(\frac{\theta}{2})|

    but how can i extract the term \frac{\theta}{\pi} from the above equation?
    Last edited by elfizia2001; July 23rd 2010 at 09:16 AM.
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  5. #5
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    hello,
    please any ideas to solve the above problem?
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