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Thread: Summation

  1. #1
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    Summation

    Hello! Thank you for helping me with this question! I have no idea how do I sum trigonometric function! [Or are we supposed to use summation by method of difference?]

    Evaluate the following:

    28
    ∑ sin [pi / (r-10)]
    r=11

    Thank you very much!
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  2. #2
    Grand Panjandrum
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    Quote Originally Posted by Tangera View Post
    Hello! Thank you for helping me with this question! I have no idea how do I sum trigonometric function! [Or are we supposed to use summation by method of difference?]

    Evaluate the following:

    28
    ∑ sin [pi / (r-10)]
    r=11

    Thank you very much!
    Well first make things easy for yourself by adjusting the summation limits:

    \sum_{r=11}^{28} \sin(\pi/(r-10)) =\sum_{r=1}^{18} \sin(\pi/r)

    RonL
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  3. #3
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    Hello! Erm....could you give me more hints as to how to solve the problem. I am still stuck. >.< Thank you!
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  4. #4
    MHF Contributor Mathstud28's Avatar
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    Quote Originally Posted by CaptainBlack View Post
    Well first make things easy for yourself by adjusting the summation limits:

    \sum_{r=11}^{28} \sin(\pi/(r-10)) =\sum_{r=1}^{18} \sin(\pi/r)

    RonL
    I dont see an easy way of doing this

    It looks as though you will just have to muddle through it the hard way and do this

    \sum_{r=1}^{18}\sin\bigg(\frac{\pi}{r}\bigg)=\sin(  \pi)+\sin\bigg(\frac{\pi}{2}\bigg)+...+\sin\bigg(\  frac{\pi}{18}\bigg)

    Which is equal to 0+1+...+0.174 ....You can't really do exact values because for example

    \sin\bigg(\frac{\pi}{18}\bigg)

    Is given by the infinitely nested radical

    \sin\bigg(\frac{\pi}{18}\bigg)=\frac{1}{2}\sqrt{2-\sqrt{2+\sqrt{2-\sqrt{2+...}}}}


    But if it is helpful mathcad says

    \sum_{r=1}^{18}\sin\bigg(\frac{\pi}{n}\bigg)=6.891
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  5. #5
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    Thank you very very much!
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