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[help] equation

  1. Jan 8, 2005 #1
    10 sin x = -x
    can anyone give me tips how to solve this equation?
    i run out of ideas even to transform this equation to another form.. sigh sigh

    thanks...
     
  2. jcsd
  3. Jan 8, 2005 #2
    It seems you have a transcendental equation0--i don't think those are solvable, unless you know how to find intercepts between trig and non-vertical/non-horizontal functions.
     
  4. Jan 8, 2005 #3

    krab

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    x=0

    Or do you want more solutions? Then look up Newton's method.
     
  5. Jan 8, 2005 #4
    there are 3 roots in this equation. 0 is the obvious one, the other two needs to estimate by computer.
     
  6. Jan 8, 2005 #5
    oh ... thanks...
    p/s : (1) what's Newton method?
    (2) find intercepts between trig and non-vertical/non-horizontal functions ?

    i not yet learn both also and my text book is doesnot contain Newton's method also.. i will try to find it out...
    my friend told me use 'trials and errors' method, is it applicable ?
    thanks
     
  7. Jan 8, 2005 #6

    krab

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    Newton's method is a clever way of correcting your guess by using the deviation. But you need to know some calculus, and I don't think you know any. In any case, if x_n is your n^th trial, then you find your next trial as follows:
    [tex]x_{n+1}=x_n-{10\sin x_n+x_n\over 10\cos x_n +1}[/tex]
    Of corse, with more than one root to 10sin x+x=0, you'll need an appropriate initial guess or you'll just keep going back to a known solution like x=0.
     
  8. Jan 9, 2005 #7

    krab

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    here are the 5 solutions to 50 digits...
    0
    +/- 3.49906381990775821737274462727340586713040476067
    +/- 5.67920779631440367042018458778408009777615397061
     
  9. Jan 14, 2005 #8
    oh .. thanks alot ... :)
     
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