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SIMPLE:how do you solve (sin x)/x = 0.99

  1. Jan 7, 2007 #1
    the answer is 0.24 (working in radians)

    how to you get this

    thanks!!
     
  2. jcsd
  3. Jan 7, 2007 #2

    Integral

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    There is no closed form solution. You might research something like a Newton's Method root finder. I did a quick fixed point interation and arrived at 0.24532 but it took over a 100 iterations to reach it.

    I started with a guess of .5 and iterated

    [tex] x = \frac { \sin x } {.99} [/tex]
     
  4. Jan 7, 2007 #3
    I did an approximation by hand,

    Take the first terms of taylor series for sine

    [tex] sin(x) = x - \frac { x^3 } {6} + \frac {x^5} {120} [/tex]

    [tex] \frac { \sin x } {x} = 1 - \frac { x^2 } {6} + \frac {x^4} {120} = 0.99 [/tex]

    [tex] x^4 - 20x^2 + 1.2 = 0 [/tex]

    Substitute, a = x^2

    [tex] a^2 - 20a + 1.2 = 0 [/tex]


    It's an easy quadratic equation, also got 0.2459674, and other solution 4.465366 which doesn't work.
     
    Last edited: Jan 7, 2007
  5. Jan 8, 2007 #4

    berkeman

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    Thread moved to math homework forum.
     
  6. Jan 8, 2007 #5

    berkeman

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    What about waht's solution?
     
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