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

  • Thread starter LM741
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the answer is 0.24 (working in radians)

how to you get this

thanks!!
 

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]
 
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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:

berkeman

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Thread moved to math homework forum.
 

berkeman

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I looked for docs that referring to this problem but couldn't find any of those, do you have a clue?
What about waht's solution?
 

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