Solving for x in a Trigonometric Equation

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Homework Help Overview

The problem involves solving the trigonometric equation sin x / x = 1 / √2. The original poster mentions a known value for x but seeks assistance with the solution process.

Discussion Character

  • Exploratory, Mathematical reasoning, Assumption checking

Approaches and Questions Raised

  • Participants discuss using series expansion as a potential method, with some expressing difficulty in managing the complexity of the series. There are also references to using sinc tables for assistance.

Discussion Status

The discussion reflects a mix of attempts to derive a solution through series expansion, with some participants questioning their results and expressing confusion. There is acknowledgment of errors in calculations, but no clear consensus on the approach has been reached.

Contextual Notes

Participants note the challenges of truncating the series and rearranging terms, indicating potential issues with assumptions or calculations. The original poster's reference to a specific value for x is also mentioned, but its validity is not confirmed within the discussion.

Jenkz
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Homework Statement



Sin x / x = 1/ (2)^1/2

how do I solve for x? I know x is 1.392

The Attempt at a Solution



I thought I might be able to use some series expansion, but it gets quite messy. Help please?
 
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Hi Jenkz! :smile:

(have a square-root: √ :wink:)

yup, only way is a series expansion or look it up in sinc tables …

see http://en.wikipedia.org/wiki/Sinc_function" :wink:
 
Last edited by a moderator:
I'm still not really getting anywhere with the answer :s

so far all I've got is:
sinx / x = 1/ √ 2 = 1 - X²/6 + X^4 / 120 - ...

Truncating the series and some re-arranging I get
1.752 = X² (1- X² /20 )

But I end upwith something completely wrong... :/
 
Ooo nvm. Thanks!
 
Jenkz said:
1.752 = X² (1- X² /20 )

But I end upwith something completely wrong... :/

Looks roughly correct to me (X = 1.4). :confused:
 
Yah.. I just did something silly. All works now! :D
 

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