Solving for x in a Trigonometric Equation

[Jenkz]

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?

 

[tiny-tim]

Hi Jenkz!

(have a square-root: √ )

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

see http://en.wikipedia.org/wiki/Sinc_function"

 

[Jenkz]

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... :/

 

[Jenkz]

Ooo nvm. Thanks!

 

[tiny-tim]

1.752 = X² (1- X² /20 )

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

Looks roughly correct to me (X = 1.4).

 

[Jenkz]

Yah.. I just did something silly. All works now! :D