- #1
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?
Solving for x in a Trigonometric Equation
- Thread starter Jenkz
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In summary, the conversation discusses solving for x in the equation sin x / x = 1/ (2)^1/2 using series expansion or referencing sinc tables. One user shares their attempt at a solution, which involves truncating the series and re-arranging, until another user points out a small mistake. The correct solution is found and the conversation ends positively.
Sin x / x = 1/ (2)^1/2
how do I solve for x? I know x is 1.392
I thought I might be able to use some series expansion, but it gets quite messy. Help please?
- #2
tiny-tim
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Homework Helper
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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"
(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"
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- #3
Jenkz
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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... :/
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... :/
- #4
Jenkz
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Ooo nvm. Thanks!
- #5
tiny-tim
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Jenkz said:
Looks roughly correct to me (X = 1.4).
- #6
Jenkz
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Yah.. I just did something silly. All works now! :D
Related to Solving for x in a Trigonometric Equation
1. What does it mean to "re-arrange in terms of x"?
Re-arranging in terms of x refers to manipulating an equation or expression so that the variable x is isolated on one side of the equation. This allows for solving for the value of x in terms of other variables or constants.
2. Why is it useful to re-arrange in terms of x?
Re-arranging in terms of x can be useful in solving equations or finding specific values of a variable. It can also help in understanding the relationship between different variables in an equation.
3. What steps are involved in re-arranging in terms of x?
The steps for re-arranging in terms of x vary depending on the equation or expression, but generally involve using inverse operations to move terms to the opposite side of the equation, canceling out like terms, and simplifying the resulting expression until x is isolated.
4. Can any equation or expression be re-arranged in terms of x?
Yes, any equation or expression with one or more variables can be re-arranged in terms of x. However, some equations may be more difficult to re-arrange and may require more advanced algebraic techniques.
5. Are there any common mistakes to avoid when re-arranging in terms of x?
One common mistake to avoid is forgetting to apply the same operation to both sides of the equation when moving terms. It is also important to be careful with signs and properly distribute any coefficients when simplifying the expression.
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