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Math Help - [SOLVED] Determine equation based on dataset

  1. #1
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    [SOLVED] Determine equation based on dataset

    I am currently working on something for my personal site. Most things I can figure out myself, but I'm having trouble with this problem.

    I need to determine an equation that's based on the following dataset:

    x=1/4
    y=4

    x=sqrt(2)/4
    y=2

    x=1/2
    y=1

    x=sqrt(2)/2
    y=1/2

    x=1
    y=1/4

    Alternatively, it can be expressed as (in radians):

    x=sin(PI/6)/2
    y=4

    x=sin(PI/4)/2
    y=2

    x=sin(PI/6)
    y=1

    x=sin(PI/4)
    y=1/2

    x=sin(PI/2)
    y=1/4

    Now what I'm trying to do is find the equation these numbers represent.

    Let's say I know y=3. How can I determine x based on the information above? I see a pattern, but I'm unable to come up with a working equation.



    I am able to test to see if a pair of values is correct.
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  2. #2
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    Joined
    Mar 2008
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    Quote Originally Posted by peaceoutside.org View Post
    I am currently working on something for my personal site. Most things I can figure out myself, but I'm having trouble with this problem.

    I need to determine an equation that's based on the following dataset:

    x=1/4
    y=4

    x=sqrt(2)/4
    y=2

    x=1/2
    y=1

    x=sqrt(2)/2
    y=1/2

    x=1
    y=1/4

    Alternatively, it can be expressed as (in radians):

    x=sin(PI/6)/2
    y=4

    x=sin(PI/4)/2
    y=2

    x=sin(PI/6)
    y=1

    x=sin(PI/4)
    y=1/2

    x=sin(PI/2)
    y=1/4

    Now what I'm trying to do is find the equation these numbers represent.

    Let's say I know y=3. How can I determine x based on the information above? I see a pattern, but I'm unable to come up with a working equation.



    I am able to test to see if a pair of values is correct.
    Do you have excel? You can put in the values in a spreadsheet, insert a scatterplot of the data, look at the type of equation it might be forming, and then insert a trendline.

    I inserted the data points in my openoffice version of excel and selected a power regression trendline that fits perfectly..unfortunately I cannot get the equation for it and I'm too tired to try to figure it out, although since it fits perfectly I'm sure someone here can probably help!
    Last edited by elizsimca; April 30th 2008 at 05:52 PM.
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  3. #3
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    ^ I've looked at the curve produced with the points I currently have.

    It looks similar to y=hyperbolic cosecant(x), but it's not correct.

    Here is my current known data set in both fractions and decimals:

    Code:
    y          x
    
    32/1       sqrt(2)/16
    16/1       1/8
     8/1       sqrt(2)/8
     4/1       1/4
     2/1       sqrt(2)/4
     1/1       1/2
     1/2       sqrt(2)/2
     1/4       1/1
     1/8       sqrt(2)/1
     1/16      2/1
     1/32      sqrt(2)/0.5
    
    32         0.088388347648318440550105545263106
    16         0.125
     8         0.17677669529663688110021109052621
     4         0.25
     2         0.35355339059327376220042218105242
     1         0.5
     0.5       0.70710678118654752440084436210485
     0.25      1
     0.125     1.4142135623730950488016887242097
     0.0625    2
     0.03125   2.8284271247461900976033774484194

    There's certainly a pattern here. I just do not know how to put it in an equation so I can solve for one variable if I have the other.


    I found it!

    y=((1/x)^2)/4

    x=1/sqrt(4*y)

    Last edited by peaceoutside.org; May 1st 2008 at 02:34 PM. Reason: formatting
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  4. #4
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    yep..looks like a power regression equation! yay!
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