# [SOLVED] Determine equation based on dataset

• Apr 30th 2008, 04:42 PM
peaceoutside.org
[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.
• Apr 30th 2008, 05:41 PM
elizsimca
Quote:

Originally Posted by peaceoutside.org
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!
• Apr 30th 2008, 10:59 PM
peaceoutside.org

^ 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)

• May 1st 2008, 01:32 PM
elizsimca
yep..looks like a power regression equation! yay!