# Thread: [SOLVED] Determine equation based on dataset

1. ## [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.

2. 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!

3. ^ 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)

4. yep..looks like a power regression equation! yay!