/sci/ - Science & Math » Thread #11395495

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Can you find the explicit formula?

Anonymous Tue 18 Feb 06:38:28 2020 No.11395495 View Reply Original Report

Quoted By: >>11395633 >>11395825

99% of /sci/ cant do it (dont cheat)

Anonymous

Anonymous Tue 18 Feb 2020 06:55:38 No.11395518 Report

Quoted By: >>11395571

f(x)=tan( pi*x - pi/2 )
with x in (0,1)
f(x) covers R

Anonymous

Anonymous Tue 18 Feb 2020 07:30:41 No.11395571 Report

Quoted By: >>11395623 >>11395628

>>11395518
Wrong, your function is an increasing function while the one in the picture is a falling one!

The function is something like
$f(x) = c \frac{1 - 2x}{\sqrt{x - x^2}}$
The problem is finding the correct parameter $c$ that gives the picture exactly.

Anonymous

Anonymous Tue 18 Feb 2020 08:16:48 No.11395623 Report

Quoted By:

>>11395571
The direction thing is whatever, the picture doesn't show which way is positive, or where zero and one are.
But anyway, if r is the radius of the circle, h is the distance between circle and R-line, then
f(x) in R =
tan(arcsin(pi*x-pi/2))*(1+h/r)
where x in (0,1)

Or -tan or arcsin(pi/2-pi*x) if you want to switch around the R-axis or the (0,1) bar that are not labelled.

Anonymous

Anonymous Tue 18 Feb 2020 08:21:01 No.11395628 Report

Quoted By:

>>11395571
>Wait no. The direction thing is whatever, the picture doesn't show which way is positive, or where zero and one are.But anyway, if r is the radius of the circle, h is the distance between circle and R-line, then f(x) in R =tan(arcsin(2*x--1))*(1+h/r) where x in (0,1)Or -tan or arcsin(pi/2-pi*x) if you want to switch around the R-axis or the (0,1) bar that are not labelled.

Anonymous

Anonymous Tue 18 Feb 2020 08:22:59 No.11395633 Report

Quoted By:

>>11395495
tan(arcsin(2*x-1))*(1+h/r) where x in (0,1)
Or -tan or arcsin(1-2*x) if you want to switch around the R-axis or the (0,1) bar

Anonymous

Anonymous Tue 18 Feb 2020 10:20:15 No.11395825 Report

Quoted By:

>>11395495
Just use the inverse of a logistic function

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