/sci/ - Science & Math

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

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


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

>>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.

>>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.

>>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

>>11395495
Just use the inverse of a logistic function