From: Rudolf Polzer <denshimeiru-sapmctacher@...>
Date: 2003-08-27T08:49:17+09:00
Subject: Re: POLS and names of mathematical functions

Scripsit illa aut ille �Josef 'Jupp' Schugt� <jupp@gmx.de>:
> * Rudolf Polzer; 2003-08-25, 12:41 UTC:
> > Until now tan and tanh don't have much in common, mathematically.
> > But this makes them nearly the same functions:
> > 
> >   irb(main):003:0> require 'complex'
> >   => true
> >   irb(main):004:0> Math.atanh(17)
> >   => Complex(0.0588915178281917, 1.5707963267949)
> >   irb(main):005:0> Math.atanh(17 * Complex::I)
> >   => Complex(0.0, 1.51204050407917)
> > 
> > That makes it obvious that it would be good to use the same prefix
> > for the inverse functions.
> 
> You mean that
> 
>  sin(Complex::I * x) = Complex::I * sinh(x)
> sinh(Complex::I * x) = Complex::I *  sin(x)
>  cos(Complex::I * x) =              cosh(x)
> cosh(Complex::I * x) =               cos(x)
> 
> explains why to use the symbols asin, asinh, acos, and acosh?

Yes - it shows that the functions DO have enough in common to be
treated similarily.