Talk:Hyperbolic function
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Why are you using sinh^2 x for (sinh x)^2?? Go to the inverse function article and it says the definition for f^2 x when not in trigonometry. Then, it has the exception and it says trigonometric functions, not hyperbolic functions. 66.245.25.240 15:42, 12 Apr 2004 (UTC)
- By convention this form is used with hyperbolic functions as well. -- Decumanus | Talk 15:43, 12 Apr 2004 (UTC)
The parenthetical comments about pronounciation could be clearer... what type of ch sound in sech, for example
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Some suggestions
What about changing the definition of arccsch(x) to ln(1/x + sqrt(1+x^2)/abs(x))?
Also, why does the definition of arcsech(x) contains the plusminus sign? As far as I know, the definition of arcsech(x) is "the inverse of (sech(x) restricted to [0,+inf))" (Howard Anton et.al., Calculus 7th ed, Chapter 7). In that case we should replace plusminus with plus.
user:Agro_r 11 Feb 2005 (GMT+7)
I need help!
I want know aplications, can somebody help me?
- If you are in a spaceship (with no gravity), and want to pretend you are on earth, you can take a piece of string, shape it like the cosh function and take a picture. Then people will think that you are affected by gravity, since a piece of string hanging freely looks like the cosh function. Don't know if they have other uses, I'll leave that to other people who know more, to answer. Κσυπ Cyp 2004年10月27日 (水) 19:56 (UTC)
I have this problem
As can be seen from plots the -cosh(x) function is concave in x.
So, if we have w positive then exp{-wcosh(x)} should alos be convex in x, right? Apparantly not always ... according to this article I have this is only valid iff w{sinh(x)}^2<cosh(x), does anybody see why??
Arc{hyperbolic function} is a misnomer
Arc{hyperbolic function} is a misnomer
The article states correctly that the parameter t represents an area, rather than a (circular) angle. Note also that t does not represent an arc length. As such, it is actually a misnomer to refer to the inverse hyperbolic functions using the prefix "arc".
OTOH, for the inverses of the trigonometric functions, the prefix "arc" is not a misnomer, since their values may indeed be thought of as representing arc lengths (or circular angles).
Arc{hyperbolic function} probably originated due to a false analogy with trigonometric functions. In any event, it is sometimes used nowadays. But IMO its usage should be deprecated in favor of one of several better alternatives. I prefer the simplest alternative: a{hyperbolic function}, in which "a" may correctly be taken to represent "area".
What do other people think? Should we change the article's currect arc{hyperbolic function} notation to my preference, or some other alternative, or leave the current notation as is?
--David W. Cantrell 07:23, 31 Dec 2004 (UTC)
- Hi, I think it the prefix for inverse hyperbolic functions used to be Sect, as in "sector". Why exactly I'm not sure, but that's what I grew up with. Orzetto 09:14, 16 Mar 2005 (UTC)
Use of exponents on function names
Hi, I have seen that there is some use of the notation <math>cosh^2()<math> to indicate <math>cosh(cosh())<math>. This should not be done as in some countries <math>cosh^2()<math> actually means <math>[cosh()]^2<math>, and this may be a source of confusion. It's evil. Orzetto 09:14, 16 Mar 2005 (UTC)