Dulanjana
2002-12-19 00:17:54 |
sinh, cosh, tanh whats this?
What exactly is the meaning of sinh, cosh, tanh? Heard that they are "hyperbolic functions" What is the meaning?
(I think there is also cosech, sech, coth too) |
friedlinguini
2002-12-19 02:54:51 |
Re: sinh, cosh, tanh whats this?
They are functions that have some properties similar to sin, cos, tan, etc. For example,
e^(ix) = cos x + i sin x => e^x = cosh x + sin x (where i = sqrt(-1))
sin x = x - x^3/3! +x^5/5! - x^7/7!... => sinh x = x + x^3/3! + x^5/5! + x^7/7!...
cos x = 1 - x^2/2! + x^4/4! -x^6/6!... => cosh x = 1 +x^2/2! + x^4/4! + x^6/6!...
They get used a lot in differential equations, which answers questions like "What path does an object take if its speed is proportional to its distance from some point?" |
Mike Graham
2004-09-06 23:07:24 |
Re: sinh, cosh, tanh whats this?
They are just shorthand for (e^x - e^-x)/2 (that's sinh, cosh is the same thing, but adding the two exponential powers, and tanh=sinh/cosh, like tan=sin/cos, same rules with other trig functions based off sine and cosine.) One real world application is that tanh is used to describe a (dully inelastic) rope's drooping when hung from two points. |
SilverKnight
2004-09-07 01:19:50 |
Re: sinh, cosh, tanh whats this?
What Mike is mentioning is commonly called a catenary and additional information about it can be found at http://mathworld.wolfram.com/Catenary.html. |
Charlie
2004-09-07 15:31:37 |
Re: sinh, cosh, tanh whats this?
That indicates it is the cosh function that corresponds to the shape of the drooping rope or chain. |
Mike Graham
2004-09-07 16:14:02 |
Re: sinh, cosh, tanh whats this?
I technically was not wrong (though I was thinking of cosh), in taht I claimed that tanh describes it, and it does describe the rope, just not its vertical distance.
I think I had hyperbolic tangent on the mind because we used it in a numerical math class I had the other day to describe velocity with drag. |
