Special Function Sets & HPs

[emece67]

(02-01-2016 07:45 PM)Jeff_Kearns Wrote:  This comment made me think of one of Valentin's replies back in 2003:
Hyperbolics everywhere ! (almost)
Message #4 Posted by Valentin Albillo on 30 June 2003, 6:38 a.m.,
in response to message #3 by Ernie Malaga
Ernesto wrote:

"How about hyperbolics? So far I haven't learned of a _single_ use for hyperbolic functions in any field."

They're used all the time in some very important Civil Engineering fields, a few assorted examples:

[...]

Thanks Jeff for such interesting insights.

There's a thing that surprises me. In your examples, the revelant hyperbolic function seems to always be the hyperbolic cosine. In my three examples, instead, it is the hyperbolic tangent.

Does anybody know of any field where the relevant hyperbolic function is the hyperbolic sine?

Edit: I have found just now that the hyperbolic functions do also play a role in the Mercator projection. The expressions relating latitude and the y coordinate in a map can be written in terms of the hyperbolic functions, and even using the Gudermannian function.