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Hyperbolic Trigonometrical Functions
By Zhidong Leong on Friday, May 17, 2002 - 06:19 pm:

What exactly is the use of sinh, cosh and tanh?
Also, how are the functions pronounced as?

By Arun Iyer on Saturday, May 18, 2002 - 04:34 pm:

Your first question (please don't mind my words) is quite absurd....I mean, they pop up often in calculus and as applications of calculus are wide and vast, so is theirs....

For the pronunciations,
sinh -- synch (as in synchronize)
cosh -- kosh
tanh -- tankh (k is silent)

I think I am right, at least that's the way I pronounce them...

love arun

By David Loeffler on Saturday, May 18, 2002 - 04:54 pm:

Arun, I don't think there is any real consensus about how people pronounce them - a lot of people, including myself, pronounce sinh as "shine" (I know it's illogical, but it's faster.) On the other hand Dr. Davis (one of our lecturers) uses "sinch" - so there's really no agreement.
I try to avoid pronouncing tanh wherever possible!

As for what they're useful for: I see that in ordinary calculus they can seem somewhat artificial; after all, why use sinh x and cosh x when you can use ex and e-x which are far easier to handle?

I really found I couldn't see much of a use for them until I started learning about complex numbers: there are two rather handy formulae:

cos ix = cosh x
sin ix = i sinh x

These you will come to know and love (or hate, depending on your taste) if you ever do complex analysis.

Also, they have some interesting applications in hyperbolic geometry.

David

By William Astle on Saturday, May 18, 2002 - 05:49 pm:


See here and here for a physical application.