Sin – or sine, in the long form, is often deliberately mispronounced “sin” in the short form. So “sine in hyperbolic form” might be sinh, possibly “sin-h” or “sin-aitch” in pronunciation. That would quickly be corrupted to “sintch” for everyday use.

The guys looking at hyperbolic sines sit right next to the guys that see a misprint in a science fiction convention schedule, and forever after dub folk singing in a science fiction environment as “filk” singing. One example that comes to mind is Leslie Fish’s “Carmen Miranda’s Ghost is Haunting Space Station Three” – a delightful little novelty ditty that resulted in a book, edited by Ester Friesner. The book is a collaboration, a collection of short stories from the science fiction author community, each written to the theme of Fish’s filk song. Esther Friesner, for those unfamiliar with her work, edited the “Chicks in Chain Mail”, “The Chick is in the Mail”, “Chicks and Chained Males” series of fantasy (sword and sorcery, mostly) stories. Well, there was “Whoops!” by Nancy Springer in Chicks in Chain Mail, that I really enjoyed, about a timid school teacher commuting on crowded LA freeways – and how annoyed her guardian angel got.

And you were worried about getting sinh to sound like cinch. Hah!

I am quite sure, if we were to let Washington DC “manage changes to the language” we would all cease to communicate, post-haste.

http://en.wikipedia.org/wiki/Hyperbolic_function

The third sound of ch is [sh] as heard in “recent” borrowings from French: chef, chamois, chic.

Phil,
What I’m referring to as the three sounds of ch are [ch], [k] and [sh]. English speakers, at least U.S. speakers, don’t usually try to get the German or Scots pronunciation of ch. I suppose the ch of Bach might be considered a “fourth” sound.