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Hyperbolic trivia

Posted: Submitted by cj on 15 June 2008 - 7:03pm.

Joined: 2006-10-10
Posts: 520

For those people who did hyperbolic trig in A level:

Do you remember ever hearing about a kinda rule-of-thumb result for hyptrig identities, where it was like "they're the same as normal trig, but if you have a cosh squared, you must reverse the sign"? It had a name, some mathematician I hadn't heard of. Our teachers kept stressing it wasn't rigourous, but we should use it in exams.

Orry

Posted: 15 June 2008 - 7:18pm

Joined: 2007-02-14
Posts: 105

I remember being told about this last year, can't remember the details. No hyperbolic trig for me at a level. :(

Posted: 15 June 2008 - 7:19pm

Joined: 2006-10-10
Posts: 520

Looooosahhh

cosmin

Posted: 15 June 2008 - 7:44pm

Joined: 2006-11-02
Posts: 1090

(hay) I didn't do A-Level but I do recall reading something like that on the internets while browsing for STEP-related stuff ages ago. I don't think it had a name there though, they were just mentioning it as a random rule of thumb.

Xedi

Posted: 15 June 2008 - 9:55pm

Joined: 2007-10-03
Posts: 397

Yes, the rule basically says to change cos to cosh, sin to sinh and change the sign of any product of two sinh.
This just comes from the fact that $\cosh(x)=\cos(ix)$ and $\sinh(x)=-i \sin(ix)$ , so when you multiply two sinh together you're getting an extra minus sign in front.
Example :
$\displaystyle \cos^2(x)+sin^2(x)=1, \,\, \cos^2(ix)-(-i)^2 \sin^2(ix) = 1, \,\, \cosh^2(x)-\sinh^2(x)=1$