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Previous Thread Next Thread Print Thread hyperbolic #97608 03/04/03 02:07 PM Joined: Jan 2001 Posts: 13,858 W wwh OP Carpal Tunnel OP wwh Carpal Tunnel W Joined: Jan 2001 Posts: 13,858 Among other complexities in math, there are the hyperbolic functions. The hyperbolic functions are defined in terms of ex and e-x. ex - e-x sinh(x) = ------------ 2 ex + e-x cosh(x) = ------------ 2 sinh(x) ex - e-x tanh(x) = ------- = ---------- cosh(x) ex + e-x coth(x) = 1/ tanh(x) csch(x) = 1/ sinh(x) sech(x) = 1/ cosh(x) Properties It is easy to prove that cosh(-x) = cosh(x) sinh(-x) = - sinh(x) tanh(-x) = - tanh(x) cosh(x) > 0 cosh(x) + sinh(x) = ex cosh(x) - sinh(x) = e-x > 0 cosh2(x) - sinh2(x) = 1 cosh(x) = + sqrt( 1 + sinh2(x) ) >= 1 1 - tanh2(x) = 1/cosh2(x) 1 cosh(x) = ------------------ sqrt(1 - tanh2(x)) tanh(x) sinh(x) = ------------------- sqrt(1 - tanh2(x)) Copy Link to Clipboard Share Post on Facebook Share Post on Twitter Re: hyperbolic #97609 03/04/03 02:25 PM Joined: Dec 2000 Posts: 13,803 Faldage Carpal Tunnel Faldage Carpal Tunnel Joined: Dec 2000 Posts: 13,803 Thus it is obvious… Copy Link to Clipboard Share Post on Facebook Share Post on Twitter Re: hyperbolic #97610 03/04/03 02:33 PM Joined: Mar 2001 Posts: 4,189 Rio Grande, Cape May County, N... WhitmanO'Neill Carpal Tunnel WhitmanO'Neill Carpal Tunnel Joined: Mar 2001 Posts: 4,189 Rio Grande, Cape May County, N... Obvious?...mebbe to ron, but. Copy Link to Clipboard Share Post on Facebook Share Post on Twitter Re: hyperbolic #97611 03/04/03 02:48 PM Joined: Jan 2001 Posts: 13,858 W wwh OP Carpal Tunnel OP wwh Carpal Tunnel W Joined: Jan 2001 Posts: 13,858 sinhx is a cinch Copy Link to Clipboard Share Post on Facebook Share Post on Twitter Re: hyperbolic #97612 03/04/03 05:13 PM Joined: Dec 2000 Posts: 13,803 Faldage Carpal Tunnel Faldage Carpal Tunnel Joined: Dec 2000 Posts: 13,803 I've been studying this since this morning and I was right; it is obvious. Copy Link to Clipboard Share Post on Facebook Share Post on Twitter Re: hyperbolic #97613 03/04/03 06:25 PM Joined: Jan 2001 Posts: 13,858 W wwh OP Carpal Tunnel OP wwh Carpal Tunnel W Joined: Jan 2001 Posts: 13,858 Cosh, Faldage, do you really mean it? Copy Link to Clipboard Share Post on Facebook Share Post on Twitter Re: hyperbolic #97614 03/04/03 07:02 PM Joined: Dec 2000 Posts: 13,803 Faldage Carpal Tunnel Faldage Carpal Tunnel Joined: Dec 2000 Posts: 13,803 Tanhx for asking, Dr Bill. Copy Link to Clipboard Share Post on Facebook Share Post on Twitter Re: hyperbolic #97615 03/04/03 07:41 PM Joined: Mar 2001 Posts: 4,189 Rio Grande, Cape May County, N... WhitmanO'Neill Carpal Tunnel WhitmanO'Neill Carpal Tunnel Joined: Mar 2001 Posts: 4,189 Rio Grande, Cape May County, N... Well, Faldage, it's just that I'm mathfully-challenged by happy choice, thank ya, thank ya very much. Copy Link to Clipboard Share Post on Facebook Share Post on Twitter Re: hyperbolic #97616 03/04/03 08:19 PM Joined: Mar 2000 Posts: 6,511 lower upstate New York AnnaStrophic Carpal Tunnel AnnaStrophic Carpal Tunnel Joined: Mar 2000 Posts: 6,511 lower upstate New York Juan, with those two, sometimes it's best to just leave them to their codgering. Signed, your equally-challenged friend Copy Link to Clipboard Share Post on Facebook Share Post on Twitter Moderated by  Jackie  Hop To General Topics ------  Information and announcements  Q&A about words  Wordplay and fun  Words and languages in schools  Miscellany  Weekly Themes  Looking for (writers, speakers,... (Old) Weekly themes. (have been... ------  Words from medicine  Beheading words  Meta-words  Words from classical mythology  Animal Safari  Words with unusual etymologies  Eponyms or words derived from p...  Loanwords from German  English as a global language Print Thread Switch to Threaded Mode Show Likes Link Copied to Clipboard View Profile Private Message Follow User Forum Posts Like Summary View Profile Private Message Website Follow User Forum Posts Like Summary View Profile Private Message Follow User Forum Posts Like Summary View Profile Private Message Follow User Forum Posts Like Summary View Profile Private Message Website Follow User Forum Posts Like Summary View Profile Private Message Follow User Forum Posts Like Summary View Profile Private Message Website Follow User Forum Posts Like Summary View Profile Private Message Follow User Forum Posts Like Summary View Profile Private Message Follow User Forum Posts Like Summary Forum Statistics Forums16 Topics13,913 Posts229,412 Members9,182 Most Online3,341 Dec 9th, 2011 Newest Members Ineffable, ddrinnan, TRIALNERRA, befuddledmind, KILL_YOUR_SUV 9,182 Registered Users Who's Online Now 0 members (), 953 guests, and 2 robots. Key: Admin, Global Mod, Mod Top Posters(30 Days) wofahulicodoc 37 A C Bowden 27 LukeJavan8 4 Top Posters wwh 13,858 Faldage 13,803 Jackie 11,613 wofahulicodoc 10,583 tsuwm 10,542 LukeJavan8 9,922 Buffalo Shrdlu 7,210 AnnaStrophic 6,511 Wordwind 6,296 of troy 5,400

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