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Previous Thread Next Thread Print Thread hyperbolic #97608 03/04/2003 2:07 PM Joined: Jan 2001 Posts: 13,858 wwh Carpal Tunnel wwh Carpal Tunnel 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 Share Post on Reddit Re: hyperbolic #97609 03/04/2003 2:25 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 Share Post on Reddit Re: hyperbolic #97610 03/04/2003 2:33 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 Share Post on Reddit Re: hyperbolic #97611 03/04/2003 2:48 PM Joined: Jan 2001 Posts: 13,858 wwh Carpal Tunnel wwh Carpal Tunnel Joined: Jan 2001 Posts: 13,858 sinhx is a cinch Copy Link to Clipboard Share Post on Facebook Share Post on Twitter Share Post on Reddit Re: hyperbolic #97612 03/04/2003 5:13 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 Share Post on Reddit Re: hyperbolic #97613 03/04/2003 6:25 PM Joined: Jan 2001 Posts: 13,858 wwh Carpal Tunnel wwh Carpal Tunnel 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 Share Post on Reddit Re: hyperbolic #97614 03/04/2003 7:02 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 Share Post on Reddit Re: hyperbolic #97615 03/04/2003 7:41 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 Share Post on Reddit Re: hyperbolic #97616 03/04/2003 8:19 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 Share Post on Reddit 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. 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