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I heard teachers say [cosh x] instead of saying "hyperbolic cosine of x".

I also heard [sinch x] for "hyperboic sine of x". Is this correct?

How would you pronounce tanh x? Instead of saying "hyperbolic tangent of x"?

Thank you very much in advance.

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    $\begingroup$ I remember with amusement the pronunciation "tank" by an applied mathematician of the old school. Don't know whether it was idiosyncratic or a Britishism. Also have heard "tsan" (with a lisp). And then there is "shine." $\endgroup$ – André Nicolas Jul 28 '12 at 2:04
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    $\begingroup$ "Cinch" and "cosh", I've heard being used for the first two hyperbolic functions. $\endgroup$ – J. M. isn't a mathematician Jul 28 '12 at 2:04
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    $\begingroup$ Looking around, apparently a number of people use "tanch" for the hyperbolic tangent... $\endgroup$ – J. M. isn't a mathematician Jul 28 '12 at 2:12
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    $\begingroup$ My professors used "cinch" (as in cinch a belt) for sinh, "cosh" (pronounced like the first part of "kosher") for cosh, and "tanch"(rhymes with branch) for tanh. None of these "verbal abbreviations" were presented as "official". $\endgroup$ – David Wheeler Jul 28 '12 at 2:26
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    $\begingroup$ I think the moderators here are being far too pernickety. Mathematicians are human beings. When it comes to things like pronunciations they all have opinions. Does that mean mathematicians shouldn't come here to express their opinions or students shouldn't come here to find out what those opinions are? Some aspects of doing maths, in particular saying it out loud, will always be opinion based, it seems churlish to try and exclude discussion about it here. $\endgroup$ – Geoff Pointer May 24 '16 at 23:20
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I usually say "sine-h", "cos-h", and "tan-h" with the "h" pronounced "aich" like the letter.

Sometimes I pronounce "cosh" as a word with a long "o".

I guess this qualifies as an answer, instead of just a comment.

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  • $\begingroup$ Wow - I got 4 upvotes on this! $\endgroup$ – marty cohen Jul 30 '12 at 0:55
  • $\begingroup$ this should be the accepted answer. $\endgroup$ – braaterAfrikaaner Aug 2 '18 at 1:28
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    $\begingroup$ In my opinion, this could be ambiguous as h could be a variable. So does "sine-h" mean $\sinh$ or $\sin(h)$? And then saying "sine-h-x" or "sine-h of x" sounds weird to me, but that is likely because I've only heard "hyperbolic sine" and "sinch". $\endgroup$ – rosterherik Oct 21 '18 at 22:49
  • $\begingroup$ In "machine learning", in my experience (so, typically more at "programmers" than pure "mathematicians", & also folks fairly used to uttering variables & symbols), I've only heard "tan-h" (i.e., /tan aich/), and you don't often need to use/pronounce sinh or cosh. This seems to be more intuitive if you've only read it before, & never heard it specifically called anything. $\endgroup$ – michael Oct 30 '18 at 4:52
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Here are some pronunciations that I use with alternate pronunciations given by others.

  • $\sinh$ - Sinch (sɪntʃ) (Others say "shine" (ʃaɪn) according to Olivier Bégassat et al.)
  • $\cosh$ - Kosh (kɒʃ or koʊʃ)
  • $\tanh$ - Tanch (tæntʃ) (Others say "tsan" (tsæn) or "tank" (teɪnk) according to André Nicolas)
  • $\coth$ - Koth (kɒθ) according to J. M.
  • $\operatorname{csch}$ - Kisch (kɪʃ) according to J. M.
  • $\operatorname{sech}$ - Seech (siːtʃ)

I'm sure many people pronounce these functions much differently; pronunciation is simply based on preference.

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  • $\begingroup$ Might as well... I've also heard "kisch" for $\mathrm{csch}$. $\mathrm{sech}$ is certainly pronounced phonetically. $\endgroup$ – J. M. isn't a mathematician Jul 28 '12 at 2:35
  • $\begingroup$ My grand-father, who was a mathematician of australian origin, used to pronounce $\sinh$ like one would pronounce shine. $\endgroup$ – Olivier Bégassat Jul 28 '12 at 2:52
  • $\begingroup$ @J.M. I have added these pronunciations along with others made by commenters for diversity. $\endgroup$ – Argon Jul 28 '12 at 3:11
  • $\begingroup$ @Argon, I wondered about csch, coth, sech too. Thank you very much for your detailed pronunciation info!! $\endgroup$ – Tony Jul 28 '12 at 22:33
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I believe that in UK and the Commonwealth countries, the accepted pronunciations are /ʃaɪn/ (like "shine"), /kɒʃ/ ("cosh") and /θæn/ (like "thank" without the k). American usage may differ.

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    $\begingroup$ One wonders if it's ever been referred to as "coshine"... $\endgroup$ – J. M. isn't a mathematician Jul 28 '12 at 6:12
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In India "sinh" is pronounced "shine", for reasons I have never known.
"cosh" is pronounced to rhyme with "posh".
"tanh" I don't recall hearing being pronounced; maybe you'd pronounce "tanh x" as "shine x by cosh x". :-)

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    $\begingroup$ In some Arabic-speaking schools, it's "shine" as well. Also "coshine" and "tansh." $\endgroup$ – user2468 Jul 28 '12 at 2:56
  • $\begingroup$ I am also an Indian, the way my teacher (in high school) pronounced is same as marty's answer i.e "sine-h", "cos-h", and "tan-h" with the "h" pronounced "aich" like the letter. I have also heard the pronunciation as stated in Argon answer during undergrad. "Shine" and "Posh" is new to me. However, I wouldn't be surprised if there exist few other pronunciation. $\endgroup$ – Quixotic Jul 28 '12 at 3:02
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    $\begingroup$ I've always thought that in India we should pronounce it Singh instead... $\endgroup$ – user856 Jul 28 '12 at 3:06
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My maths professor Siegfried Goeldner who got his PhD in mathematics at the Courant Institute at New York University under one of the German refugees from Goetingen, in 1960, pronounced sinh as /ʃaɪn/, cosh as /kɒʃ/ ("cosh") and tanh as /θæn/, i.e., as shine, cosh and than with a soft th like in theta---the same pronunciation in three countries, in three continents, but 53 years ago.

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In your lecture, pronounce it "hyperbolic sine" the first time, then after that use whatever short form you like.

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My school pronounces them as 'shine' 'cosh' and 'than'. Where in 'than', the 'th' is pronounced as the 'th' in 'thyme', so a soft 'th' sound.

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    $\begingroup$ In English, thyme is pronounced the same as time. You probably want the soft th as in thank or theme or theta. $\endgroup$ – Geoff Pointer May 24 '16 at 23:11
  • $\begingroup$ @GeoffPointer What is a hard "th" sound then? $\endgroup$ – rosterherik Oct 21 '18 at 22:50
  • $\begingroup$ @rosterherik: As with the th in thyme, which is pronounced the same as time. $\endgroup$ – Geoff Pointer Oct 22 '18 at 6:00

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