# pronunciation of sinh x, cosh x, tanh x for short [closed]

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.

• 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." Jul 28, 2012 at 2:04
• "Cinch" and "cosh", I've heard being used for the first two hyperbolic functions. Jul 28, 2012 at 2:04
• Looking around, apparently a number of people use "tanch" for the hyperbolic tangent... Jul 28, 2012 at 2:12
• 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". Jul 28, 2012 at 2:26
• 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. May 24, 2016 at 23:20

## 7 Answers

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.

• Wow - I got 4 upvotes on this! Jul 30, 2012 at 0:55
• this should be the accepted answer. Aug 2, 2018 at 1:28
• 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". Oct 21, 2018 at 22:49
• 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. Oct 30, 2018 at 4:52

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.

• Might as well... I've also heard "kisch" for $\mathrm{csch}$. $\mathrm{sech}$ is certainly pronounced phonetically. Jul 28, 2012 at 2:35
• My grand-father, who was a mathematician of australian origin, used to pronounce $\sinh$ like one would pronounce shine. Jul 28, 2012 at 2:52
• @J.M. I have added these pronunciations along with others made by commenters for diversity. Jul 28, 2012 at 3:11
• @Argon, I wondered about csch, coth, sech too. Thank you very much for your detailed pronunciation info!!
– Tony
Jul 28, 2012 at 22:33

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.

• One wonders if it's ever been referred to as "coshine"... Jul 28, 2012 at 6:12

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". :-)

• In some Arabic-speaking schools, it's "shine" as well. Also "coshine" and "tansh."
– user2468
Jul 28, 2012 at 2:56
• 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. Jul 28, 2012 at 3:02
• I've always thought that in India we should pronounce it Singh instead...
– user856
Jul 28, 2012 at 3:06

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.

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

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.

• In English, thyme is pronounced the same as time. You probably want the soft th as in thank or theme or theta. May 24, 2016 at 23:11
• @GeoffPointer What is a hard "th" sound then? Oct 21, 2018 at 22:50
• @rosterherik: As with the th in thyme, which is pronounced the same as time. Oct 22, 2018 at 6:00