# pronunciation of sinh x, cosh x, tanh x for short

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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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." –  André Nicolas Jul 28 '12 at 2:04
"Cinch" and "cosh", I've heard being used for the first two hyperbolic functions. –  Ｊ. Ｍ. Jul 28 '12 at 2:04
Looking around, apparently a number of people use "tanch" for the hyperbolic tangent... –  Ｊ. Ｍ. Jul 28 '12 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". –  David Wheeler Jul 28 '12 at 2:26
@J.M. Thank you very much for your kind info!! –  Tony Jul 28 '12 at 22:47

Here are some pronunciations that I use with alternate pronunciations given by others.

• $\sinh$ - Sinch (sɪntʃ)
• $\cosh$ - 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) (Others say "shine" (ʃaɪn) according to Olivier Bégassat et al.)

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

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Might as well... I've also heard "kisch" for $\mathrm{csch}$. $\mathrm{sech}$ is certainly pronounced phonetically. –  Ｊ. Ｍ. Jul 28 '12 at 2:35
My grand-father, who was a mathematician of australian origin, used to pronounce $\sinh$ like one would pronounce shine. –  Olivier Bégassat Jul 28 '12 at 2:52
@J.M. I have added these pronunciations along with others made by commenters for diversity. –  Argon Jul 28 '12 at 3:11
@Argon, I wondered about csch, coth, sech too. Thank you very much for your detailed pronunciation info!! –  Tony Jul 28 '12 at 22:33

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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Wow - I got 4 upvotes on this! –  marty cohen Jul 30 '12 at 0:55

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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One wonders if it's ever been referred to as "coshine"... –  Ｊ. Ｍ. Jul 28 '12 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". :-)

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In some Arabic-speaking schools, it's "shine" as well. Also "coshine" and "tansh." –  user2468 Jul 28 '12 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. –  Quixotic Jul 28 '12 at 3:02
I've always thought that in India we should pronounce it Singh instead... –  Rahul Jul 28 '12 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.

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