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

Question

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.

Answer 1

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.

Answer 2

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.

Answer 3

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". :-)

Answer 4

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.

Answer 5

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.

Answer 6

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