# Clearly, it's pronounced "kisskshhh of ex"November 19, 2011 11:59 PM   Subscribe

How do you pronounce the hyperbolic trigonometric functions?

This has been on my mind recently. I'm talking about the hyperbolic trig functions, sinh(x), cosh(x), tanh(x), and so on. I know people pronounce "sinh(x)" as "cinch of ex" and cosh(x) as "kosh of ex" (kosh, rhyming with gosh, as in gosh, those are awesome trig functions).

I think I've heard people pronounce "tanh(x)" as "tanch of ex" (rhyming with branch). I don't think I've heard, out loud, coth, sech, or csch. That last one just looks absurd anyway.

I'm talking about these on Monday, and it occurs to me that I've never thought of trying to pronounce some of these out loud. I've always said "hyperbolic \$TRIG_FUNCTION" when I've needed to.

Do people just say "hyperbolic cosecant"? Do you say "cotch" for "coth", rhyming with "crotch"? Halp me!
posted by King Bee to Education (21 answers total) 1 user marked this as a favorite

I say "hyperbolic tangent" when I'm trying to be clear, or "tan h" when clarity isn't a problem. "Hyperbolic sine" and "hyperbolic cosine," or "sine h" and "cosine h." Same with secants and such.
posted by WasabiFlux at 12:02 AM on November 20, 2011 [3 favorites]

I regularly use asinh x and usually call it "inverse hyperbolic sine." I don't think I would ever call it "aycinch" or know what people were talking about if they did. "A sine aitch" I would understand.
posted by grouse at 12:35 AM on November 20, 2011 [3 favorites]

In my UK A-level Math(s!) course, I was taught "shine", "cosh", "than" with a hard "th", like "thick".
posted by cogat at 12:54 AM on November 20, 2011

Also used shine, cosh and than... The "Drunken" functions :)
posted by dave99 at 1:33 AM on November 20, 2011

I would say cinch, cosh (rhymes with posh), and tansch (rhymes with ranch) and considered the other three to be "one over cinch," "one over cosh," and "one over tansch." At least in my physics undergrad and grad courses, we never much used secant/cosecant/cotangent or their hyperbolic equivalents.
posted by Schismatic at 1:54 AM on November 20, 2011

sinech, cosh, tanch, one over sinech, one over cosh, etc. I've heard a fair number of people say "shine".

Alternatively, rewrite everything in terms of exponentials and reduce this problem to the already solved one of how to say "e to to the power of".
posted by doop at 2:56 AM on November 20, 2011 [2 favorites]

Tanch (with a hard a), Cosh, sinch.
posted by Urtylug at 3:38 AM on November 20, 2011

Best answer: I say cosh (long 'o'), sinch, tanch, seetch, coseetch, and cotanch.
posted by monkeymadness at 5:34 AM on November 20, 2011

I used variations on the above suggestions (cosh, sinch, tanch, etc) when working on problem sets with friends, where we developed a slang, and it was easy to figure out what each was saying, and to ask a quick clarifying question.

If I were giving a talk to a group of folks, I would probably use the whole thing (inverse hyperbolic sin) to avoid confusion.
posted by rockindata at 6:36 AM on November 20, 2011

If I'm not saying "hyperbolic sine" etc., I say sine-aitch, cose-aitch, tan-aitch.
posted by dfan at 6:53 AM on November 20, 2011

Shine. Cosh. Tanch.

I could be flexible on the pronunciation of tanh. But not sinh or cosh.
posted by plonkee at 7:26 AM on November 20, 2011

Best answer: "Shine"? Why not "shin"? This makes no sense to me.

UK-Canada math(s) graduate here, who just says "hyperbolic cosecant" or whatever. I seem to recall being told to say "cinch" and "cosh" at some point, but I find this a little silly.

King Bee, in what context are you talking about these functions, on Monday? If you're teaching a class, I strongly recommend calling them by their full names to reduce the chance of confusion.
posted by kengraham at 8:59 AM on November 20, 2011

Canadian physics (late eighties to present): sinch, cosh and tanch.
posted by bonehead at 9:56 AM on November 20, 2011

When I did this stuff, in a land long ago and far away (Leeds, UK, 1977 - 1980) we said sinch, cosh and tanch.
posted by Decani at 10:44 AM on November 20, 2011

US engineer. My teachers invariably said "sine-H", "tan-H", "cos-H". Only in the last year have I ever heard anything like "cosh". Never "tanch" or "sinch", until this thread.
posted by IAmBroom at 11:07 AM on November 20, 2011

Another UK A level maths person here:

sinh = shine
cosh = kosh (to rhyme with 'gosh')
tanh = fan or than (with a hard 'th')
posted by Nufkin at 12:45 PM on November 20, 2011

Since everyone else is qualifying their qualifications, I'll add mine to my comment above. I'm a programmer in the US. That can lead to all kinds of odd pronunciations of abbreviated words (char, enum, ceil, etc, fputs, and so on). It's not only regional, but depends on the field and group. I don't know what it might be like in Texas.

If you're teaching these for the first time, whatever you choose is what they'll learn to use. Choose whatever looks least confusing.
posted by WasabiFlux at 1:04 PM on November 20, 2011

Another UK maths graduate here: I agree with shine, kosh, tanch. Don't remember anything about how the others were said. Always thought "shine" was a bizarre way to pronounce sinh - but that's how most people seem to say it.
posted by Jabberwocky at 1:24 PM on November 20, 2011

Best answer: Since everyone else is qualifying their qualifications...

Ok, US math prof. What I posted above is how I learned it and how I teach it. I always say "It's the hyperbolic sine, written 'sinh' and pronounced 'sinch'". It's also how engineers I've known refer to them. Honestly, though, I'd talk to any engineering faculty at your school if you're worried about confusion, and just use what they use.
posted by monkeymadness at 4:59 PM on November 20, 2011 [1 favorite]

I also learned these as "shine", "kosh" and "than" in Canada.
posted by emeiji at 6:26 PM on November 20, 2011

Response by poster: Thanks for the answers, everyone.

The context in which I'm talking about them today is indeed teaching them to students. I just wanted to know what the consensus was on pronunciation in case they ask about it (they generally have a knack for asking the wrong questions).

I'll probably just end up sticking with what I've been doing, which is referring to them as "hyperbolic \$TRIG_FUNCTION", but I appreciate your input.

I am, of course, going to give the students the exponential function formulas for these functions, but I'm starting with their geometric definitions (so it makes a whole lot more sense why they are called "hyperbolic" trig functions), then showing that they are equivalent to the algebraic ones.
posted by King Bee at 2:17 AM on November 21, 2011

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