Question

How do you pronounce the word "sinh" and the names of the other hyperbolic functions?

Answer 1

It is pronounced as shine, cosh is pronounced as written, and tanh is tanch

Answer 2

It's not really an attempt to treat "sinh" as a word, more a convention to convey that it's a hyperbolic version of "sine"

Explanation:

The full names of the six trigonometric functions are:

"sine" (`tt"sin"`), called "sine" (sounds like "sign").

"cosine" (`tt"cos"`), called "cosine" (like "co-sign") or "cos".

"tangent" (`tt"tan"`), called "tan"

"secant", (`tt"sec"`), called "sec"

"cosecant", (`tt"csc"` or `tt"cosec"`), called "cosec"

"cotangent", (`tt"cot"`), called "cot"

To denote the hyperbolic versions, an `tt"h"` is appended to their abbreviations and the name by which they are called pronounced with some obvious "h". This is done in different ways, but the idea is simply to briefly convey that the given function is a hyperbolic version of a corresponding trigonometric one. After all "hyperbolic cosecant" is a bit of a mouthful.

"hyperbolic sine" (`tt"sinh"`), called "shine" or "cinch"

"hyperbolic cosine" (`tt"cosh"`), called "cosh"

"hyperbolic tangent" (`tt"tanh"`), called "tanch"

"hyperbolic secant" (`tt"sech"`), called "shek" or "sech"

"hyperbolic cosecant" (`tt"csch"` or `tt"cosech"`), called "coshek" or "cosech"

"hyperbolic cotangent" (`tt"coth"`), called "coth"