TITLE: Do "other" trigonometric functions than Tan Sin Cos and their derivatives exist?
QUESTION [30 upvotes]: I remember my physics teacher mentioning that other trigonometric functions exist apart from the Sin Cos and Tan, he mentioned a few and they did not sound familiar, nothing like Sec Csc and Cot. I would like to learn more about them, if they exist.

REPLY [6 votes]: There are four other reasonable possibilities which he could have meant: 

Inverse trigonometric functions, e.g. $\arcsin$, $\arccos$, $\arctan$, but these are no trigonometric functions.
Hyperbolic trigonometric functions, e.g. $\sinh$, $\cosh$ and $\tanh$
$\mathrm{cis}(x)=\cos(x)+ i \sin(x) = e^{ix}$, and its inverse $\mathrm{arccis}(x)=\arg(x)$, but these are no trigonometric functions.
$\mathrm{sinc}(x)$, which is $\frac{\sin(x)}{x}$ for $x\neq0$ and $1$ for $x=0$. This is also no trigonometric function.

Yet another possibility is that he was talking about gyrotrigonometry, which has some applications in physics (quantum theory and special relativity, maybe your course was about this?). In fact, this seems the most likely to me.