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Some of you may have heard Richard Feynman talk about a notation he invented for trigonometric functions to give them a more symbolic representation. He stopped using the notation in his teens and I can't find any published examples of it so I had to make assumptions as to what it would have looked like.

"While I was doing all this trigonometry, I didn't like the symbols for sine, cosine, tangent, and so on. To me, "sin f" looked like s times i times n times f! So I invented another symbol, like a square root sign, that was a sigma with a long arm sticking out of it, and I put the f underneath. For the tangent it was a tau with the top of the tau extended, and for the cosine I made a kind of gamma, but it looked a little bit like the square root sign. Now the inverse sine was the same sigma, but left -to-right reflected so that it started with the horizontal line with the value underneath, and then the sigma. That was the inverse sine, NOT sink f--that was crazy! They had that in books! To me, sin_i meant i/sine, the reciprocal. So my symbols were better."

Reference https://www.physicsforums.com/threads/feynmans-trig-notations.78087/

Here is my interpretation of that: [edit: after re-listening to him describe it he was definitely using lower case greek letters, not upper case as I previously thought. Image edited to reflect this.]

enter image description here

How could I create these symbols in Latex and have them extend over terms of any length?

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    I find the arguments by Feynman quite weak and the notation outstandingly horrible. ;-)
    – egreg
    Oct 22, 2015 at 20:53
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    Regardless of the practicality of this notation, it's still an interesting exercise in tinkering with Latex. Oct 22, 2015 at 21:24
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    Using gamma for the cosine is nonsense. The Greek initials for sine is “eta” (ημίτονο), and for “cosine” is “sigma” (συνημίτονο). For the tangent it's “epsilon” (εφαπτομένη).
    – egreg
    Oct 22, 2015 at 21:28
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    The trigonometric functions and their names are not of Greek origin, so the use of greek letters is just for symbols to represent the functions. If you have a suggestion for alternative symbols please share. Oct 22, 2015 at 22:05
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    @OliverBurt I was wondering how did you create the image above?
    – Maesumi
    Oct 23, 2015 at 1:23

1 Answer 1

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Here you go. I didn't put too much effort into it, as I hope you will realize that it is ill-advised to use this.

\documentclass{article}
\usepackage{graphicx}% provides \resizebox
\makeatletter
\def\fsin#1{\mathpalette\f@op{{#1}{\sigma}}}
\def\fcos#1{\mathpalette\f@op{{#1}{\gamma}}}
\def\ftan#1{\mathpalette\f@op{{#1}{\tau}}}
\def\f@op#1#2{%
  \f@@op{#1}#2
}
\def\f@@op#1#2#3{%
  \sbox0{$#1#2$}%
  \resizebox{\width}{\dimexpr\ht0+1.4pt\relax}{$#3$}%
  \hskip-.6pt% <-- this is a guess
  \vrule height \dimexpr\ht0+1.4pt\relax depth -\dimexpr\ht0+.4pt\relax width \wd0\relax
  \llap{\box0}%
}
\makeatother
\begin{document}
$\fcos{\theta} = \cos\theta$

$\fsin{\theta} = \sin\theta$

$\ftan{\theta} = \tan\theta$
\end{document}

enter image description here

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