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Consider the three "main" trigonometric functions, sine cosine and tangent; whose notations are sin(x); cos(x); tan(x).

Are there instances of alternative notations being used for these particular functions? The only one I could find so far was the use of "tang" by Leonard Euler for even when referencing trigonometry from Indian Babylonian, Egyptian or Chinese antic cultures, wikipedia uses the standard notation.

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    $\begingroup$ In Spanish, "sine" is "seno" and the notation for "sin(x)" is "sen(x)." $\endgroup$
    – JRN
    Dec 29, 2017 at 13:46
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    $\begingroup$ In Soviet Union they used $\mathrm{tg}, \mathrm{ctg}, \mathrm{csc}$ for $\tan, \cot,$ and $\mathrm{cosec}$. $\endgroup$
    – Alexandre Eremenko
    Dec 29, 2017 at 14:31
  • $\begingroup$ There was no true trigonometry in Babylonian and Egyptian culture. The Greeks (who invented trigonometry) had only one trigonometric function, the chord $\mathrm{chd}(x)=2\sin(x/2)$, but they did not use this notation; it was invented by 20 century historians to deal with the Greek science. The rest of trig functions are medieval inventions. $\endgroup$
    – Alexandre Eremenko
    Dec 29, 2017 at 14:37
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    $\begingroup$ @AlexandreEremenko you got the use of csc and cosec backwards. The only place I've seen cosec is in Russian math books. $\endgroup$
    – KCd
    Dec 30, 2017 at 5:18
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    $\begingroup$ Have you also heard about versine, haversine, etc. functions (en.wikipedia.org/wiki/Versine) ? $\endgroup$
    – Jean Marie Becker
    Dec 30, 2017 at 6:05

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Notation in indian trigonometry

The Indian mathematician and astronomer Aryabhata (476-550 CE) was the author of first sine table ever. It was a stanza composed of sanscrit Alphanumerals and words, which contained relations between arcs and half-chords of a circle.

So in this way of writing, notation for sine would just be it's name. The sanscrit word for half-chord is ardha-jyā what we would commonly see today as the sine.

litteral meaning

However, the word jyā ( ज्या in sanscrit ) came to mean half-chord when ardha-jyā was shortened : technical meaning

So the notations would be:

   sine : ज्या (jyā)
   cosine : कोटिज्या (koti-jyā)

jyā passed into Arabic as jība and was corrupted into jaib which means "bosom" and translates to sine in Latin

Feynman Notation

Apparently, during his younger years, The physicist Richard Feynman invented his own notation for the trig functions (which was never really used afterwards) :

Feynman trig notation

sources : https://tex.stackexchange.com/questions/274463/feynman-trig-notation-creating-custom-characters

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

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