# Instances of alternative notation being used for the trigonometric functions?

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.

• In Spanish, "sine" is "seno" and the notation for "sin(x)" is "sen(x)." – Joel Reyes Noche Dec 29 '17 at 13:46
• In Soviet Union they used $\mathrm{tg}, \mathrm{ctg}, \mathrm{csc}$ for $\tan, \cot,$ and $\mathrm{cosec}$. – Alexandre Eremenko Dec 29 '17 at 14:31
• 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. – Alexandre Eremenko Dec 29 '17 at 14:37
• @AlexandreEremenko you got the use of csc and cosec backwards. The only place I've seen cosec is in Russian math books. – KCd Dec 30 '17 at 5:18
• Have you also heard about versine, haversine, etc. functions (en.wikipedia.org/wiki/Versine) ? – Jean Marie Becker Dec 30 '17 at 6:05

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