# First appearance of the sine function [duplicate]

I was wondering when was the sine function (I suppose cosine too) first introduced or defined and what was the need for?

## 2 Answers

Trigonometry was invented by the Greeks of Hellenistic period. The only trigonometric function they used was the chord related to the sine by $$\mathrm{chd}\,x=2\sin(x/2).$$ The first known tables of the chord were composed by Ptolemy. Sine was introduced in the Indian treatease Surya Siddhanta, see https://en.wikipedia.org/wiki/Jy%C4%81,_koti-jy%C4%81_and_utkrama-jy%C4%81 whose exact date is unknown (6th century), and the first table of sines was in Ariabhata (6th century).

The name sine is due to Gerard of Cremona who translated Arab text to the Latin in 12th century.

The use of sine vs chord is a question of convenience in a particular problem. (There are even modern papers in which the chord function is used). The main application of trigonometry was in astronomy. See also https://en.wikipedia.org/wiki/History_of_trigonometry

• Do you know what's the original arabic name for sine? and what was the chord function useful for? – Learn_and_Share Feb 8 '17 at 10:50
• The Arabic name for sine is in the Wikipedia article I refered to. Chord (and all trig) was used in astronomy, as I wrote. For example, for coordinate changes between horizontal, polar and ecliptic coordinates. – Alexandre Eremenko Feb 8 '17 at 12:09
• @AlexandreEremenko Presumably you meant to write "sine vs chord", rather than "sign vs chord"? – njuffa Feb 11 '17 at 19:06

To add more details to Alexandre Eremenko's good answer, here is what I've found here (in French):

• First time: introduced by the indian astronomer Âryabhata (6th century) who used the word "jîva" meaning rope or chord.
• Then: the arabic mathematician Al-Fazzârî (8th century) translated this word to arabic as "jîba", a word that doesn't necessarily have an arabic meaning.
• After that: the italian writer and translator Gerard of Cremona (12th century) confused this word with the arabic word "jaîb" meaning pocket, sinus or cavity and hence translated it to latin as sinus.