# History of sine function

I'm doing some research about the beginning of trigonometry. I want to know why and who draw the first time the sine function. Do you have one site or something that can help me ?

Ancient Greeks did not have the sine function; their only trigonometric function was the chord which is related to sine by the formula $\mathrm{chd(x)}=2\sin(x/2)$. The first known tables of chords are due to Ptolemy. Greek trigonometry penetrated to India during the Hellenistic period. Sine was introduced Aryabhata in India (476-550).

From India it penetrated to the Muslim world, where several astronomers developed trigonometry further, one notable figure was Abu al Wafa (940-998), who composed sine tables. He also introduced tangent.

In Europe people were not interested in mathematics at that time. Later the knowledge penetrated Europe, and the first European sine tables (other than copies of the Arab tables) were made by Johannes Muller (Regiomontanus, 1436-1476).

See Wikipedia articles on Abu al Wafa and Johann Muller.

See at least :

An overview of the early history of trigonometry is into:

The first modern textbook: Bartholomaeus Pitiscus, Trigonometriae sive de dimensione triangulorum libri quinque (1600, first edition 1595) does not seem to have graphs, but only tables.

We may suppose that to draw the graph of the trigonometric functions, we must have a "modern" idea of function.

The first (quite) clear understanding of it is:

Functio quantitatis variabilis, est expressio analytica quomodocunque composita ex illa quantitate variabili, et numeris seu quantitatibus constantibus.

See also CAPUT VIII De quantitatibus trascendentibus ex Circulo оrtis, page 90-on, for trigonometry.

Maybe in the Plates... see Planche 12, Fig.104.

• Is link-only answer tolerable? – user1709 Feb 13 '16 at 6:34
• @user36790, this isn't "link only" in my eyes. – vonbrand Feb 13 '16 at 21:12
• @vonbrand: Have you seen his answer before the edit? – user1709 Feb 14 '16 at 2:46

In the second century CE, Ptolemy created a table of chords that is in some sense equivalent to the sine function.