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But the first work to refer explicitly to the sine as a function of an angle is the Aryabhatiya of Aryabhata (ca. 510), considered the earliest Hindu treatise on pure mathematics. In the work Aryabhata uses the word ardha-jya for the half-chord, ... in due time he shortens it to jya or jiva

Now begins an interesting etymological evolution that would eventually lead to our modern word "sine". When the Arabs translated the Aryabhatiya, they retained the word jiva without translating its meaning. In Arabic -- as also in Hebrew -- words consist mostly of consonants, the pronunciation of the missing vowels being understood through common usage. Thus jiva could be pronounced as jiba or jaib, and jaib in Arabic means bosom, fold, or bay. When the Arabic version was translated into Latin, jaib was translated into sinus, which means bosom, bay, or curve (on lunar maps regions resembling bays are called sinus). We find the word sinus in the writings of Gherardo of Cremona (c.1114-1187) who translated many of the old Greek works, incl the almagest from Arabic into Latin. Other writers followed, and soon the word sinus -- or sine in its Engl version - became common in mathematical texts throughout Europe. p. 35

 
   page from the suryasiddhAnta in Hindi, for astronomical calculations
   based on Aryabhata's table of sines. The 24 rows of values each
   represent an increment of 3:45 degrees (225 min), for which Aryabhata
   had tabulated the sine differences. (p. 36)