The sine function
AI-drafted · awaiting admin review
Greek astronomers used chords; Indian astronomers switched to the half-chord, our sine. Aryabhata's sine table (499 CE) is the earliest securely dated one, and the word 'sine' itself comes from Sanskrit jya.
India first (well documented)Mathematics & astronomy
Indian claim
Trigonometry's sine and cosine were invented in India; even the word 'sine' comes from Sanskrit.
Evidence for the Indian claim
- The Aryabhatiya (499 CE) gives a table of half-chords (ardha-jya) for 24 angles at intervals of 3¾ degrees, in a circle of radius 3438.
- Indian astronomers also used the cosine (koti-jya) and versine (utkrama-jya).
- Sanskrit jya became Arabic jiba, misread as jaib ('fold'), which was translated into Latin as sinus, giving 'sine' (MacTutor).
Commonly credited to
Trigonometry began with Hipparchus and Ptolemy, who made tables of chords in a circle.
Evidence for the other claim
- Hipparchus (c. 140 BCE) compiled chord tables, and Ptolemy's Almagest (2nd century CE) has a full chord table.
- A chord table can be converted to sines, so the Greek work is the foundation of trigonometry.
What historians and scientists say
Trigonometry began with Greek chord tables, but the sine function itself, as used today, was introduced by Indian astronomers. The earliest securely dated sine table is Indian.