Aryabhata's Invention of the Sine Function

In 499 CE, Indian mathematician-astronomer Aryabhata introduced sine tables in his work 'Aryabhatiya' at Pataliputra. He conceptualized the sine ('jya' in Sanskrit) as a half-chord, departing from Greek chord functions. Aryabhata created tables of sines at 3.75° intervals with 4-digit precision, using a reference circle with radius 3438. These tables enabled more accurate calculations of planetary positions and eclipses. The Sanskrit term 'jya' was transliterated into Arabic as 'jiba', later misinterpreted as 'jaib', and translated into Latin as 'sinus', producing the modern term 'sine'. This mathematical technique spread across civilizations and influenced subsequent trigonometric development.