Trigonometry
Hindu name for the science of Trigonometry is Jyotpatti-ganita or "the science of calculation for the construction of the sine". It is found as early as in the Brāhma-sphuṭa-siddhānta of Brahmagupta (628). In the recent years name appeared as Trikoṇamiti.
The Hindus introduced and employed three trigonometrical functions namely jyā , koṭi-jyā , utkrama-jyā. They are functions of an arc of a circle, but not of an angle. If AP is an arc of a circle with centre at O, then its jyā=PM, koṭi-jyā=OM and utkrama-jyā=OA-OM =AM. Hence their relation with modern trigonometrical functions will be
jyā AP=Rsinθ, koṭi-jyā AP=Rcosθ, utkrama-jyā AP=R-Rcosθ=Rversinθ, where R is the radius of the circle and θ the angle subtended at the centre by the arc AP. Thus the values of the Hindu trigonometrical functions vary with the radius chosen. The earliest Hindu treatise in which the above trigonometrical functions are now found recorded is the Sūrya-siddhānta.
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