Trigonometry: Difference between revisions
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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''. | 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''. | ||
[[File:Trigonometry.jpg|alt=Fig.1|thumb|Fig.1]] | [[File:Trigonometry.jpg|alt=Fig.1|thumb|Fig.1]] | ||
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 | 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. | ''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. | ||
== <u>''Jyā''</u> == | |||
''Jyā'' in sanskrit means "a bow-string" and hence the " chord of an arc" for the arc is called " a bow" (dhanu, cāpa) | |||
Revision as of 14:19, 23 December 2022
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.
Jyā
Jyā in sanskrit means "a bow-string" and hence the " chord of an arc" for the arc is called " a bow" (dhanu, cāpa)
