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Jyā, koti-jyā and utkrama-jyā are three trigonometric functions introduced by Indian astronomers and mathematicians. The earliest known Indian treatise containing references to these functions is Surya Siddhanta. These are functions of arcs of circles and not functions of angles. Jyā and koti-jyā are closely related to the modern trigonometric functions of sine and cosine. In fact, the origins of the modern terms of "sine" and "cosine" have been traced back to the Sanskrit words jyā and koti-jyā.〔 ==Definition== Let 'arc AB' denote an arc whose two extremities are A and B of a circle with center O. If a perpendicular BM be dropped from B to OA, then: * ''jyā'' of arc AB = BM * ''koti-jyā'' of arc AB = OM * ''utkrama-jyā'' of arc AB = MA If the radius of the circle is ''R'' and the length of arc AB is ''s'', the angle subtended by arc AB at O measured in radians is θ = ''s'' / ''R''. The three Indian functions are related to modern trigonometric functions as follows: * ''jyā'' ( arc AB ) = ''R'' sin ( ''s'' / ''R'' ) * ''koti-jyā'' ( arc AB ) = ''R'' cos ( ''s'' / ''R'' ) * ''utkrama-jyā'' ( arc AB ) = ''R'' ( 1 - cos ( ''s'' / ''R'' ) ) = ''R'' versin ( ''s'' / ''R'' ) 抄文引用元・出典: フリー百科事典『 ウィキペディア（Wikipedia）』 ■ウィキペディアで「Jyā, koti-jyā and utkrama-jyā」の詳細全文を読む スポンサード リンク
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