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Indian sine tables were constructed and improved upon by several ancient Indian mathematicians including the authors of [[Surya Siddhanta (सूर्य सिद्धांता)|Surya Siddhanta]] and [[Āryabhaṭa]]. Earliest sine table is found in Surya Siddhanta and another text is the astronomical treatise Āryabhaṭīya which was composed during the fifth century by the  [[Indian mathematician]] and astronomer  [[Aryabhata|Āryabhaṭa]] (476–550 CE),  for the computation of the half-chords of certain set of arcs of a circle. The table found in Surya Siddhanta is a table (in modern terms) of values of R.sinθ where R is the Indian standard radius of 3438 minutes. Āryabhaṭa's table is also not a set of values of the trigonometric sine function in a conventional sense; it is a table of the first differences of the values of trigonometric sines expressed in arcminutes, and because of this the table is also referred to as ''Āryabhaṭa's table of sine-differences''.

Indian sine tables were constructed and improved upon by several ancient Indian mathematicians including the authors of [[Surya Siddhanta (सूर्य सिद्धांता)|Surya Siddhanta]] and [[Āryabhaṭa]]. Earliest sine table is found in Surya Siddhanta and another text is the astronomical treatise Āryabhaṭīya which was composed during the fifth century by the  [[Indian mathematician]] and astronomer  [[Aryabhata|Āryabhaṭa]] (476–550 CE),  for the computation of the half-chords of certain set of arcs of a circle. The table found in Surya Siddhanta is a table (in modern terms) of values of R.sinθ where R is the Indian standard radius of 3438 minutes. Āryabhaṭa's table is also not a set of values of the trigonometric sine function in a conventional sense; it is a table of the first differences of the values of trigonometric sines expressed in arcminutes, and because of this the table is also referred to as ''Āryabhaṭa's table of sine-differences''.<ref>Āryabhat·a's Rule and Table for Sine-Differences - ScienceDirect</ref>

Some believe that the Āryabhaṭa's table was the first sine table ever constructed in the history of mathematics. Āryabhaṭa's table remained as the standard sine table of ancient India. There were continuous attempts to improve the accuracy of this table. These endeavors culminated in the eventual discovery of the power series expansions of the sine and cosine functions by [[Madhava of Sangamagrama]] (c.1350 – c.1425), the founder of the Kerala school of astronomy and mathematics, and the tabulation of a sine table by Madhava with values accurate to seven or eight decimal places.

Some believe that the Āryabhaṭa's table was the first sine table ever constructed in the history of mathematics. Āryabhaṭa's table remained as the standard sine table of ancient India. There were continuous attempts to improve the accuracy of this table. These endeavors culminated in the eventual discovery of the power series expansions of the sine and cosine functions by [[Madhava of Sangamagrama]] (c.1350 – c.1425), the founder of the Kerala school of astronomy and mathematics, and the tabulation of a sine table by Madhava with values accurate to seven or eight decimal places.

== Ancient Indian concepts of Jya (chord) and Chaap or Dhanu (arc) ==

== Ancient Indian concepts of Jya (chord) and Chaap or Dhanu (arc) ==

'''Jyā''', '''koti-jyā''' and  '''utkrama-jyā''' are three trigonometric functions introduced  by [[Indian mathematics|Indian mathematician]]s and astronomers. 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 kotijyā 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 kotijyā.<ref name="Datta" />

'''Jyā''', '''koti-jyā''' and  '''utkrama-jyā''' are three trigonometric functions introduced  by [[Indian mathematics|Indian mathematician]]s and astronomers. 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 kotijyā 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 kotijyā.

===Definition===

===Definition===