subject: Vedic Trignometry [print this page] In Hindu Trignometry ( which is derived from Trikonamithi, trikona = triangle and trignon = triangle ), Jya resembles the modern Sine and Koti Jya, the cosine.
But in actuality, Jya is R Sin, that is Radius multiplied by modern sine.
By Jya, Brahmagupta meant 5 degrees of a circle. In Hindu Sine Tables and Tan Tables, the values are given for 5 degrees, 10 degrees, 15 degrees etc so that the Astro Maths students need not bother about using the Indian trignometric and inverse functions. Aryabhata's sine tables are found to be accurate, when compared to modern sine tables.
In other words, one Zodiacal Constellation, which is 30 degrees is made up of 6 jyas and a total of 72 Jyas constitute the Zodiac.
Koti Jya is R Cos, that is Radius multiplied by modern cosine.
Utkram Jya is the reverse sine, defined as 1- cos x. Since the Reverse sine resembled an arrow, Brahmagupta called it Sara. And since the Arcsine resembled a bow, he called itChapa.
Bhujajya is radius multiplied by modern sine and bhujachapa is the arcsine. Kotijya is radius multiplied by modern cosine and Kotichapa is arccos. Sparshjya is tan and sparshachapa is arctan.
Aryabhata's Sine Table was the first ever constructed sine table in the History of Maths.
This is Aryabhata's Sine Table given for different Kakshyas ( One Kakshya is 3 degrees 45 mins, one eighth of 30 degrees Zodiacal Sign )
Sl. No Angle ( A ) (in degrees, arcminutes) Value in ryabhaa's numerical notation
(in Devanagari) Value in ryabhaa's numerical notation (in ISO 15919 transliteration) Value in Arabic numerals ryabhaa's value of jya (A) Modern value of jya (A)
