Vedic Trignometry
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)
(3438 sin (A))
1 03 45 makhi 225 225 224.8560
2 07 30 bhakhi 224 449 448.7490
3 11 15 phakhi 222 671 670.7205
4 15 00 dhakhi 219 890 889.8199
5 18 45 akhi 215 1105 1105.1089
6 22 30 akhi 210 1315 1315.6656
7 26 15 akhi 205 1520 1520.5885
8 30 00 hasjha 199 1719 1719.0000
9 33 45 skaki 191 1910 1910.0505
10 37 30 kiga 183 2093 2092.9218
11 41 15 ghaki 174 2267 2266.8309
12 45 00 kighva 164 2431 2431.0331
13 48 45 ghlaki 154 2585 2584.8253
14 52 30 kigra 143 2728 2727.5488
15 56 15 hakya 131 2859 2858.5925
16 60 00 dhaki 119 2978 2977.3953
17 63 45 kica 106 3084 3083.4485
18 67 30 sga 93 3177 3176.2978
19 71 15 jhaa 79 3256 3255.5458
20 75 00 va 65 3321 3320.8530
21 78 45 kla 51 3372 3371.9398
22 82 30 pta 37 3409 3408.5874
23 86 15 pha 22 3431 3430.6390
24 90 00 cha 7 3438 3438.0000
by: newagephilosopher
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