{"id":4444,"date":"2011-07-13T09:24:00","date_gmt":"2011-07-13T09:24:00","guid":{"rendered":"https:\/\/www.eastrovedica.com\/wordpress\/?p=4444"},"modified":"2011-07-13T09:24:00","modified_gmt":"2011-07-13T09:24:00","slug":"aryabhatas-sine-tables","status":"publish","type":"post","link":"https:\/\/www.eastrovedica.com\/wordpress\/?p=4444","title":{"rendered":"Aryabhata’s Sine Tables"},"content":{"rendered":"

\"\"id=\"BLOGGER_PHOTO_ID_5628761879046949106\"<\/a><\/p>\n

In Hindu Trignometry ( which is derived from Trikonamithi<\/span>, trikona = triangle and trignon = triangle ), Jya resembles the modern Sine and Koti Jya, the cosine.<\/span><\/p>\n

But in actuality, Jya<\/span> is R Sin, that is Radius multiplied by modern sine.<\/p>\n

By Jya<\/span>, 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. <\/p>\n

In other words, one Zodiacal Constellation, which is 30 degrees is made up of 6 jyas<\/span> and a total of 72 Jyas<\/span> constitute the Zodiac. <\/p>\n

Koti Jya<\/span> is R Cos, that is Radius multiplied by modern cosine.<\/p>\n

Utkram Jya <\/span>is the reverse sine, defined as 1- cos x. Since the Reverse sine resembled an arrow, Brahmagupta called it Sara<\/span>. And since the Arcsine resembled a bow, he called it Chap<\/span>a.<\/p>\n

Bhujajya<\/span> is radius multiplied by modern sine and bhujachapa<\/span> is the arcsine. Kotijya<\/span> is radius multiplied by modern cosine and Kotichapa<\/span> is arccos. Sparshjya<\/span> is tan and sparshachapa<\/span> is arctan. <\/p>\n

Aryabhata’s Sine Table was the first ever constructed sine table in the History of Maths.<\/p>\n

This is Aryabhata’s Sine Table given for different Kakshyas <\/span> ( One Kakshya is 3 degrees 45 mins, one eighth of 30 degrees Zodiacal Sign )<\/p>\n

Sl. No Angle ( A ) (in degrees, arcminutes) Value in \u0100ryabha\u1e6da’s numerical notation
(in Devanagari) Value in \u0100ryabha\u1e6da’s numerical notation (in ISO 15919 transliteration) Value in Arabic numerals \u0100ryabha\u1e6da’s value of jya (A) Modern value of jya (A)
(3438 \u00d7 sin (A)) <\/p>\n

1 03\u00b0 45\u2032 \u092e\u0916\u093f makhi 225 225\u2032 224.8560
2 07\u00b0 30\u2032 \u092d\u0916\u093f bhakhi 224 449\u2032 448.7490
3 11\u00b0 15\u2032 \u092b\u0916\u093f phakhi 222 671\u2032 670.7205
4 15\u00b0 00\u2032 \u0927\u0916\u093f dhakhi 219 890\u2032 889.8199
5 18\u00b0 45\u2032 \u0923\u0916\u093f \u1e47akhi 215 1105\u2032 1105.1089
6 22\u00b0 30\u2032 \u091e\u0916\u093f \u00f1akhi 210 1315\u2032 1315.6656
7 26\u00b0 15\u2032 \u0919\u0916\u093f \u1e45akhi 205 1520\u2032 1520.5885
8 30\u00b0 00\u2032 \u0939\u0938\u094d\u091d hasjha 199 1719\u2032 1719.0000
9 33\u00b0 45\u2032 \u0938\u094d\u0915\u0915\u093f skaki 191 1910\u2032 1910.0505
10 37\u00b0 30\u2032 \u0915\u093f\u0937\u094d\u0917 ki\u1e63ga 183 2093\u2032 2092.9218
11 41\u00b0 15\u2032 \u0936\u094d\u0918\u0915\u093f \u015bghaki 174 2267\u2032 2266.8309
12 45\u00b0 00\u2032 \u0915\u093f\u0918\u094d\u0935 kighva 164 2431\u2032 2431.0331
13 48\u00b0 45\u2032 \u0918\u094d\u0932\u0915\u093f ghlaki 154 2585\u2032 2584.8253
14 52\u00b0 30\u2032 \u0915\u093f\u0917\u094d\u0930 kigra 143 2728\u2032 2727.5488
15 56\u00b0 15\u2032 \u0939\u0915\u094d\u092f hakya 131 2859\u2032 2858.5925
16 60\u00b0 00\u2032 \u0927\u0915\u093f dhaki 119 2978\u2032 2977.3953
17 63\u00b0 45\u2032 \u0915\u093f\u091a kica 106 3084\u2032 3083.4485
18 67\u00b0 30\u2032 \u0938\u094d\u0917 sga 93 3177\u2032 3176.2978
19 71\u00b0 15\u2032 \u091d\u0936 jha\u015ba 79 3256\u2032 3255.5458
20 75\u00b0 00\u2032 \u0919\u094d\u0935 \u1e45va 65 3321\u2032 3320.8530
21 78\u00b0 45\u2032 \u0915\u094d\u0932 kla 51 3372\u2032 3371.9398
22 82\u00b0 30\u2032 \u092a\u094d\u0924 pta 37 3409\u2032 3408.5874
23 86\u00b0 15\u2032 \u092b pha 22 3431\u2032 3430.6390
24 90\u00b0 00\u2032 \u091b cha 7 3438\u2032 3438.0000 <\/p>\n

Sine Table by courtesy www.wikipedia.org
<\/a><\/p>\n","protected":false},"excerpt":{"rendered":"

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 … <\/p>\n

Continue reading “Aryabhata’s Sine Tables”<\/span><\/a><\/p>\n","protected":false},"author":2,"featured_media":0,"comment_status":"open","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[1],"tags":[],"class_list":["post-4444","post","type-post","status-publish","format-standard","hentry","category-uncategorized"],"jetpack_featured_media_url":"","_links":{"self":[{"href":"https:\/\/www.eastrovedica.com\/wordpress\/index.php?rest_route=\/wp\/v2\/posts\/4444","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/www.eastrovedica.com\/wordpress\/index.php?rest_route=\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/www.eastrovedica.com\/wordpress\/index.php?rest_route=\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/www.eastrovedica.com\/wordpress\/index.php?rest_route=\/wp\/v2\/users\/2"}],"replies":[{"embeddable":true,"href":"https:\/\/www.eastrovedica.com\/wordpress\/index.php?rest_route=%2Fwp%2Fv2%2Fcomments&post=4444"}],"version-history":[{"count":0,"href":"https:\/\/www.eastrovedica.com\/wordpress\/index.php?rest_route=\/wp\/v2\/posts\/4444\/revisions"}],"wp:attachment":[{"href":"https:\/\/www.eastrovedica.com\/wordpress\/index.php?rest_route=%2Fwp%2Fv2%2Fmedia&parent=4444"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.eastrovedica.com\/wordpress\/index.php?rest_route=%2Fwp%2Fv2%2Fcategories&post=4444"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.eastrovedica.com\/wordpress\/index.php?rest_route=%2Fwp%2Fv2%2Ftags&post=4444"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}