{"id":3893,"date":"2010-07-02T07:04:00","date_gmt":"2010-07-02T07:04:00","guid":{"rendered":"https:\/\/www.eastrovedica.com\/wordpress\/?p=3893"},"modified":"2010-07-02T07:04:00","modified_gmt":"2010-07-02T07:04:00","slug":"about-sine-cosine-and-reverse-sine","status":"publish","type":"post","link":"https:\/\/www.eastrovedica.com\/wordpress\/?p=3893","title":{"rendered":"About Sine, Cosine and Reverse Sine"},"content":{"rendered":"<p><a href=\"http:\/\/4.bp.blogspot.com\/_65HA53jcYIU\/TC2PlxCJYNI\/AAAAAAAABks\/5tbzVZ_CTrE\/s1600\/Jya_and_kotijya.JPG\"><img decoding=\"async\" style=\"display:block; margin:0px auto 10px; text-align:center;cursor:pointer; cursor:hand;width: 320px; height: 277px;\" src=\"http:\/\/4.bp.blogspot.com\/_65HA53jcYIU\/TC2PlxCJYNI\/AAAAAAAABks\/5tbzVZ_CTrE\/s320\/Jya_and_kotijya.JPG\" border=\"0\" alt=\"\"id=\"BLOGGER_PHOTO_ID_5489201399814774994\" \/><\/a><\/p>\n<p><em>Jya<\/em> ( Sine ), <em>Kotijya<\/em> ( Cosine ) and <em>Utkram Jya<\/em> ( Versine ) are the three trignometric functions introduced by the Indian astronomers and mathematicians.<\/p>\n<p>In order to compute the celestial longitudes of planets, these functions were used by the trinity of Indian Astronomy, Bhaskara, Brahnmagupta and Aryabhata. <\/p>\n<p>Thrijya, the Radius or R <\/p>\n<p>If         360 = 2 Pi r<br \/>then,    r =  360\/2Pi    in degrees <\/p>\n<p>One degree is 60 minutes and one minute is 60 seconds and hence one degree is 3600 seconds.<\/p>\n<p>R in seconds will be ((360\/2pi)* 3600 ) Vikalas or 206265 seconds. This figure 206265 is known as the Magic Figure of Astronomy.  <\/p>\n<p>Bhujajya  = R Sin<br \/>Kotijya   = R Cos <\/p>\n<p>The arc sine of the angle is <em>Bhujachapa <\/em><br \/>The arc cosine of the angle is <em>Kotichapa<\/em><br \/>The arc tangent of the angle is <em>Sparshachapa<\/em><\/p>\n<p>By <em>Jya<\/em>, Bramhmagupta meant 5 degrees of a sign of 30 degrees. Hence a Zodiacal Sign consists of 6 Jyas ( 30 degrees ) . The Zodiac of 360 degrees was divided into 4 quarters of 90 degrees each. Three <em>Jyas<\/em> of 30 degrees each becomes a quadrant of the Zodiac and was called <em>Thrijya.<\/em><em> Thrijya <\/em>is also the Radius, the<em> Vyasardha.<\/em><\/p>\n<p>His magnum opus, the <em>Brahmasphuta Siddhanta <\/em>was translated by the Arabs as As Sind Hind. <em>Jya <\/em>became<em> jiba<\/em> and Kotijya became <em>kojiba<\/em> in Arabic.  It was translated into Latin as sinus ( meaning &#8221; bosom &#8221; ). So Sinus and Co-sinus when translated into English became Sine and Cosine !<\/p>\n<p>The <em>Aryabhateeyam<\/em> of Aryabhata was translated by the Arabs as <em>Al Arjabhat.<\/em> Trignometry is derived from the Sanskrit <em>Thrikonamithi<\/em> and Geometry from<em> Jyamithi !<\/em><\/p>\n","protected":false},"excerpt":{"rendered":"<p>Jya ( Sine ), Kotijya ( Cosine ) and Utkram Jya ( Versine ) are the three trignometric functions introduced by the Indian astronomers and mathematicians. In order to compute the celestial longitudes of planets, these functions were used by the trinity of Indian Astronomy, Bhaskara, Brahnmagupta and Aryabhata. Thrijya, the Radius or R If &hellip; <\/p>\n<p class=\"link-more\"><a href=\"https:\/\/www.eastrovedica.com\/wordpress\/?p=3893\" class=\"more-link\">Continue reading<span class=\"screen-reader-text\"> &#8220;About Sine, Cosine and Reverse Sine&#8221;<\/span><\/a><\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"open","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[1],"tags":[],"class_list":["post-3893","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\/3893","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\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/www.eastrovedica.com\/wordpress\/index.php?rest_route=%2Fwp%2Fv2%2Fcomments&post=3893"}],"version-history":[{"count":0,"href":"https:\/\/www.eastrovedica.com\/wordpress\/index.php?rest_route=\/wp\/v2\/posts\/3893\/revisions"}],"wp:attachment":[{"href":"https:\/\/www.eastrovedica.com\/wordpress\/index.php?rest_route=%2Fwp%2Fv2%2Fmedia&parent=3893"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.eastrovedica.com\/wordpress\/index.php?rest_route=%2Fwp%2Fv2%2Fcategories&post=3893"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.eastrovedica.com\/wordpress\/index.php?rest_route=%2Fwp%2Fv2%2Ftags&post=3893"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}