{"id":3613,"date":"2026-03-21T01:49:26","date_gmt":"2026-03-21T01:49:26","guid":{"rendered":"https:\/\/npk1169-001-site1.mtempurl.com\/?p=3613"},"modified":"2026-04-13T07:56:26","modified_gmt":"2026-04-13T07:56:26","slug":"the-sine-function-of-trigonometry","status":"publish","type":"post","link":"https:\/\/www.bharatwisdom.com\/hi\/mathematics\/the-sine-function-of-trigonometry\/","title":{"rendered":"The Sine Function of Trigonometry \u2013 The Lost-in-Translation Star Map"},"content":{"rendered":"<div class=\"fusion-fullwidth fullwidth-box fusion-builder-row-1 fusion-flex-container nonhundred-percent-fullwidth non-hundred-percent-height-scrolling\" style=\"--awb-border-radius-top-left:0px;--awb-border-radius-top-right:0px;--awb-border-radius-bottom-right:0px;--awb-border-radius-bottom-left:0px;--awb-flex-wrap:wrap;\" ><div class=\"fusion-builder-row fusion-row fusion-flex-align-items-flex-start fusion-flex-content-wrap\" style=\"max-width:1279.2px;margin-left: calc(-4% \/ 2 );margin-right: calc(-4% \/ 2 );\"><div class=\"fusion-layout-column fusion_builder_column fusion-builder-column-0 fusion_builder_column_1_1 1_1 fusion-flex-column\" style=\"--awb-bg-size:cover;--awb-width-large:100%;--awb-margin-top-large:0px;--awb-spacing-right-large:1.92%;--awb-margin-bottom-large:0px;--awb-spacing-left-large:1.92%;--awb-width-medium:100%;--awb-spacing-right-medium:1.92%;--awb-spacing-left-medium:1.92%;--awb-width-small:100%;--awb-spacing-right-small:1.92%;--awb-spacing-left-small:1.92%;\"><div class=\"fusion-column-wrapper fusion-flex-justify-content-flex-start fusion-content-layout-column\"><div class=\"fusion-text fusion-text-1\"><p id=\"p-rc_ed88986f39805c81-220\" data-path-to-node=\"44\"><span data-path-to-node=\"44,0\"><b data-path-to-node=\"44,0\" data-index-in-node=\"0\">\u0905\u0935\u0927\u093e\u0930\u0923\u093e<\/b> <\/span><span data-path-to-node=\"44,2\"><span class=\"citation-981\">Trigonometry is the study of the relationships between triangle sides and angles<\/span><\/span><span data-path-to-node=\"44,4\">. <\/span><span data-path-to-node=\"44,6\"><span class=\"citation-980\">We can use the \u2018Sine\u2019 function to calculate distances that cannot be measured, such as the distance to a star or the height of a mountain<\/span><\/span><span data-path-to-node=\"44,8\">.<\/span><\/p>\n<p id=\"p-rc_ed88986f39805c81-221\" data-path-to-node=\"45\"><span data-path-to-node=\"45,0\"><b data-path-to-node=\"45,0\" data-index-in-node=\"0\">\u0915\u0939\u093e\u0928\u0940<\/b> The word \u2018Sine\u2019 is actually a thousand-year-old linguistic accident. <\/span><span data-path-to-node=\"45,2\"><span class=\"citation-979\">Ancient Indian astronomers like those who wrote the Surya Siddhanta used the Jya (half-chord) to measure the distance to the stars<\/span><\/span><span data-path-to-node=\"45,4\">. <\/span><span data-path-to-node=\"45,6\"><span class=\"citation-978\">When this knowledge reached the Arab world, they called it Jiba<\/span><\/span><span data-path-to-node=\"45,8\">. <\/span><span data-path-to-node=\"45,10\"><span class=\"citation-977\">But when Latin translators saw the word, they mistook it for the Arabic Jaib, which means a \u2018pocket\u2019 or \u2018fold\u2019 of a garment<\/span><\/span><span data-path-to-node=\"45,12\">. <\/span><span data-path-to-node=\"45,14\"><span class=\"citation-976\">They translated it into the Latin Sinus, and the name stuck<\/span><\/span><span data-path-to-node=\"45,16\">. <\/span><span data-path-to-node=\"45,18\"><span class=\"citation-975\">Every time a modern student uses a sine function in a GPS app, they are using a piece of Indian star-mapping that was literally \u2018lost in translation\u2019<\/span><\/span><span data-path-to-node=\"45,20\">.<\/span><\/p>\n<p data-path-to-node=\"46\"><b data-path-to-node=\"46\" data-index-in-node=\"0\">\u0938\u092e\u092f\u0930\u0947\u0916\u093e<\/b><\/p>\n<table data-path-to-node=\"47\">\n<thead>\n<tr>\n<td><strong>\u092e\u0940\u0932 \u0915\u093e \u092a\u0924\u094d\u0925\u0930<\/strong><\/td>\n<td><strong>\u0935\u093f\u0935\u0930\u0923<\/strong><\/td>\n<\/tr>\n<\/thead>\n<tbody>\n<tr>\n<td><span data-path-to-node=\"47,1,0,0\"><b data-path-to-node=\"47,1,0,0\" data-index-in-node=\"0\">\u092a\u0936\u094d\u091a\u093f\u092e\u0940 \u0938\u0902\u0926\u0930\u094d\u092d.<\/b><\/span><\/td>\n<td>\n<p id=\"p-rc_ed88986f39805c81-222\" data-path-to-node=\"47,1,1,0\"><span data-path-to-node=\"47,1,1,0,1\"><span class=\"citation-974\">1500s CE (Modern Trigonometry in Europe) <\/span><\/span><\/p>\n<div class=\"source-inline-chip-container ng-star-inserted\"><\/div>\n<\/td>\n<\/tr>\n<tr>\n<td><span data-path-to-node=\"47,2,0,0\"><b data-path-to-node=\"47,2,0,0\" data-index-in-node=\"0\">\u092d\u093e\u0930\u0924\u0940\u092f \u0938\u094d\u0930\u094b\u0924<\/b><\/span><\/td>\n<td>\n<p id=\"p-rc_ed88986f39805c81-223\" data-path-to-node=\"47,2,1,0\"><span data-path-to-node=\"47,2,1,0,1\"><span class=\"citation-973\">Prior to 10,000 BCE (Surya Siddhanta) &amp; 499 CE (Arabhata) <\/span><\/span><\/p>\n<div class=\"source-inline-chip-container ng-star-inserted\"><\/div>\n<\/td>\n<\/tr>\n<tr>\n<td><span data-path-to-node=\"47,3,0,0\"><b data-path-to-node=\"47,3,0,0\" data-index-in-node=\"0\">\u0915\u093e\u0932 \u0905\u0902\u0924\u0930\u093e\u0932<\/b><\/span><\/td>\n<td>\n<p id=\"p-rc_ed88986f39805c81-224\" data-path-to-node=\"47,3,1,0\"><span data-path-to-node=\"47,3,1,0,1\"><span class=\"citation-972\">Over 11,000 Years <\/span><\/span><\/p>\n<div class=\"source-inline-chip-container ng-star-inserted\"><\/div>\n<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<p data-path-to-node=\"48\"><b data-path-to-node=\"48\" data-index-in-node=\"0\">The Evidence<\/b><\/p>\n<blockquote data-path-to-node=\"49\">\n<p id=\"p-rc_ed88986f39805c81-225\" data-path-to-node=\"49,0\"><span data-path-to-node=\"49,0,0\"><b data-path-to-node=\"49,0,0\" data-index-in-node=\"0\">\u0938\u0902\u0938\u094d\u0915\u0943\u0924 \u0936\u094d\u0932\u094b\u0915:<\/b> \u091c\u094d\u092f\u093e\u0930\u094d\u0927\u0902 \u092e\u094c\u0930\u094d\u0935\u093f\u0915\u093e \u091c\u0940\u0935\u093e \u0938\u0930\u094d\u0935\u093e \u0935\u0915\u094d\u0930\u0947\u0937\u0941 \u0915\u0925\u094d\u092f\u0924\u0947 \u0964 <\/span><span data-path-to-node=\"49,0,2\"><span class=\"citation-971\">\u0924\u0938\u094d\u092e\u093e\u091c\u094d\u091c\u094d\u092f\u093e\u0930\u094d\u0927\u0917\u0941\u0923\u093e\u0903 \u0915\u093e\u0930\u094d\u092f\u093e \u092d\u0935\u0928\u094d\u0924\u093f \u0915\u094b\u091f\u093f\u091c\u0940\u0935\u093e\u0903 \u0965 <\/span><\/span><span data-path-to-node=\"49,0,4\"> <b data-path-to-node=\"49,0,4\" data-index-in-node=\"1\">\u0932\u093f\u092a\u094d\u092f\u0902\u0924\u0930\u0923:<\/b> Jy\u0101rdha\u1e43 maurvik\u0101 j\u012bv\u0101 sarv\u0101 vakre\u1e63u kathyate | Tasm\u0101jjy\u0101rdhagu\u1e47\u0101\u1e25 k\u0101ry\u0101 bhavanti ko\u1e6dij\u012bv\u0101\u1e25 || <\/span><span data-path-to-node=\"49,0,6\"><span class=\"citation-970\">Surya Siddhanta (2.57) <\/span><\/span><span data-path-to-node=\"49,0,8\"> <b data-path-to-node=\"49,0,8\" data-index-in-node=\"1\">\u0905\u0930\u094d\u0925:<\/b> \u2018The half of the chord is called the Jya (Sine) or Jiva. <\/span><span data-path-to-node=\"49,0,10\"><span class=\"citation-969\">From that half-chord, the Kotijya (Cosine, literally the sine of the complement) is derived.\u2019 <\/span><\/span><\/p>\n<div class=\"source-inline-chip-container ng-star-inserted\"><\/div>\n<\/blockquote>\n<p id=\"p-rc_ed88986f39805c81-226\" data-path-to-node=\"50\"><span data-path-to-node=\"50,0\"><b data-path-to-node=\"50,0\" data-index-in-node=\"0\">\u0938\u0902\u092c\u0902\u0927\u093f\u0924 \u0928\u0935\u093e\u091a\u093e\u0930<\/b> <\/span><span data-path-to-node=\"50,2\"><span class=\"citation-968\">Ancient Indian texts such as the Surya Siddhanta and Aryabhatiya employed Koti-Jya (cosine) to calculate horizontal distances and Utkrama-Jya (versine, 1-cos(x)) to locate planets<\/span><\/span><span data-path-to-node=\"50,4\">.<\/span><\/p>\n<p id=\"p-rc_ed88986f39805c81-227\" data-path-to-node=\"51\"><span data-path-to-node=\"51,0\"><b data-path-to-node=\"51,0\" data-index-in-node=\"0\">\u0906\u0927\u0941\u0928\u093f\u0915 \u0935\u093f\u0930\u093e\u0938\u0924<\/b> <\/span><span data-path-to-node=\"51,2\"><span class=\"citation-967\">Trigonometry is useful in GPS technology, building structures, and researching waves (sound, light, and radio)<\/span><\/span><span data-path-to-node=\"51,4\">.<\/span><\/p>\n<\/div><\/div><\/div><\/div><\/div>","protected":false},"excerpt":{"rendered":"","protected":false},"author":1,"featured_media":3501,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"_acf_changed":false,"footnotes":""},"categories":[74],"tags":[],"class_list":["post-3613","post","type-post","status-publish","format-standard","has-post-thumbnail","hentry","category-mathematics"],"acf":[],"yoast_head":"<!-- This site is optimized with the Yoast SEO plugin v27.4 - https:\/\/yoast.com\/product\/yoast-seo-wordpress\/ -->\r\n<title>The Sine Function of Trigonometry \u2013 The Lost-in-Translation Star Map - BharatWisdom<\/title>\r\n<meta name=\"robots\" content=\"index, follow, max-snippet:-1, max-image-preview:large, max-video-preview:-1\" \/>\r\n<link rel=\"canonical\" href=\"https:\/\/www.bharatwisdom.com\/hi\/mathematics\/the-sine-function-of-trigonometry\/\" \/>\r\n<meta property=\"og:locale\" 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