{"id":11632,"date":"2022-08-03T20:41:37","date_gmt":"2022-08-03T15:11:37","guid":{"rendered":"https:\/\/mathemerize.com\/?p=11632"},"modified":"2022-08-03T20:41:45","modified_gmt":"2022-08-03T15:11:45","slug":"given-sec-theta-13over-12-calculate-all-other-trigonometric-ratios","status":"publish","type":"post","link":"https:\/\/mathemerize.com\/given-sec-theta-13over-12-calculate-all-other-trigonometric-ratios\/","title":{"rendered":"Given \\(sec \\theta\\) = \\(13\\over 12\\), calculate all other trigonometric ratios."},"content":{"rendered":"<h2>Solution :<\/h2>\n<p>Consider a triangle ABC in which \\(\\angle\\) A = \\(\\theta\\) and \\(\\angle\\) B = 90<img decoding=\"async\" loading=\"lazy\" class=\" wp-image-11639 alignright\" src=\"https:\/\/i0.wp.com\/mathemerize.com\/wp-content\/uploads\/2022\/08\/trigonometry8-1-5.jpeg?resize=212%2C162&#038;ssl=1\" alt=\"triangle\" width=\"212\" height=\"162\" srcset=\"https:\/\/i0.wp.com\/mathemerize.com\/wp-content\/uploads\/2022\/08\/trigonometry8-1-5.jpeg?resize=300%2C229&amp;ssl=1 300w, https:\/\/i0.wp.com\/mathemerize.com\/wp-content\/uploads\/2022\/08\/trigonometry8-1-5.jpeg?resize=1024%2C782&amp;ssl=1 1024w, https:\/\/i0.wp.com\/mathemerize.com\/wp-content\/uploads\/2022\/08\/trigonometry8-1-5.jpeg?resize=768%2C586&amp;ssl=1 768w, https:\/\/i0.wp.com\/mathemerize.com\/wp-content\/uploads\/2022\/08\/trigonometry8-1-5.jpeg?resize=1536%2C1173&amp;ssl=1 1536w, https:\/\/i0.wp.com\/mathemerize.com\/wp-content\/uploads\/2022\/08\/trigonometry8-1-5.jpeg?w=1700&amp;ssl=1 1700w\" sizes=\"(max-width: 212px) 100vw, 212px\" data-recalc-dims=\"1\" \/><\/p>\n<p>Then, Base = AB, perp = BC and Hypo. = AC,<\/p>\n<p>\\(\\therefore\\)\u00a0 \\(sec \\theta\\) = \\(perp\\over hypo\\) = \\(BC\\over AC\\) = \\(3\\over 4\\)<\/p>\n<p>Let AC = 13k and AB = 12k. Then,<\/p>\n<p>By using Pythagoras Theorem,<\/p>\n<p>\\({BC}^2\\) = \\({AC}^2\\) &#8211; \\({AB}^2\\)<\/p>\n<p>= \\(169k^2\\) &#8211; \\(125k^2\\) = \\(25k^2\\)<\/p>\n<p>\\(\\implies\\) BC = 5k<\/p>\n<p>\\(sin \\theta\\) = \\(BC\\over AC\\) = <strong>\\(5\\over 13\\)<\/strong><\/p>\n<p>\\(cos \\theta\\) = \\(AB\\over AC\\) = <strong>\\(12\\over 13\\)<\/strong><\/p>\n<p>\\(tan \\theta\\) = \\(BC\\over AB\\) = <strong>\\(5\\over 12\\)<\/strong><\/p>\n<p>\\(cot \\theta\\) = \\(AB\\over BC\\) =<strong> \\(12\\over 5\\)<\/strong><\/p>\n<p>\\(cosec \\theta\\) = \\(AC\\over BC\\) = <strong>\\(13\\over 5\\)<\/strong><\/p>\n","protected":false},"excerpt":{"rendered":"<p>Solution : Consider a triangle ABC in which \\(\\angle\\) A = \\(\\theta\\) and \\(\\angle\\) B = 90 Then, Base = AB, perp = BC and Hypo. = AC, \\(\\therefore\\)\u00a0 \\(sec \\theta\\) = \\(perp\\over hypo\\) = \\(BC\\over AC\\) = \\(3\\over 4\\) Let AC = 13k and AB = 12k. Then, By using Pythagoras Theorem, \\({BC}^2\\) = &hellip;<\/p>\n<p class=\"read-more\"> <a class=\"\" href=\"https:\/\/mathemerize.com\/given-sec-theta-13over-12-calculate-all-other-trigonometric-ratios\/\"> <span class=\"screen-reader-text\">Given \\(sec \\theta\\) = \\(13\\over 12\\), calculate all other trigonometric ratios.<\/span> Read More &raquo;<\/a><\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"site-sidebar-layout":"default","site-content-layout":"default","ast-global-header-display":"","ast-main-header-display":"","ast-hfb-above-header-display":"","ast-hfb-below-header-display":"","ast-hfb-mobile-header-display":"","site-post-title":"","ast-breadcrumbs-content":"","ast-featured-img":"","footer-sml-layout":"","theme-transparent-header-meta":"","adv-header-id-meta":"","stick-header-meta":"","header-above-stick-meta":"","header-main-stick-meta":"","header-below-stick-meta":""},"categories":[43,60],"tags":[],"yoast_head":"<!-- This site is optimized with the Yoast SEO plugin v20.12 - https:\/\/yoast.com\/wordpress\/plugins\/seo\/ -->\n<title>Given \\(sec \\theta\\) = \\(13\\over 12\\), calculate all other trigonometric ratios. - Mathemerize<\/title>\n<meta name=\"robots\" content=\"index, follow, max-snippet:-1, max-image-preview:large, max-video-preview:-1\" \/>\n<link rel=\"canonical\" href=\"https:\/\/mathemerize.com\/given-sec-theta-13over-12-calculate-all-other-trigonometric-ratios\/\" \/>\n<meta property=\"og:locale\" content=\"en_US\" \/>\n<meta property=\"og:type\" content=\"article\" \/>\n<meta property=\"og:title\" content=\"Given \\(sec \\theta\\) = \\(13\\over 12\\), calculate all other trigonometric ratios. - Mathemerize\" \/>\n<meta property=\"og:description\" content=\"Solution : Consider a triangle ABC in which (angle) A = (theta) and (angle) B = 90 Then, Base = AB, perp = BC and Hypo. = AC, (therefore)\u00a0 (sec theta) = (perpover hypo) = (BCover AC) = (3over 4) Let AC = 13k and AB = 12k. Then, By using Pythagoras Theorem, ({BC}^2) = &hellip; Given (sec theta) = (13over 12), calculate all other trigonometric ratios. 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Mathemerize","robots":{"index":"index","follow":"follow","max-snippet":"max-snippet:-1","max-image-preview":"max-image-preview:large","max-video-preview":"max-video-preview:-1"},"canonical":"https:\/\/mathemerize.com\/given-sec-theta-13over-12-calculate-all-other-trigonometric-ratios\/","og_locale":"en_US","og_type":"article","og_title":"Given \\(sec \\theta\\) = \\(13\\over 12\\), calculate all other trigonometric ratios. - Mathemerize","og_description":"Solution : Consider a triangle ABC in which (angle) A = (theta) and (angle) B = 90 Then, Base = AB, perp = BC and Hypo. = AC, (therefore)\u00a0 (sec theta) = (perpover hypo) = (BCover AC) = (3over 4) Let AC = 13k and AB = 12k. Then, By using Pythagoras Theorem, ({BC}^2) = &hellip; Given (sec theta) = (13over 12), calculate all other trigonometric ratios. 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