{"id":356,"date":"2022-04-13T10:46:25","date_gmt":"2022-04-13T10:46:25","guid":{"rendered":"http:\/\/10thclass.deltapublications.in\/?page_id=356"},"modified":"2024-11-28T11:03:53","modified_gmt":"2024-11-28T11:03:53","slug":"s-1-trigonometric-ratios-sin-cos-and-tan","status":"publish","type":"page","link":"https:\/\/10thclass.deltapublications.in\/index.php\/s-1-trigonometric-ratios-sin-cos-and-tan\/","title":{"rendered":"S.1 Trigonometric ratios: sin, cos and tan"},"content":{"rendered":"\n<h2 class=\"wp-block-heading has-text-align-center has-text-color\" style=\"color:#00056d;text-transform:uppercase\"><strong> Trigonometric ratios: sin, cos and tan<\/strong><\/h2>\n\n\n\n<p class=\"has-text-color has-link-color has-huge-font-size wp-elements-87982a1885f28362b0345dcf26d18c66\" style=\"color:#74008b\"><strong>Key notes :<\/strong><\/p>\n\n\n\n<p class=\"has-text-color has-link-color has-large-font-size wp-elements-b9772d10875a7ca16956d8a90f8d2187\" style=\"color:#000060\"><strong>1. Introduction to Trigonometric Ratios<\/strong><\/p>\n\n\n\n<ul class=\"wp-block-list has-large-font-size\">\n<li>Trigonometric ratios are used to relate the angles of a right triangle to the lengths of its sides.<\/li>\n\n\n\n<li>These ratios are fundamental for solving problems involving right-angled triangles and are widely used in geometry, physics, engineering, and various other fields.<\/li>\n<\/ul>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity is-style-wide\"\/>\n\n\n\n<h3 class=\"wp-block-heading has-text-color has-link-color has-large-font-size wp-elements-32e471b74cad08d61c85d797e67ea328\" style=\"color:#000060\"><strong>2. Basic Trigonometric Ratios<\/strong><\/h3>\n\n\n\n<p class=\"has-large-font-size\">In a right-angled triangle, for an angle \u03b8\\theta\u03b8, the three primary trigonometric ratios are:<\/p>\n\n\n\n<h4 class=\"wp-block-heading has-large-font-size\"><strong>Sine (sin)<\/strong><\/h4>\n\n\n\n<ul class=\"wp-block-list\">\n<li class=\"has-large-font-size\">The sine of an angle is the ratio of the length of the <strong>opposite side<\/strong> to the length of the <strong>hypotenuse<\/strong>.<\/li>\n<\/ul>\n\n\n\n<figure class=\"wp-block-image size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"463\" height=\"102\" src=\"https:\/\/10thclass.deltapublications.in\/wp-content\/uploads\/2024\/11\/image-98.png\" alt=\"\" class=\"wp-image-14956\" srcset=\"https:\/\/10thclass.deltapublications.in\/wp-content\/uploads\/2024\/11\/image-98.png 463w, https:\/\/10thclass.deltapublications.in\/wp-content\/uploads\/2024\/11\/image-98-300x66.png 300w\" sizes=\"auto, (max-width: 463px) 100vw, 463px\" \/><\/figure>\n\n\n\n<h4 class=\"wp-block-heading has-large-font-size\"><strong>Cosine (cos)<\/strong><\/h4>\n\n\n\n<ul class=\"wp-block-list has-large-font-size\">\n<li>The cosine of an angle is the ratio of the length of the <strong>adjacent side<\/strong> to the length of the <strong>hypotenuse<\/strong>.<\/li>\n<\/ul>\n\n\n\n<figure class=\"wp-block-image size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"512\" height=\"92\" src=\"https:\/\/10thclass.deltapublications.in\/wp-content\/uploads\/2024\/11\/image-99.png\" alt=\"\" class=\"wp-image-14957\" srcset=\"https:\/\/10thclass.deltapublications.in\/wp-content\/uploads\/2024\/11\/image-99.png 512w, https:\/\/10thclass.deltapublications.in\/wp-content\/uploads\/2024\/11\/image-99-300x54.png 300w\" sizes=\"auto, (max-width: 512px) 100vw, 512px\" \/><\/figure>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity is-style-wide\"\/>\n\n\n\n<h3 class=\"wp-block-heading has-text-color has-link-color has-large-font-size wp-elements-bd0895375b7971d55d0ecbbb4c68ab44\" style=\"color:#000060\"><strong>3. Relationship Between the Trigonometric Ratios<\/strong><\/h3>\n\n\n\n<ul class=\"wp-block-list has-large-font-size\">\n<li>The three basic trigonometric ratios are interrelated. For example:<\/li>\n<\/ul>\n\n\n<div class=\"wp-block-image\">\n<figure class=\"aligncenter size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"169\" height=\"53\" src=\"https:\/\/10thclass.deltapublications.in\/wp-content\/uploads\/2024\/11\/image-100.png\" alt=\"\" class=\"wp-image-14958\"\/><\/figure><\/div>\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity is-style-wide\"\/>\n\n\n\n<h3 class=\"wp-block-heading has-text-color has-link-color has-large-font-size wp-elements-71d6ea1aa4e924a7ea98c343a3979121\" style=\"color:#000060\"><strong>4. Reciprocal Trigonometric Ratios<\/strong><\/h3>\n\n\n\n<ul class=\"wp-block-list has-large-font-size\">\n<li><strong>Cosecant (csc)<\/strong>: The reciprocal of sine:<\/li>\n<\/ul>\n\n\n<div class=\"wp-block-image\">\n<figure class=\"aligncenter size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"170\" height=\"72\" src=\"https:\/\/10thclass.deltapublications.in\/wp-content\/uploads\/2024\/11\/image-101.png\" alt=\"\" class=\"wp-image-14959\"\/><\/figure><\/div>\n\n\n<p class=\"has-large-font-size\"><strong>Secant (sec)<\/strong>: The reciprocal of cosine:<\/p>\n\n\n<div class=\"wp-block-image\">\n<figure class=\"aligncenter size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"170\" height=\"57\" src=\"https:\/\/10thclass.deltapublications.in\/wp-content\/uploads\/2024\/11\/image-102.png\" alt=\"\" class=\"wp-image-14960\"\/><\/figure><\/div>\n\n\n<p class=\"has-large-font-size\"><strong>Cotangent (cot)<\/strong>: The reciprocal of tangent:<\/p>\n\n\n<div class=\"wp-block-image\">\n<figure class=\"aligncenter size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"167\" height=\"68\" src=\"https:\/\/10thclass.deltapublications.in\/wp-content\/uploads\/2024\/11\/image-103.png\" alt=\"\" class=\"wp-image-14961\"\/><\/figure><\/div>\n\n\n<p class=\"has-text-align-center has-text-color has-large-font-size\" style=\"color:#105000\"><strong>Learn with an example<\/strong><\/p>\n\n\n\n<div class=\"wp-block-group has-background has-large-font-size\" style=\"background-color:#9895f2\"><div class=\"wp-block-group__inner-container is-layout-constrained wp-block-group-is-layout-constrained\">\n<div class=\"wp-block-group\"><div class=\"wp-block-group__inner-container is-layout-constrained wp-block-group-is-layout-constrained\">\n<div class=\"wp-block-group has-background-background-color has-background\"><div class=\"wp-block-group__inner-container is-layout-constrained wp-block-group-is-layout-constrained\">\n<p class=\"has-text-color has-link-color wp-elements-3650342b519600c9a020740a58231844\" style=\"color:#b00012\"><strong>Find the sine of \u2220Y.<\/strong><\/p>\n\n\n\n<figure class=\"wp-block-image size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"670\" height=\"300\" src=\"https:\/\/10thclass.deltapublications.in\/wp-content\/uploads\/2023\/12\/Untitled-design-7.png\" alt=\"\" class=\"wp-image-10551\" srcset=\"https:\/\/10thclass.deltapublications.in\/wp-content\/uploads\/2023\/12\/Untitled-design-7.png 670w, https:\/\/10thclass.deltapublications.in\/wp-content\/uploads\/2023\/12\/Untitled-design-7-300x134.png 300w\" sizes=\"auto, (max-width: 670px) 100vw, 670px\" \/><\/figure>\n\n\n\n<p class=\"has-primary-color has-text-color has-link-color wp-elements-e880533a1c4b2744f8a8e1d5d4488b1c\">Simplify your answer and write it as a proper fraction, improper fraction, or whole number.<\/p>\n\n\n\n<p class=\"has-primary-color has-text-color has-link-color wp-elements-96fff06be10c418ca610aa210dcabe6d\">sin(Y)= ______<\/p>\n<\/div><\/div>\n<\/div><\/div>\n\n\n\n<p class=\"has-primary-color has-text-color has-link-color wp-elements-86126eb735225d5bdb5e008300e5d55f\">Take the formula for the sine of \u2220Y and plug in the relevant side lengths.<\/p>\n\n\n\n<figure class=\"wp-block-image size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"670\" height=\"300\" src=\"https:\/\/10thclass.deltapublications.in\/wp-content\/uploads\/2023\/12\/Untitled_design__9_-removebg-preview.png\" alt=\"\" class=\"wp-image-10567\" srcset=\"https:\/\/10thclass.deltapublications.in\/wp-content\/uploads\/2023\/12\/Untitled_design__9_-removebg-preview.png 670w, https:\/\/10thclass.deltapublications.in\/wp-content\/uploads\/2023\/12\/Untitled_design__9_-removebg-preview-300x134.png 300w\" sizes=\"auto, (max-width: 670px) 100vw, 670px\" \/><\/figure>\n\n\n\n<p class=\"has-primary-color has-text-color has-link-color wp-elements-166c55565037b5e8095d71d8ebcab9b8\">sin ( Y ) = opp \/ hyp                  Definition&nbsp;of&nbsp;sine<\/p>\n\n\n\n<p class=\"has-primary-color has-text-color has-link-color wp-elements-e5d621e114f9a479e851d2c1ecebf729\">= WX \/ XY               Substitute opp=WX and hyp=XY<\/p>\n\n\n\n<p class=\"has-primary-color has-text-color has-link-color wp-elements-2c00fb053430e16e14a39820ba384c24\">= 56 \/ 65                    Plug in WX=56 and XY=65<\/p>\n\n\n\n<p class=\"has-primary-color has-text-color has-link-color wp-elements-7045e890235cb80d7fd0686d5dd11358\">So, sin(Y)= 56\/65 ,<\/p>\n<\/div><\/div>\n\n\n\n<div class=\"wp-block-group has-background has-large-font-size\" style=\"background-color:#f4f8ad\"><div class=\"wp-block-group__inner-container is-layout-constrained wp-block-group-is-layout-constrained\">\n<div class=\"wp-block-group has-background-background-color has-background\"><div class=\"wp-block-group__inner-container is-layout-constrained wp-block-group-is-layout-constrained\">\n<p class=\"has-text-color has-link-color wp-elements-640c7d7295fa8a3243a94f4b2b37ea52\" style=\"color:#b00012\"><strong>Find the cosine of \u2220T.<\/strong><\/p>\n\n\n<div class=\"wp-block-image\">\n<figure class=\"aligncenter size-full is-resized\"><img loading=\"lazy\" decoding=\"async\" width=\"670\" height=\"300\" src=\"https:\/\/10thclass.deltapublications.in\/wp-content\/uploads\/2023\/12\/Untitled-design.png\" alt=\"\" class=\"wp-image-10572\" style=\"width:489px;height:auto\" srcset=\"https:\/\/10thclass.deltapublications.in\/wp-content\/uploads\/2023\/12\/Untitled-design.png 670w, https:\/\/10thclass.deltapublications.in\/wp-content\/uploads\/2023\/12\/Untitled-design-300x134.png 300w\" sizes=\"auto, (max-width: 670px) 100vw, 670px\" \/><\/figure><\/div>\n\n\n<p>Simplify your answer and write it as a proper fraction, improper fraction, or whole number.<\/p>\n\n\n\n<p>cos(T)= ______<\/p>\n<\/div><\/div>\n\n\n\n<p class=\"has-primary-color has-text-color has-link-color wp-elements-d4fa5e1af95ca5a4fdfc3282d4330e33\">Take the formula for the cosine of \u2220T and plug in the relevant side lengths.<\/p>\n\n\n<div class=\"wp-block-image\">\n<figure class=\"aligncenter size-full is-resized\"><img loading=\"lazy\" decoding=\"async\" width=\"670\" height=\"300\" src=\"https:\/\/10thclass.deltapublications.in\/wp-content\/uploads\/2023\/12\/Untitled_design__1_-removebg-preview.png\" alt=\"\" class=\"wp-image-10575\" style=\"width:485px;height:auto\" srcset=\"https:\/\/10thclass.deltapublications.in\/wp-content\/uploads\/2023\/12\/Untitled_design__1_-removebg-preview.png 670w, https:\/\/10thclass.deltapublications.in\/wp-content\/uploads\/2023\/12\/Untitled_design__1_-removebg-preview-300x134.png 300w\" sizes=\"auto, (max-width: 670px) 100vw, 670px\" \/><\/figure><\/div>\n\n\n<p class=\"has-primary-color has-text-color has-link-color wp-elements-5dcf773394995b761c13cf1a2910b2b3\">cos ( T ) = adj \/ hyb                   Definition of cosine<\/p>\n\n\n\n<p class=\"has-primary-color has-text-color has-link-color wp-elements-500315cea9cba0abb8bcee6c19835510\">= TV \/ TU                  Substitute adj=TV and hyp=TU<\/p>\n\n\n\n<p class=\"has-primary-color has-text-color has-link-color wp-elements-71e4e39171d18c1c6f7840bc686384b5\">= 65 \/ 97                           Plug in TV=65 and TU=97<\/p>\n\n\n\n<p class=\"has-primary-color has-text-color has-link-color wp-elements-971185ebea9f215dd661716148c227ad\">So, cos(T) = 65\/97 .<\/p>\n<\/div><\/div>\n\n\n\n<div class=\"wp-block-group has-background has-large-font-size\" style=\"background-color:#c5f8ce\"><div class=\"wp-block-group__inner-container is-layout-constrained wp-block-group-is-layout-constrained\">\n<div class=\"wp-block-group has-background-background-color has-background\"><div class=\"wp-block-group__inner-container is-layout-constrained wp-block-group-is-layout-constrained\">\n<p class=\"has-text-color has-link-color wp-elements-79af0d7610d58c0a46976d9977b69ecf\" style=\"color:#b00012\"><strong>Find the cosine of \u2220U.<\/strong><\/p>\n\n\n<div class=\"wp-block-image\">\n<figure class=\"aligncenter size-full is-resized\"><img loading=\"lazy\" decoding=\"async\" width=\"670\" height=\"300\" src=\"https:\/\/10thclass.deltapublications.in\/wp-content\/uploads\/2023\/12\/Untitled-design-2.png\" alt=\"\" class=\"wp-image-10591\" style=\"width:473px;height:auto\" srcset=\"https:\/\/10thclass.deltapublications.in\/wp-content\/uploads\/2023\/12\/Untitled-design-2.png 670w, https:\/\/10thclass.deltapublications.in\/wp-content\/uploads\/2023\/12\/Untitled-design-2-300x134.png 300w\" sizes=\"auto, (max-width: 670px) 100vw, 670px\" \/><\/figure><\/div>\n\n\n<p>Simplify your answer and write it as a proper fraction, improper fraction, or whole number.<\/p>\n\n\n\n<p>cos(U)= _______<\/p>\n<\/div><\/div>\n\n\n\n<p>Take the formula for the cosine of \u2220U and plug in the relevant side lengths.<\/p>\n\n\n<div class=\"wp-block-image\">\n<figure class=\"aligncenter size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"670\" height=\"300\" src=\"https:\/\/10thclass.deltapublications.in\/wp-content\/uploads\/2023\/12\/Untitled_design__3_-removebg-preview.png\" alt=\"\" class=\"wp-image-10594\" srcset=\"https:\/\/10thclass.deltapublications.in\/wp-content\/uploads\/2023\/12\/Untitled_design__3_-removebg-preview.png 670w, https:\/\/10thclass.deltapublications.in\/wp-content\/uploads\/2023\/12\/Untitled_design__3_-removebg-preview-300x134.png 300w\" sizes=\"auto, (max-width: 670px) 100vw, 670px\" \/><\/figure><\/div>\n\n\n<p>cos ( U )  = adj \/ hyb                   Definition of cosine<\/p>\n\n\n\n<p>= UV \/ TU                  Substitute adj= UV and hyp= TU<\/p>\n\n\n\n<p>= 5\/13                    Plug in UV=5 and TU=13<\/p>\n\n\n\n<p>So, cos(U)= 5\/13 .<\/p>\n<\/div><\/div>\n\n\n\n<p class=\"has-text-color has-large-font-size\" style=\"color:#d90000\"><strong>let&#8217;s practice!<\/strong><\/p>\n\n\n\n<div class=\"wp-block-columns is-layout-flex wp-container-core-columns-is-layout-9d6595d7 wp-block-columns-is-layout-flex\">\n<div class=\"wp-block-column is-layout-flow wp-block-column-is-layout-flow\">\n<figure class=\"wp-block-image size-full\"><a href=\"https:\/\/wordwall.net\/play\/81371\/528\/759\"><img loading=\"lazy\" decoding=\"async\" width=\"500\" height=\"500\" src=\"https:\/\/10thclass.deltapublications.in\/wp-content\/uploads\/2023\/05\/Worksheet-1-3-123.png\" alt=\"\" class=\"wp-image-7359\" srcset=\"https:\/\/10thclass.deltapublications.in\/wp-content\/uploads\/2023\/05\/Worksheet-1-3-123.png 500w, https:\/\/10thclass.deltapublications.in\/wp-content\/uploads\/2023\/05\/Worksheet-1-3-123-300x300.png 300w, https:\/\/10thclass.deltapublications.in\/wp-content\/uploads\/2023\/05\/Worksheet-1-3-123-150x150.png 150w\" sizes=\"auto, (max-width: 500px) 100vw, 500px\" \/><\/a><\/figure>\n<\/div>\n\n\n\n<div class=\"wp-block-column is-layout-flow wp-block-column-is-layout-flow\">\n<figure class=\"wp-block-image size-full\"><a href=\"https:\/\/wordwall.net\/play\/80852\/126\/792\"><img loading=\"lazy\" decoding=\"async\" width=\"500\" height=\"500\" src=\"https:\/\/10thclass.deltapublications.in\/wp-content\/uploads\/2023\/05\/Worksheet-1-1-2-142.png\" alt=\"\" class=\"wp-image-7360\" srcset=\"https:\/\/10thclass.deltapublications.in\/wp-content\/uploads\/2023\/05\/Worksheet-1-1-2-142.png 500w, https:\/\/10thclass.deltapublications.in\/wp-content\/uploads\/2023\/05\/Worksheet-1-1-2-142-300x300.png 300w, https:\/\/10thclass.deltapublications.in\/wp-content\/uploads\/2023\/05\/Worksheet-1-1-2-142-150x150.png 150w\" sizes=\"auto, (max-width: 500px) 100vw, 500px\" \/><\/a><\/figure>\n<\/div>\n<\/div>\n","protected":false},"excerpt":{"rendered":"<p>Trigonometric ratios: sin, cos and tan Key notes : 1. Introduction to Trigonometric Ratios 2. Basic Trigonometric Ratios In a right-angled triangle, for an angle \u03b8\\theta\u03b8, the three primary trigonometric ratios are: Sine (sin) Cosine (cos) 3. Relationship Between the Trigonometric Ratios 4. Reciprocal Trigonometric Ratios Secant (sec): The reciprocal of cosine: Cotangent (cot): The<a class=\"more-link\" href=\"https:\/\/10thclass.deltapublications.in\/index.php\/s-1-trigonometric-ratios-sin-cos-and-tan\/\">Continue reading <span class=\"screen-reader-text\">&#8220;S.1 Trigonometric ratios: sin, cos and tan&#8221;<\/span><\/a><\/p>\n","protected":false},"author":1,"featured_media":0,"parent":0,"menu_order":0,"comment_status":"closed","ping_status":"closed","template":"","meta":{"om_disable_all_campaigns":false,"_monsterinsights_skip_tracking":false,"_monsterinsights_sitenote_active":false,"_monsterinsights_sitenote_note":"","_monsterinsights_sitenote_category":0,"footnotes":""},"class_list":["post-356","page","type-page","status-publish","hentry","entry"],"aioseo_notices":[],"_links":{"self":[{"href":"https:\/\/10thclass.deltapublications.in\/index.php\/wp-json\/wp\/v2\/pages\/356","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/10thclass.deltapublications.in\/index.php\/wp-json\/wp\/v2\/pages"}],"about":[{"href":"https:\/\/10thclass.deltapublications.in\/index.php\/wp-json\/wp\/v2\/types\/page"}],"author":[{"embeddable":true,"href":"https:\/\/10thclass.deltapublications.in\/index.php\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/10thclass.deltapublications.in\/index.php\/wp-json\/wp\/v2\/comments?post=356"}],"version-history":[{"count":19,"href":"https:\/\/10thclass.deltapublications.in\/index.php\/wp-json\/wp\/v2\/pages\/356\/revisions"}],"predecessor-version":[{"id":14964,"href":"https:\/\/10thclass.deltapublications.in\/index.php\/wp-json\/wp\/v2\/pages\/356\/revisions\/14964"}],"wp:attachment":[{"href":"https:\/\/10thclass.deltapublications.in\/index.php\/wp-json\/wp\/v2\/media?parent=356"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}