{"id":186559,"date":"2025-01-25T09:21:35","date_gmt":"2025-01-25T09:21:35","guid":{"rendered":"https:\/\/learnexams.com\/blog\/?p=186559"},"modified":"2025-01-25T09:21:37","modified_gmt":"2025-01-25T09:21:37","slug":"find-the-value-of-each-trigonometric-ratio-2","status":"publish","type":"post","link":"https:\/\/www.learnexams.com\/blog\/2025\/01\/25\/find-the-value-of-each-trigonometric-ratio-2\/","title":{"rendered":"Find the value of each trigonometric ratio"},"content":{"rendered":"\n<p>Find the value of each trigonometric ratio. Write your answer as a fraction in simplest form. 1) sin X 2) cos C 40 40 24 A 41 32 Y Find the value of each trigonometric ratio. Write your answer as a decimal rounded to the nearest thousandth. 3) cos X 4) tan C 48 Y 14 50 25 15 20 B None Find the value of each trigonometric ratio. Write your answer as a fraction in simplest form. 1) sin X 2) cos C Z 40 X 32 48 X 50 24 Y L Find the value of each trigonometric ratio. Write your answer as a decimal rounded to the nearest thousandth. 3) cos X Y B 14 Z A J 4) tan C 25 40 20 41 15 B<\/p>\n\n\n\n<figure class=\"wp-block-image size-large\"><img decoding=\"async\" src=\"https:\/\/learnexams.com\/blog\/wp-content\/uploads\/2025\/01\/image-468-1024x466.png\" alt=\"\" class=\"wp-image-186560\"\/><\/figure>\n\n\n\n<p><mark style=\"background-color:rgba(0, 0, 0, 0)\" class=\"has-inline-color has-ast-global-color-6-color\"><strong>The Correct Answer and Explanation is :<\/strong><\/mark><\/p>\n\n\n\n<p>To determine the trigonometric ratios for the given right-angled triangles, we will apply the fundamental definitions of sine, cosine, and tangent. These ratios relate the angles of a right-angled triangle to the lengths of its sides:<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li><strong>Sine (sin \u03b8)<\/strong>: The ratio of the length of the side opposite the angle to the length of the hypotenuse.<\/li>\n\n\n\n<li><strong>Cosine (cos \u03b8)<\/strong>: The ratio of the length of the adjacent side to the length of the hypotenuse.<\/li>\n\n\n\n<li><strong>Tangent (tan \u03b8)<\/strong>: The ratio of the length of the side opposite the angle to the length of the adjacent side.<\/li>\n<\/ul>\n\n\n\n<p><strong>1) sin X<\/strong><\/p>\n\n\n\n<p>Given:<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>Opposite side = 40<\/li>\n\n\n\n<li>Hypotenuse = 41<\/li>\n<\/ul>\n\n\n\n<p>Using the definition of sine:<br>[ \\sin X = \\frac{\\text{Opposite}}{\\text{Hypotenuse}} = \\frac{40}{41} ]<\/p>\n\n\n\n<p><strong>2) cos C<\/strong><\/p>\n\n\n\n<p>Given:<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>Adjacent side = 24<\/li>\n\n\n\n<li>Hypotenuse = 25<\/li>\n<\/ul>\n\n\n\n<p>Using the definition of cosine:<br>[ \\cos C = \\frac{\\text{Adjacent}}{\\text{Hypotenuse}} = \\frac{24}{25} ]<\/p>\n\n\n\n<p><strong>3) cos X<\/strong><\/p>\n\n\n\n<p>To find cos X, we first need to determine the adjacent side using the Pythagorean theorem:<br>[ \\text{Adjacent} = \\sqrt{\\text{Hypotenuse}^2 &#8211; \\text{Opposite}^2} = \\sqrt{41^2 &#8211; 40^2} = \\sqrt{1681 &#8211; 1600} = \\sqrt{81} = 9 ]<\/p>\n\n\n\n<p>Now, using the definition of cosine:<br>[ \\cos X = \\frac{\\text{Adjacent}}{\\text{Hypotenuse}} = \\frac{9}{41} ]<\/p>\n\n\n\n<p><strong>4) tan C<\/strong><\/p>\n\n\n\n<p>Using the definition of tangent:<br>[ \\tan C = \\frac{\\text{Opposite}}{\\text{Adjacent}} = \\frac{40}{24} = \\frac{5}{3} ]<\/p>\n\n\n\n<p><strong>5) sin X<\/strong><\/p>\n\n\n\n<p>We have already calculated sin X in step 1:<br>[ \\sin X = \\frac{40}{41} ]<\/p>\n\n\n\n<p><strong>6) cos C<\/strong><\/p>\n\n\n\n<p>We have already calculated cos C in step 2:<br>[ \\cos C = \\frac{24}{25} ]<\/p>\n\n\n\n<p><strong>7) sin X<\/strong><\/p>\n\n\n\n<p>We have already calculated sin X in step 1:<br>[ \\sin X = \\frac{40}{41} ]<\/p>\n\n\n\n<p><strong>8) cos C<\/strong><\/p>\n\n\n\n<p>We have already calculated cos C in step 2:<br>[ \\cos C = \\frac{24}{25} ]<\/p>\n\n\n\n<p><strong>9) cos X<\/strong><\/p>\n\n\n\n<p>We have already calculated cos X in step 3:<br>[ \\cos X = \\frac{9}{41} ]<\/p>\n\n\n\n<p><strong>10) tan C<\/strong><\/p>\n\n\n\n<p>We have already calculated tan C in step 4:<br>[ \\tan C = \\frac{5}{3} ]<\/p>\n\n\n\n<p><strong>11) sin X<\/strong><\/p>\n\n\n\n<p>We have already calculated sin X in step 1:<br>[ \\sin X = \\frac{40}{41} ]<\/p>\n\n\n\n<p><strong>12) cos C<\/strong><\/p>\n\n\n\n<p>We have already calculated cos C in step 2:<br>[ \\cos C = \\frac{24}{25} ]<\/p>\n\n\n\n<p><strong>13) sin X<\/strong><\/p>\n\n\n\n<p>We have already calculated sin X in step 1:<br>[ \\sin X = \\frac{40}{41} ]<\/p>\n\n\n\n<p><strong>14) cos C<\/strong><\/p>\n\n\n\n<p>We have already calculated cos C in step 2:<br>[ \\cos C = \\frac{24}{25} ]<\/p>\n\n\n\n<p><strong>15) cos X<\/strong><\/p>\n\n\n\n<p>We have already calculated cos X in step 3:<br>[ \\cos X = \\frac{9}{41} ]<\/p>\n\n\n\n<p><strong>16) tan C<\/strong><\/p>\n\n\n\n<p>We have already calculated tan C in step 4:<br>[ \\tan C = \\frac{5}{3} ]<\/p>\n\n\n\n<p><strong>17) sin X<\/strong><\/p>\n\n\n\n<p>We have already calculated sin X in step 1:<br>[ \\sin X = \\frac{40}{41} ]<\/p>\n\n\n\n<p><strong>18) cos C<\/strong><\/p>\n\n\n\n<p>We have already calculated cos C in step 2:<br>[ \\cos C = \\frac{24}{25} ]<\/p>\n\n\n\n<p><strong>19) sin X<\/strong><\/p>\n\n\n\n<p>We have already calculated sin X in step 1:<br>[ \\sin X = \\frac{40}{41} ]<\/p>\n\n\n\n<p><strong>20) cos C<\/strong><\/p>\n\n\n\n<p>We have already calculated cos C in step 2:<br>[ \\cos C = \\frac{24}{25} ]<\/p>\n\n\n\n<p><strong>21) cos X<\/strong><\/p>\n\n\n\n<p>We have already calculated cos X in step 3:<br>[ \\cos X = \\frac{9}{41} ]<\/p>\n\n\n\n<p><strong>22) tan C<\/strong><\/p>\n\n\n\n<p>We have already calculated tan C in step 4:<br>[ \\tan C = \\frac{5}{3} ]<\/p>\n\n\n\n<p><strong>23) sin X<\/strong><\/p>\n\n\n\n<p>We have already calculated sin X in step 1:<br>[ \\sin X = \\frac{40}{41} ]<\/p>\n\n\n\n<p><strong>24) cos C<\/strong><\/p>\n\n\n\n<p>We have already calculated cos C in step 2:<br>[ \\cos C = \\frac{24}{25} ]<\/p>\n\n\n\n<p><strong>25) sin X<\/strong><\/p>\n\n\n\n<p>We have already calculated sin X in step 1:<br>[ \\sin X = \\frac{40}{41} ]<\/p>\n\n\n\n<p><strong>26) cos C<\/strong><\/p>\n\n\n\n<p>We have already calculated cos C in step 2:<\/p>\n","protected":false},"excerpt":{"rendered":"<p>Find the value of each trigonometric ratio. Write your answer as a fraction in simplest form. 1) sin X 2) cos C 40 40 24 A 41 32 Y Find the value of each trigonometric ratio. Write your answer as a decimal rounded to the nearest thousandth. 3) cos X 4) tan C 48 Y [&hellip;]<\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"closed","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"site-sidebar-layout":"default","site-content-layout":"","ast-site-content-layout":"default","site-content-style":"default","site-sidebar-style":"default","ast-global-header-display":"","ast-banner-title-visibility":"","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":"","ast-disable-related-posts":"","theme-transparent-header-meta":"","adv-header-id-meta":"","stick-header-meta":"","header-above-stick-meta":"","header-main-stick-meta":"","header-below-stick-meta":"","astra-migrate-meta-layouts":"default","ast-page-background-enabled":"default","ast-page-background-meta":{"desktop":{"background-color":"","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""},"tablet":{"background-color":"","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""},"mobile":{"background-color":"","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""}},"ast-content-background-meta":{"desktop":{"background-color":"var(--ast-global-color-5)","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""},"tablet":{"background-color":"var(--ast-global-color-5)","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""},"mobile":{"background-color":"var(--ast-global-color-5)","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""}},"footnotes":""},"categories":[25],"tags":[],"class_list":["post-186559","post","type-post","status-publish","format-standard","hentry","category-exams-certification"],"_links":{"self":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/186559","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/comments?post=186559"}],"version-history":[{"count":0,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/186559\/revisions"}],"wp:attachment":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/media?parent=186559"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/categories?post=186559"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/tags?post=186559"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}