{"id":186556,"date":"2025-01-25T09:10:20","date_gmt":"2025-01-25T09:10:20","guid":{"rendered":"https:\/\/learnexams.com\/blog\/?p=186556"},"modified":"2025-01-25T09:10:23","modified_gmt":"2025-01-25T09:10:23","slug":"find-the-value-of-each-trigonometric-ratio","status":"publish","type":"post","link":"https:\/\/www.learnexams.com\/blog\/2025\/01\/25\/find-the-value-of-each-trigonometric-ratio\/","title":{"rendered":"Find the value of each trigonometric ratio"},"content":{"rendered":"\n

Find the value of each trigonometric ratio. Make sure you reduce\/simplify the fractions. 1) sin z 2) sinc 40 24 36 39 32 3) cos X 4) cos X X 15 Z 37 12 9 12 35 5) tan 2 6) tan C Z 24 40 30 32 50 C X 7) sin A 8) tanz B \u0441 30 40 24 50 For 9) and 10) find ALL SIX trigonometric ratios ( sin, cos, tan, sec, csc, and cot) NOT only the one that is typed. 9) tan 4<\/p>\n\n\n\n

\"\"<\/figure>\n\n\n\n

The Correct Answer and Explanation is :<\/strong><\/mark><\/p>\n\n\n\n

To determine the values of the six trigonometric ratios for an angle \u03b8, we need to know the lengths of the sides of a right-angled triangle relative to \u03b8. The six trigonometric functions are:<\/p>\n\n\n\n

    \n
  1. Sine (sin \u03b8)<\/strong>: \ue203Opposite side \/ Hypotenuse\ue204\ue206<\/li>\n\n\n\n
  2. Cosine (cos \u03b8)<\/strong>: \ue203Adjacent side \/ Hypotenuse\ue204\ue206<\/li>\n\n\n\n
  3. Tangent (tan \u03b8)<\/strong>: \ue203Opposite side \/ Adjacent side\ue204\ue206<\/li>\n\n\n\n
  4. Cosecant (csc \u03b8)<\/strong>: \ue203Hypotenuse \/ Opposite side\ue204\ue206<\/li>\n\n\n\n
  5. Secant (sec \u03b8)<\/strong>: \ue203Hypotenuse \/ Adjacent side\ue204\ue206<\/li>\n\n\n\n
  6. Cotangent (cot \u03b8)<\/strong>: \ue203Adjacent side \/ Opposite side\ue204\ue206<\/li>\n<\/ol>\n\n\n\n

    Given the information provided, it appears that some of the data might be incomplete or unclear. However, based on the available details, let’s attempt to calculate the trigonometric ratios for the following scenarios:<\/p>\n\n\n\n

    1) sin z<\/strong><\/p>\n\n\n\n

    Without specific information about the sides of the triangle or the angle z, it’s not possible to determine sin z. \ue203To calculate sin z, we need the length of the side opposite angle z and the hypotenuse.\ue204\ue206<\/p>\n\n\n\n

    2) sinc 40 24 36 39 32<\/strong><\/p>\n\n\n\n

    This expression is unclear. \ue203If it refers to a triangle with sides 24, 36, and 40, we can use the Pythagorean theorem to check if it’s a right-angled triangle:\ue204\ue206<\/p>\n\n\n\n

    \ue20324\u00b2 + 36\u00b2 = 576 + 1296 = 1872\ue204\ue206 \ue20340\u00b2 = 1600\ue204\ue206<\/p>\n\n\n\n

    Since 1872 \u2260 1600, this is not a right-angled triangle, and trigonometric ratios cannot be determined without additional information.<\/p>\n\n\n\n

    3) cos X<\/strong><\/p>\n\n\n\n

    Without details about the sides of the triangle or the angle X, it’s not possible to determine cos X. \ue203To calculate cos X, we need the length of the adjacent side and the hypotenuse.\ue204\ue206<\/p>\n\n\n\n

    4) cos X X 15 Z 37 12 9 12 35<\/strong><\/p>\n\n\n\n

    This expression is unclear. \ue203If it refers to a triangle with sides 9, 12, and 15, we can check if it’s a right-angled triangle:\ue204\ue206<\/p>\n\n\n\n

    \ue2039\u00b2 + 12\u00b2 = 81 + 144 = 225\ue204\ue206 \ue20315\u00b2 = 225\ue204\ue206<\/p>\n\n\n\n

    Since 225 = 225, this is a right-angled triangle. \ue203For angle X, cos X = Adjacent \/ Hypotenuse = 12 \/ 15 = 4 \/ 5.\ue204\ue206<\/p>\n\n\n\n

    5) tan 2<\/strong><\/p>\n\n\n\n

    Without information about the sides of the triangle or the angle, it’s not possible to determine tan 2. \ue203To calculate tan 2, we need the length of the opposite side and the adjacent side.\ue204\ue206<\/p>\n\n\n\n

    6) tan C Z 24 40 30 32 50 C X<\/strong><\/p>\n\n\n\n

    This expression is unclear. \ue203If it refers to a triangle with sides 24, 32, and 40, we can check if it’s a right-angled triangle:\ue204\ue206<\/p>\n\n\n\n

    \ue20324\u00b2 + 32\u00b2 = 576 + 1024 = 1600\ue204\ue206 \ue20340\u00b2 = 1600\ue204\ue206<\/p>\n\n\n\n

    Since 1600 = 1600, this is a right-angled triangle. \ue203For angle C, tan C = Opposite \/ Adjacent = 24 \/ 32 = 3 \/ 4.\ue204\ue206<\/p>\n\n\n\n

    7) sin A<\/strong><\/p>\n\n\n\n

    Without information about the sides of the triangle or the angle A, it’s not possible to determine sin A. \ue203To calculate sin A, we need the length of the opposite side and the hypotenuse.\ue204\ue206<\/p>\n\n\n\n

    8) tan B \u0441 30 40 24 50<\/strong><\/p>\n\n\n\n

    This expression is unclear. \ue203If it refers to a triangle with sides 24, 30, and 50, we can check if it’s a right-angled triangle:\ue204\ue206<\/p>\n\n\n\n

    \ue20324\u00b2 + 30\u00b2 = 576 + 900 = 1476\ue204\ue206 \ue20350\u00b2 = 2500\ue204\ue206<\/p>\n\n\n\n

    Since 1476 \u2260 2500, this is not a right-angled triangle, and trigonometric ratios cannot be determined without additional information.<\/p>\n\n\n\n

    9) tan 4<\/strong><\/p>\n\n\n\n

    Without information about the sides of the triangle or the angle, it’s not possible to determine tan 4. \ue203To calculate tan 4, we need the length of the opposite side and the adjacent side.\ue204\ue206<\/p>\n\n\n\n

    10) tan 4<\/strong><\/p>\n\n\n\n

    This is a repeat of question 9. \ue203Without information about the sides of the triangle or the angle, it’s not possible to determine tan 4.\ue204\ue206<\/p>\n\n\n\n

    General Approach to Finding Trigonometric Ratios:<\/strong><\/p>\n\n\n\n

      \n
    1. Identify the Triangle Type<\/strong>: Determine if the triangle is a right-angled triangle. \ue203If it is, you can use the Pythagorean theorem to find missing sides.\ue204\ue206<\/li>\n\n\n\n
    2. Label the Sides<\/strong>: Label the sides of the triangle as opposite, adjacent, and hypotenuse relative to the angle of interest.\ue206<\/li>\n\n\n\n
    3. Apply Trigonometric Definitions<\/strong>: Use the definitions of the trigonometric functions to find the desired ratios.\ue206<\/li>\n\n\n\n
    4. Simplify the Results<\/strong>: \ue203Ensure that all fractions are in their simplest form.\ue204\ue206<\/li>\n<\/ol>\n\n\n\n

      For a more detailed explanation and visual demonstration, you might find the following video helpful:<\/p>\n\n\n\n

      \ue200video\ue2024 3 Right Triangle Trigonometry\ue202turn0search7\ue201<\/p>\n","protected":false},"excerpt":{"rendered":"

      Find the value of each trigonometric ratio. Make sure you reduce\/simplify the fractions. 1) sin z 2) sinc 40 24 36 39 32 3) cos X 4) cos X X 15 Z 37 12 9 12 35 5) tan 2 6) tan C Z 24 40 30 32 50 C X 7) sin A 8) […]<\/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-186556","post","type-post","status-publish","format-standard","hentry","category-exams-certification"],"_links":{"self":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/186556","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=186556"}],"version-history":[{"count":0,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/186556\/revisions"}],"wp:attachment":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/media?parent=186556"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/categories?post=186556"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/tags?post=186556"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}