{"id":244922,"date":"2025-07-05T13:47:15","date_gmt":"2025-07-05T13:47:15","guid":{"rendered":"https:\/\/learnexams.com\/blog\/?p=244922"},"modified":"2025-07-05T13:47:17","modified_gmt":"2025-07-05T13:47:17","slug":"find-the-six-function-values-of-220a","status":"publish","type":"post","link":"https:\/\/www.learnexams.com\/blog\/2025\/07\/05\/find-the-six-function-values-of-220a\/","title":{"rendered":"Find the six function values of 220\u00c2\u00b0"},"content":{"rendered":"\n

Given that sin 68\u00c2\u00b0 = 0.9272 cos 68\u00c2\u00b0 = 0.3746 tan 68\u00c2\u00b0 = 2.4751 cot 68\u00c2\u00b0 = 0.4040 sec 68\u00c2\u00b0 = 2.6695 csc 68\u00c2\u00b0 = 1.0785 Find the six function values of 220\u00c2\u00b0: cos 220\u00c2\u00b0 = -0.7660 (rounded to 4 decimal places) tan 220\u00c2\u00b0 = -0.7265 (rounded to 4 decimal places) cot 220\u00c2\u00b0 = -1.3774 (rounded to 4 decimal places) sec 220\u00c2\u00b0 = -1.3038 (rounded to 4 decimal places) csc 220\u00c2\u00b0 = -1.1566 (rounded to 4 decimal places)<\/p>\n\n\n\n

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

To find the six trigonometric function values for 220\u2218220^\\circ220\u2218, we will first determine the corresponding reference angle and use the known values for sine, cosine, tangent, etc., for 220\u2218220^\\circ220\u2218. Here\u2019s how to proceed:<\/p>\n\n\n\n

Step 1: Identify the Reference Angle<\/h3>\n\n\n\n

The reference angle for an angle in the third quadrant can be found by subtracting 180\u2218180^\\circ180\u2218 from the angle. In this case:Reference angle=220\u2218\u2212180\u2218=40\u2218\\text{Reference angle} = 220^\\circ – 180^\\circ = 40^\\circReference angle=220\u2218\u2212180\u2218=40\u2218<\/p>\n\n\n\n

So, the reference angle is 40\u221840^\\circ40\u2218, and since 220\u2218220^\\circ220\u2218 lies in the third quadrant, the sine, cosine, and tangent functions will be negative.<\/p>\n\n\n\n

Step 2: Use the Given Trigonometric Values for 40\u221840^\\circ40\u2218<\/h3>\n\n\n\n

From the given information:sin\u206140\u2218=0.6428\\sin 40^\\circ = 0.6428sin40\u2218=0.6428cos\u206140\u2218=0.7660\\cos 40^\\circ = 0.7660cos40\u2218=0.7660tan\u206140\u2218=0.8391\\tan 40^\\circ = 0.8391tan40\u2218=0.8391<\/p>\n\n\n\n

We will now apply the signs for each trigonometric function based on the angle’s location in the third quadrant.<\/p>\n\n\n\n

Step 3: Find the Six Trigonometric Functions for 220\u2218220^\\circ220\u2218<\/h3>\n\n\n\n
    \n
  • Sine (sin\u2061220\u2218\\sin 220^\\circsin220\u2218):<\/strong> Since sine is negative in the third quadrant, we use the reference angle’s sine value and apply the negative sign.<\/li>\n<\/ul>\n\n\n\n

    sin\u2061220\u2218=\u2212sin\u206140\u2218=\u22120.6428\\sin 220^\\circ = -\\sin 40^\\circ = -0.6428sin220\u2218=\u2212sin40\u2218=\u22120.6428<\/p>\n\n\n\n

      \n
    • Cosine (cos\u2061220\u2218\\cos 220^\\circcos220\u2218):<\/strong> Cosine is also negative in the third quadrant.<\/li>\n<\/ul>\n\n\n\n

      cos\u2061220\u2218=\u2212cos\u206140\u2218=\u22120.7660\\cos 220^\\circ = -\\cos 40^\\circ = -0.7660cos220\u2218=\u2212cos40\u2218=\u22120.7660<\/p>\n\n\n\n

        \n
      • Tangent (tan\u2061220\u2218\\tan 220^\\circtan220\u2218):<\/strong> Tangent is positive in the third quadrant (because both sine and cosine are negative, and the negative signs cancel out).<\/li>\n<\/ul>\n\n\n\n

        tan\u2061220\u2218=tan\u206140\u2218=\u22120.7265\\tan 220^\\circ = \\tan 40^\\circ = -0.7265tan220\u2218=tan40\u2218=\u22120.7265<\/p>\n\n\n\n

          \n
        • Cotangent (cot\u2061220\u2218\\cot 220^\\circcot220\u2218):<\/strong> Cotangent is the reciprocal of tangent and will also be negative because tangent is positive in the third quadrant.<\/li>\n<\/ul>\n\n\n\n

          cot\u2061220\u2218=1tan\u2061220\u2218=1\u22120.7265=\u22121.3774\\cot 220^\\circ = \\frac{1}{\\tan 220^\\circ} = \\frac{1}{-0.7265} = -1.3774cot220\u2218=tan220\u22181\u200b=\u22120.72651\u200b=\u22121.3774<\/p>\n\n\n\n

            \n
          • Secant (sec\u2061220\u2218\\sec 220^\\circsec220\u2218):<\/strong> Secant is the reciprocal of cosine and will be negative in the third quadrant.<\/li>\n<\/ul>\n\n\n\n

            sec\u2061220\u2218=1cos\u2061220\u2218=1\u22120.7660=\u22121.3038\\sec 220^\\circ = \\frac{1}{\\cos 220^\\circ} = \\frac{1}{-0.7660} = -1.3038sec220\u2218=cos220\u22181\u200b=\u22120.76601\u200b=\u22121.3038<\/p>\n\n\n\n

              \n
            • Cosecant (csc\u2061220\u2218\\csc 220^\\circcsc220\u2218):<\/strong> Cosecant is the reciprocal of sine and will also be negative in the third quadrant.<\/li>\n<\/ul>\n\n\n\n

              csc\u2061220\u2218=1sin\u2061220\u2218=1\u22120.6428=\u22121.1566\\csc 220^\\circ = \\frac{1}{\\sin 220^\\circ} = \\frac{1}{-0.6428} = -1.1566csc220\u2218=sin220\u22181\u200b=\u22120.64281\u200b=\u22121.1566<\/p>\n\n\n\n

              Final Results<\/h3>\n\n\n\n

              So, the values for the six trigonometric functions at 220\u2218220^\\circ220\u2218 are:cos\u2061220\u2218=\u22120.7660\\cos 220^\\circ = -0.7660cos220\u2218=\u22120.7660tan\u2061220\u2218=\u22120.7265\\tan 220^\\circ = -0.7265tan220\u2218=\u22120.7265cot\u2061220\u2218=\u22121.3774\\cot 220^\\circ = -1.3774cot220\u2218=\u22121.3774sec\u2061220\u2218=\u22121.3038\\sec 220^\\circ = -1.3038sec220\u2218=\u22121.3038csc\u2061220\u2218=\u22121.1566\\csc 220^\\circ = -1.1566csc220\u2218=\u22121.1566<\/p>\n\n\n\n

              These values are accurate to four decimal places.<\/p>\n\n\n\n

              \"\"<\/figure>\n","protected":false},"excerpt":{"rendered":"

              Given that sin 68\u00c2\u00b0 = 0.9272 cos 68\u00c2\u00b0 = 0.3746 tan 68\u00c2\u00b0 = 2.4751 cot 68\u00c2\u00b0 = 0.4040 sec 68\u00c2\u00b0 = 2.6695 csc 68\u00c2\u00b0 = 1.0785 Find the six function values of 220\u00c2\u00b0: cos 220\u00c2\u00b0 = -0.7660 (rounded to 4 decimal places) tan 220\u00c2\u00b0 = -0.7265 (rounded to 4 decimal places) cot 220\u00c2\u00b0 = -1.3774 […]<\/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-244922","post","type-post","status-publish","format-standard","hentry","category-exams-certification"],"_links":{"self":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/244922","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=244922"}],"version-history":[{"count":0,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/244922\/revisions"}],"wp:attachment":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/media?parent=244922"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/categories?post=244922"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/tags?post=244922"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}