{"id":45637,"date":"2025-07-01T09:32:03","date_gmt":"2025-07-01T09:32:03","guid":{"rendered":"https:\/\/gaviki.com\/blog\/?p=45637"},"modified":"2025-07-01T09:32:04","modified_gmt":"2025-07-01T09:32:04","slug":"find-the-exact-value-of-sec-3pi-2","status":"publish","type":"post","link":"https:\/\/gaviki.com\/blog\/find-the-exact-value-of-sec-3pi-2\/","title":{"rendered":"Find the exact value of sec 3pi\/2"},"content":{"rendered":"\n<p class=\"wp-block-paragraph\">Find the exact value of sec 3pi\/2 If not defined, write undefined.<\/p>\n\n\n\n<p class=\"wp-block-paragraph\"><strong><mark style=\"background-color:rgba(0, 0, 0, 0)\" class=\"has-inline-color has-vivid-cyan-blue-color\">The Correct Answer and Explanation is:<\/mark><\/strong><\/p>\n\n\n\n<p class=\"wp-block-paragraph\">To find the exact value of sec\u2061(3\u03c02)\\sec \\left( \\frac{3\\pi}{2} \\right)sec(23\u03c0\u200b), let&#8217;s break it down step by step.<\/p>\n\n\n\n<h3 class=\"wp-block-heading\">Step 1: Understand the relationship between secant and cosine<\/h3>\n\n\n\n<p class=\"wp-block-paragraph\">The secant function is the reciprocal of the cosine function. In other words:sec\u2061(\u03b8)=1cos\u2061(\u03b8)\\sec(\\theta) = \\frac{1}{\\cos(\\theta)}sec(\u03b8)=cos(\u03b8)1\u200b<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">So, to find sec\u2061(3\u03c02)\\sec \\left( \\frac{3\\pi}{2} \\right)sec(23\u03c0\u200b), we need to first find cos\u2061(3\u03c02)\\cos \\left( \\frac{3\\pi}{2} \\right)cos(23\u03c0\u200b).<\/p>\n\n\n\n<h3 class=\"wp-block-heading\">Step 2: Find cos\u2061(3\u03c02)\\cos \\left( \\frac{3\\pi}{2} \\right)cos(23\u03c0\u200b)<\/h3>\n\n\n\n<p class=\"wp-block-paragraph\">The angle 3\u03c02\\frac{3\\pi}{2}23\u03c0\u200b corresponds to 270\u00b0 on the unit circle. At this angle, the point on the unit circle is at (0,\u22121)(0, -1)(0,\u22121). The cosine of an angle is the x-coordinate of the point on the unit circle, so:cos\u2061(3\u03c02)=0\\cos \\left( \\frac{3\\pi}{2} \\right) = 0cos(23\u03c0\u200b)=0<\/p>\n\n\n\n<h3 class=\"wp-block-heading\">Step 3: Find sec\u2061(3\u03c02)\\sec \\left( \\frac{3\\pi}{2} \\right)sec(23\u03c0\u200b)<\/h3>\n\n\n\n<p class=\"wp-block-paragraph\">Now that we know cos\u2061(3\u03c02)=0\\cos \\left( \\frac{3\\pi}{2} \\right) = 0cos(23\u03c0\u200b)=0, we can substitute this into the equation for secant:sec\u2061(3\u03c02)=1cos\u2061(3\u03c02)=10\\sec \\left( \\frac{3\\pi}{2} \\right) = \\frac{1}{\\cos \\left( \\frac{3\\pi}{2} \\right)} = \\frac{1}{0}sec(23\u03c0\u200b)=cos(23\u03c0\u200b)1\u200b=01\u200b<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Dividing by zero is undefined in mathematics. Therefore, we conclude:sec\u2061(3\u03c02)=undefined\\sec \\left( \\frac{3\\pi}{2} \\right) = \\text{undefined}sec(23\u03c0\u200b)=undefined<\/p>\n\n\n\n<h3 class=\"wp-block-heading\">Final Answer:<\/h3>\n\n\n\n<p class=\"wp-block-paragraph\">The exact value of sec\u2061(3\u03c02)\\sec \\left( \\frac{3\\pi}{2} \\right)sec(23\u03c0\u200b) is <strong>undefined<\/strong>.<\/p>\n\n\n\n<h3 class=\"wp-block-heading\">Explanation:<\/h3>\n\n\n\n<p class=\"wp-block-paragraph\">The secant function relies on the cosine function, and when the cosine value is zero, the secant function becomes undefined. This is because division by zero is not a valid mathematical operation. In the case of 3\u03c02\\frac{3\\pi}{2}23\u03c0\u200b, the cosine function equals zero, so the secant function is also undefined.<\/p>\n\n\n\n<figure class=\"wp-block-image size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"1024\" height=\"1024\" src=\"https:\/\/gaviki.com\/blog\/wp-content\/uploads\/2025\/07\/learnexams-banner5-53.jpeg\" alt=\"\" class=\"wp-image-45638\" srcset=\"https:\/\/gaviki.com\/blog\/wp-content\/uploads\/2025\/07\/learnexams-banner5-53.jpeg 1024w, https:\/\/gaviki.com\/blog\/wp-content\/uploads\/2025\/07\/learnexams-banner5-53-300x300.jpeg 300w, https:\/\/gaviki.com\/blog\/wp-content\/uploads\/2025\/07\/learnexams-banner5-53-150x150.jpeg 150w, https:\/\/gaviki.com\/blog\/wp-content\/uploads\/2025\/07\/learnexams-banner5-53-768x768.jpeg 768w\" sizes=\"auto, (max-width: 1024px) 100vw, 1024px\" \/><\/figure>\n","protected":false},"excerpt":{"rendered":"<p>Find the exact value of sec 3pi\/2 If not defined, write undefined. The Correct Answer and Explanation is: To find the exact value of sec\u2061(3\u03c02)\\sec \\left( \\frac{3\\pi}{2} \\right)sec(23\u03c0\u200b), let&#8217;s break it down step by step. Step 1: Understand the relationship between secant and cosine The secant function is the reciprocal of the cosine function. In [&hellip;]<\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[1],"tags":[],"class_list":["post-45637","post","type-post","status-publish","format-standard","hentry","category-quiz-questions"],"_links":{"self":[{"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/posts\/45637","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/comments?post=45637"}],"version-history":[{"count":1,"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/posts\/45637\/revisions"}],"predecessor-version":[{"id":45639,"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/posts\/45637\/revisions\/45639"}],"wp:attachment":[{"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/media?parent=45637"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/categories?post=45637"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/tags?post=45637"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}