{"id":218166,"date":"2025-04-29T06:48:44","date_gmt":"2025-04-29T06:48:44","guid":{"rendered":"https:\/\/namso-gen.co\/blog\/how-to-find-the-exact-value-of-cosine-of-135-degrees\/"},"modified":"2025-04-29T06:48:44","modified_gmt":"2025-04-29T06:48:44","slug":"how-to-find-the-exact-value-of-cosine-of-135-degrees","status":"publish","type":"post","link":"https:\/\/namso-gen.co\/blog\/how-to-find-the-exact-value-of-cosine-of-135-degrees\/","title":{"rendered":"How to find the exact value of cosine of 135 degrees?"},"content":{"rendered":"<p>Finding the exact value of cosine for any given angle can be a challenging task, especially when dealing with non-standard angles. In this article, we will explore a step-by-step approach to determining the exact value of cosine for the angle 135 degrees.<\/p>\n<div id=\"ez-toc-container\" class=\"ez-toc-v2_0_62 counter-hierarchy ez-toc-counter ez-toc-grey ez-toc-container-direction\">\n<div class=\"ez-toc-title-container\">\n<p class=\"ez-toc-title \" >Table of Contents<\/p>\n<span class=\"ez-toc-title-toggle\"><a href=\"#\" class=\"ez-toc-pull-right ez-toc-btn ez-toc-btn-xs ez-toc-btn-default ez-toc-toggle\" aria-label=\"Toggle Table of Content\"><span class=\"ez-toc-js-icon-con\"><span class=\"\"><span class=\"eztoc-hide\" style=\"display:none;\">Toggle<\/span><span class=\"ez-toc-icon-toggle-span\"><svg style=\"fill: #999;color:#999\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\" class=\"list-377408\" width=\"20px\" height=\"20px\" viewBox=\"0 0 24 24\" fill=\"none\"><path d=\"M6 6H4v2h2V6zm14 0H8v2h12V6zM4 11h2v2H4v-2zm16 0H8v2h12v-2zM4 16h2v2H4v-2zm16 0H8v2h12v-2z\" fill=\"currentColor\"><\/path><\/svg><svg style=\"fill: #999;color:#999\" class=\"arrow-unsorted-368013\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\" width=\"10px\" height=\"10px\" viewBox=\"0 0 24 24\" version=\"1.2\" baseProfile=\"tiny\"><path d=\"M18.2 9.3l-6.2-6.3-6.2 6.3c-.2.2-.3.4-.3.7s.1.5.3.7c.2.2.4.3.7.3h11c.3 0 .5-.1.7-.3.2-.2.3-.5.3-.7s-.1-.5-.3-.7zM5.8 14.7l6.2 6.3 6.2-6.3c.2-.2.3-.5.3-.7s-.1-.5-.3-.7c-.2-.2-.4-.3-.7-.3h-11c-.3 0-.5.1-.7.3-.2.2-.3.5-.3.7s.1.5.3.7z\"\/><\/svg><\/span><\/span><\/span><\/a><\/span><\/div>\n<nav><ul class='ez-toc-list ez-toc-list-level-1 ' ><li class='ez-toc-page-1 ez-toc-heading-level-2'><a class=\"ez-toc-link ez-toc-heading-1\" href=\"https:\/\/namso-gen.co\/blog\/how-to-find-the-exact-value-of-cosine-of-135-degrees\/#Understanding_Cosine\" title=\"Understanding Cosine\">Understanding Cosine<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-2'><a class=\"ez-toc-link ez-toc-heading-2\" href=\"https:\/\/namso-gen.co\/blog\/how-to-find-the-exact-value-of-cosine-of-135-degrees\/#Finding_the_Exact_Value_of_Cosine_of_135_Degrees\" title=\"Finding the Exact Value of Cosine of 135 Degrees\">Finding the Exact Value of Cosine of 135 Degrees<\/a><ul class='ez-toc-list-level-3' ><li class='ez-toc-heading-level-3'><a class=\"ez-toc-link ez-toc-heading-3\" href=\"https:\/\/namso-gen.co\/blog\/how-to-find-the-exact-value-of-cosine-of-135-degrees\/#Step_1\" title=\"Step 1:\">Step 1:<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-3'><a class=\"ez-toc-link ez-toc-heading-4\" href=\"https:\/\/namso-gen.co\/blog\/how-to-find-the-exact-value-of-cosine-of-135-degrees\/#Step_2\" title=\"Step 2:\">Step 2:<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-3'><a class=\"ez-toc-link ez-toc-heading-5\" href=\"https:\/\/namso-gen.co\/blog\/how-to-find-the-exact-value-of-cosine-of-135-degrees\/#Step_3\" title=\"Step 3:\">Step 3:<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-3'><a class=\"ez-toc-link ez-toc-heading-6\" href=\"https:\/\/namso-gen.co\/blog\/how-to-find-the-exact-value-of-cosine-of-135-degrees\/#Step_4\" title=\"Step 4:\">Step 4:<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-3'><a class=\"ez-toc-link ez-toc-heading-7\" href=\"https:\/\/namso-gen.co\/blog\/how-to-find-the-exact-value-of-cosine-of-135-degrees\/#Step_5\" title=\"Step 5:\">Step 5:<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-3'><a class=\"ez-toc-link ez-toc-heading-8\" href=\"https:\/\/namso-gen.co\/blog\/how-to-find-the-exact-value-of-cosine-of-135-degrees\/#Step_6\" title=\"Step 6:\">Step 6:<\/a><\/li><\/ul><\/li><li class='ez-toc-page-1 ez-toc-heading-level-2'><a class=\"ez-toc-link ez-toc-heading-9\" href=\"https:\/\/namso-gen.co\/blog\/how-to-find-the-exact-value-of-cosine-of-135-degrees\/#The_exact_value_of_the_cosine_of_135_degrees_is_-%E2%88%9A22\" title=\"The exact value of the cosine of 135 degrees is -\u221a2\/2.\">The exact value of the cosine of 135 degrees is -\u221a2\/2.<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-2'><a class=\"ez-toc-link ez-toc-heading-10\" href=\"https:\/\/namso-gen.co\/blog\/how-to-find-the-exact-value-of-cosine-of-135-degrees\/#Related_FAQs\" title=\"Related FAQs:\">Related FAQs:<\/a><ul class='ez-toc-list-level-3' ><li class='ez-toc-heading-level-3'><a class=\"ez-toc-link ez-toc-heading-11\" href=\"https:\/\/namso-gen.co\/blog\/how-to-find-the-exact-value-of-cosine-of-135-degrees\/#1_What_is_the_cosine_of_45_degrees\" title=\"1. What is the cosine of 45 degrees?\">1. What is the cosine of 45 degrees?<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-3'><a class=\"ez-toc-link ez-toc-heading-12\" href=\"https:\/\/namso-gen.co\/blog\/how-to-find-the-exact-value-of-cosine-of-135-degrees\/#2_How_can_I_find_the_cosine_of_an_obtuse_angle\" title=\"2. How can I find the cosine of an obtuse angle?\">2. How can I find the cosine of an obtuse angle?<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-3'><a class=\"ez-toc-link ez-toc-heading-13\" href=\"https:\/\/namso-gen.co\/blog\/how-to-find-the-exact-value-of-cosine-of-135-degrees\/#3_What_is_the_cosine_of_180_degrees\" title=\"3. What is the cosine of 180 degrees?\">3. What is the cosine of 180 degrees?<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-3'><a class=\"ez-toc-link ez-toc-heading-14\" href=\"https:\/\/namso-gen.co\/blog\/how-to-find-the-exact-value-of-cosine-of-135-degrees\/#4_Can_cosine_be_greater_than_1_or_less_than_-1\" title=\"4. Can cosine be greater than 1 or less than -1?\">4. Can cosine be greater than 1 or less than -1?<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-3'><a class=\"ez-toc-link ez-toc-heading-15\" href=\"https:\/\/namso-gen.co\/blog\/how-to-find-the-exact-value-of-cosine-of-135-degrees\/#5_How_does_cosine_relate_to_the_unit_circle\" title=\"5. How does cosine relate to the unit circle?\">5. How does cosine relate to the unit circle?<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-3'><a class=\"ez-toc-link ez-toc-heading-16\" href=\"https:\/\/namso-gen.co\/blog\/how-to-find-the-exact-value-of-cosine-of-135-degrees\/#6_What_is_the_cosine_of_0_degrees\" title=\"6. What is the cosine of 0 degrees?\">6. What is the cosine of 0 degrees?<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-3'><a class=\"ez-toc-link ez-toc-heading-17\" href=\"https:\/\/namso-gen.co\/blog\/how-to-find-the-exact-value-of-cosine-of-135-degrees\/#7_What_is_the_cosine_of_90_degrees\" title=\"7. What is the cosine of 90 degrees?\">7. What is the cosine of 90 degrees?<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-3'><a class=\"ez-toc-link ez-toc-heading-18\" href=\"https:\/\/namso-gen.co\/blog\/how-to-find-the-exact-value-of-cosine-of-135-degrees\/#8_How_does_cosine_relate_to_sine\" title=\"8. How does cosine relate to sine?\">8. How does cosine relate to sine?<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-3'><a class=\"ez-toc-link ez-toc-heading-19\" href=\"https:\/\/namso-gen.co\/blog\/how-to-find-the-exact-value-of-cosine-of-135-degrees\/#9_What_is_the_cosine_of_270_degrees\" title=\"9. What is the cosine of 270 degrees?\">9. What is the cosine of 270 degrees?<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-3'><a class=\"ez-toc-link ez-toc-heading-20\" href=\"https:\/\/namso-gen.co\/blog\/how-to-find-the-exact-value-of-cosine-of-135-degrees\/#10_How_can_I_find_the_cosine_of_a_non-standard_angle\" title=\"10. How can I find the cosine of a non-standard angle?\">10. How can I find the cosine of a non-standard angle?<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-3'><a class=\"ez-toc-link ez-toc-heading-21\" href=\"https:\/\/namso-gen.co\/blog\/how-to-find-the-exact-value-of-cosine-of-135-degrees\/#11_What_is_the_cosine_of_60_degrees\" title=\"11. What is the cosine of 60 degrees?\">11. What is the cosine of 60 degrees?<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-3'><a class=\"ez-toc-link ez-toc-heading-22\" href=\"https:\/\/namso-gen.co\/blog\/how-to-find-the-exact-value-of-cosine-of-135-degrees\/#12_Are_there_any_special_angles_to_remember_for_cosine\" title=\"12. Are there any special angles to remember for cosine?\">12. Are there any special angles to remember for cosine?<\/a><\/li><\/ul><\/li><\/ul><\/nav><\/div>\n<h2><span class=\"ez-toc-section\" id=\"Understanding_Cosine\"><\/span>Understanding Cosine<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p>Before we dive into the process of finding the exact value of cosine for 135 degrees, it is essential to understand what cosine represents. Cosine is a trigonometric function that relates the ratio of the length of the adjacent side to the hypotenuse in a right-angled triangle.<\/p>\n<p>To visualize this, consider a right-angled triangle with one angle measuring 135 degrees. The adjacent side of this angle is the side that is closest to it, while the hypotenuse is the longest side of the triangle. By determining the ratio of these two sides, we can find the cosine of the angle.<\/p>\n<h2><span class=\"ez-toc-section\" id=\"Finding_the_Exact_Value_of_Cosine_of_135_Degrees\"><\/span>Finding the Exact Value of Cosine of 135 Degrees<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p>To find the exact value of cosine for 135 degrees, we can utilize the periodicity of the cosine function. Cosine has a period of 360 degrees, meaning the cosine of an angle repeats after adding or subtracting multiples of 360 degrees.<\/p>\n<p>Therefore, we can convert the given angle, 135 degrees, into an equivalent angle within one period of the cosine function. By subtracting 360 degrees from 135 degrees, we obtain an equivalent angle of -225 degrees. The cosine of -225 degrees is equal to the cosine of the original angle, 135 degrees.<\/p>\n<p>Now, let&#8217;s find the exact value of the cosine of -225 degrees. We can use the unit circle, a circle with a radius of 1 unit, to evaluate the cosine function.<\/p>\n<h3><span class=\"ez-toc-section\" id=\"Step_1\"><\/span>Step 1:<span class=\"ez-toc-section-end\"><\/span><\/h3>\n<p>\nDraw a circle and mark the point where the circle intersects the positive x-axis as the origin.<\/p>\n<h3><span class=\"ez-toc-section\" id=\"Step_2\"><\/span>Step 2:<span class=\"ez-toc-section-end\"><\/span><\/h3>\n<p>\nDivide the circle into four equal quadrants by drawing two perpendicular lines, one passing through the origin and the other through the top of the circle.<\/p>\n<h3><span class=\"ez-toc-section\" id=\"Step_3\"><\/span>Step 3:<span class=\"ez-toc-section-end\"><\/span><\/h3>\n<p>\nSince we are interested in the cosine value, focus on the x-coordinate of the unit circle at -225 degrees.<\/p>\n<h3><span class=\"ez-toc-section\" id=\"Step_4\"><\/span>Step 4:<span class=\"ez-toc-section-end\"><\/span><\/h3>\n<p>\nDraw a line from the origin to the point on the unit circle at -225 degrees.<\/p>\n<h3><span class=\"ez-toc-section\" id=\"Step_5\"><\/span>Step 5:<span class=\"ez-toc-section-end\"><\/span><\/h3>\n<p>\nDetermine the length of the x-coordinate (the adjacent side) where the line intersects the unit circle.<\/p>\n<h3><span class=\"ez-toc-section\" id=\"Step_6\"><\/span>Step 6:<span class=\"ez-toc-section-end\"><\/span><\/h3>\n<p>\nThe length of the x-coordinate is the exact value of cosine for the angle -225 degrees.<\/p>\n<h2><span class=\"ez-toc-section\" id=\"The_exact_value_of_the_cosine_of_135_degrees_is_-%E2%88%9A22\"><\/span><b>The exact value of the cosine of 135 degrees is -\u221a2\/2.<\/b><span class=\"ez-toc-section-end\"><\/span><\/h2>\n<h2><span class=\"ez-toc-section\" id=\"Related_FAQs\"><\/span>Related FAQs:<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<h3><span class=\"ez-toc-section\" id=\"1_What_is_the_cosine_of_45_degrees\"><\/span>1. What is the cosine of 45 degrees?<span class=\"ez-toc-section-end\"><\/span><\/h3>\n<p>\nThe cosine of 45 degrees is equal to \u221a2\/2.<\/p>\n<h3><span class=\"ez-toc-section\" id=\"2_How_can_I_find_the_cosine_of_an_obtuse_angle\"><\/span>2. How can I find the cosine of an obtuse angle?<span class=\"ez-toc-section-end\"><\/span><\/h3>\n<p>\nTo find the cosine of an obtuse angle, follow the same steps as mentioned above but ensure the angle falls within one period of the cosine function (0 to 360 degrees).<\/p>\n<h3><span class=\"ez-toc-section\" id=\"3_What_is_the_cosine_of_180_degrees\"><\/span>3. What is the cosine of 180 degrees?<span class=\"ez-toc-section-end\"><\/span><\/h3>\n<p>\nThe cosine of 180 degrees is -1.<\/p>\n<h3><span class=\"ez-toc-section\" id=\"4_Can_cosine_be_greater_than_1_or_less_than_-1\"><\/span>4. Can cosine be greater than 1 or less than -1?<span class=\"ez-toc-section-end\"><\/span><\/h3>\n<p>\nNo, the cosine function ranges between -1 and 1, inclusive.<\/p>\n<h3><span class=\"ez-toc-section\" id=\"5_How_does_cosine_relate_to_the_unit_circle\"><\/span>5. How does cosine relate to the unit circle?<span class=\"ez-toc-section-end\"><\/span><\/h3>\n<p>\nCosine represents the x-coordinate of a point on the unit circle corresponding to a specific angle.<\/p>\n<h3><span class=\"ez-toc-section\" id=\"6_What_is_the_cosine_of_0_degrees\"><\/span>6. What is the cosine of 0 degrees?<span class=\"ez-toc-section-end\"><\/span><\/h3>\n<p>\nThe cosine of 0 degrees is 1.<\/p>\n<h3><span class=\"ez-toc-section\" id=\"7_What_is_the_cosine_of_90_degrees\"><\/span>7. What is the cosine of 90 degrees?<span class=\"ez-toc-section-end\"><\/span><\/h3>\n<p>\nThe cosine of 90 degrees is 0.<\/p>\n<h3><span class=\"ez-toc-section\" id=\"8_How_does_cosine_relate_to_sine\"><\/span>8. How does cosine relate to sine?<span class=\"ez-toc-section-end\"><\/span><\/h3>\n<p>\nCosine and sine are related through the Pythagorean identity: sin^2\u03b8 + cos^2\u03b8 = 1.<\/p>\n<h3><span class=\"ez-toc-section\" id=\"9_What_is_the_cosine_of_270_degrees\"><\/span>9. What is the cosine of 270 degrees?<span class=\"ez-toc-section-end\"><\/span><\/h3>\n<p>\nThe cosine of 270 degrees is 0.<\/p>\n<h3><span class=\"ez-toc-section\" id=\"10_How_can_I_find_the_cosine_of_a_non-standard_angle\"><\/span>10. How can I find the cosine of a non-standard angle?<span class=\"ez-toc-section-end\"><\/span><\/h3>\n<p>\nTo find the cosine of a non-standard angle, convert it to an equivalent angle within one period of the cosine function and then evaluate it using the unit circle or other trigonometric identities.<\/p>\n<h3><span class=\"ez-toc-section\" id=\"11_What_is_the_cosine_of_60_degrees\"><\/span>11. What is the cosine of 60 degrees?<span class=\"ez-toc-section-end\"><\/span><\/h3>\n<p>\nThe cosine of 60 degrees is 1\/2.<\/p>\n<h3><span class=\"ez-toc-section\" id=\"12_Are_there_any_special_angles_to_remember_for_cosine\"><\/span>12. Are there any special angles to remember for cosine?<span class=\"ez-toc-section-end\"><\/span><\/h3>\n<p>\nYes, the values of cosine for 0, 30, 45, 60, and 90 degrees are easy to remember and frequently used in trigonometric calculations.<\/p>\n","protected":false},"excerpt":{"rendered":"<p>Finding the exact value of cosine for any given angle can be a challenging task, especially when dealing with non-standard angles. In this article, we will explore a step-by-step approach to determining the exact value of cosine for the angle 135 degrees. Understanding Cosine Before we dive into the process of finding the exact value &#8230; <\/p>\n<p class=\"read-more-container\"><a title=\"How to find the exact value of cosine of 135 degrees?\" class=\"read-more button\" href=\"https:\/\/namso-gen.co\/blog\/how-to-find-the-exact-value-of-cosine-of-135-degrees\/#more-218166\">Read more<span class=\"screen-reader-text\">How to find the exact value of cosine of 135 degrees?<\/span><\/a><\/p>\n","protected":false},"author":55,"featured_media":107420,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[86279],"tags":[],"class_list":["post-218166","post","type-post","status-publish","format-standard","has-post-thumbnail","hentry","category-learn","no-featured-image-padding"],"yoast_head":"<!-- This site is optimized with the Yoast SEO plugin v22.1 - https:\/\/yoast.com\/wordpress\/plugins\/seo\/ -->\n<title>How to find the exact value of cosine of 135 degrees?<\/title>\n<meta name=\"description\" content=\"Finding the exact value of cosine for any given angle can be a challenging task, especially when dealing with non-standard angles. 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