{"id":228022,"date":"2024-04-01T08:02:32","date_gmt":"2024-04-01T08:02:32","guid":{"rendered":"https:\/\/namso-gen.co\/blog\/?p=228022"},"modified":"2024-04-01T08:02:32","modified_gmt":"2024-04-01T08:02:32","slug":"what-is-the-exact-value-of-cos-105","status":"publish","type":"post","link":"https:\/\/namso-gen.co\/blog\/what-is-the-exact-value-of-cos-105\/","title":{"rendered":"What is the exact value of cos 105?"},"content":{"rendered":"<p>**What is the exact value of cos 105?**<\/p>\n<p>When it comes to evaluating trigonometric functions, especially those of angles that are not commonly found on the unit circle, it can be a bit tricky. In this case, we are interested in finding the exact value of cos 105.<\/p>\n<p>To determine the value of cos 105, we need to understand a few key concepts and utilize certain trigonometric identities.<\/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-3'><a class=\"ez-toc-link ez-toc-heading-1\" href=\"https:\/\/namso-gen.co\/blog\/what-is-the-exact-value-of-cos-105\/#FAQs\" title=\"FAQs:\">FAQs:<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-3'><a class=\"ez-toc-link ez-toc-heading-2\" href=\"https:\/\/namso-gen.co\/blog\/what-is-the-exact-value-of-cos-105\/#1_What_is_cosine\" title=\"1. What is cosine?\">1. What is cosine?<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-3'><a class=\"ez-toc-link ez-toc-heading-3\" href=\"https:\/\/namso-gen.co\/blog\/what-is-the-exact-value-of-cos-105\/#2_What_is_the_unit_circle\" title=\"2. What is the unit circle?\">2. What is the unit circle?<\/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\/what-is-the-exact-value-of-cos-105\/#3_How_can_we_find_the_exact_value_of_cos_105\" title=\"3. How can we find the exact value of cos 105?\">3. How can we find the exact value of cos 105?<\/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\/what-is-the-exact-value-of-cos-105\/#4_Why_do_we_split_cos_105_into_cos_60_and_cos_45\" title=\"4. Why do we split cos 105 into cos 60 and cos 45?\">4. Why do we split cos 105 into cos 60 and cos 45?<\/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\/what-is-the-exact-value-of-cos-105\/#5_What_is_the_value_of_cos_60\" title=\"5. What is the value of cos 60?\">5. What is the value of cos 60?<\/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\/what-is-the-exact-value-of-cos-105\/#6_What_is_the_value_of_cos_45\" title=\"6. What is the value of cos 45?\">6. What is the value of cos 45?<\/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\/what-is-the-exact-value-of-cos-105\/#7_How_do_we_use_the_angle_sum_formula_to_find_cos_105\" title=\"7. How do we use the angle sum formula to find cos 105?\">7. How do we use the angle sum formula to find cos 105?<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-3'><a class=\"ez-toc-link ez-toc-heading-9\" href=\"https:\/\/namso-gen.co\/blog\/what-is-the-exact-value-of-cos-105\/#8_What_are_the_trigonometric_values_for_sin_60_and_sin_45\" title=\"8. What are the trigonometric values for sin 60 and sin 45?\">8. What are the trigonometric values for sin 60 and sin 45?<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-3'><a class=\"ez-toc-link ez-toc-heading-10\" href=\"https:\/\/namso-gen.co\/blog\/what-is-the-exact-value-of-cos-105\/#9_How_do_we_evaluate_the_product_cos_60_cos_45\" title=\"9. How do we evaluate the product cos 60 * cos 45?\">9. How do we evaluate the product cos 60 * cos 45?<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-3'><a class=\"ez-toc-link ez-toc-heading-11\" href=\"https:\/\/namso-gen.co\/blog\/what-is-the-exact-value-of-cos-105\/#10_How_do_we_evaluate_the_product_sin_60_sin_45\" title=\"10. How do we evaluate the product sin 60 * sin 45?\">10. How do we evaluate the product sin 60 * sin 45?<\/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\/what-is-the-exact-value-of-cos-105\/#11_What_is_the_value_of_cos_105\" title=\"11. What is the value of cos 105?\">11. What is the value of cos 105?<\/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\/what-is-the-exact-value-of-cos-105\/#12_Can_we_simplify_%E2%88%9A24_%E2%80%93_%E2%88%9A64_further\" title=\"12. Can we simplify (\u221a2)\/4 &#8211; (\u221a6)\/4 further?\">12. Can we simplify (\u221a2)\/4 &#8211; (\u221a6)\/4 further?<\/a><\/li><\/ul><\/nav><\/div>\n<h3><span class=\"ez-toc-section\" id=\"FAQs\"><\/span>FAQs:<span class=\"ez-toc-section-end\"><\/span><\/h3>\n<h3><span class=\"ez-toc-section\" id=\"1_What_is_cosine\"><\/span>1. What is cosine?<span class=\"ez-toc-section-end\"><\/span><\/h3>\n<p>\nCosine (cos) is one of the trigonometric functions that relates the angles of a right triangle to the ratios of its sides.<\/p>\n<h3><span class=\"ez-toc-section\" id=\"2_What_is_the_unit_circle\"><\/span>2. What is the unit circle?<span class=\"ez-toc-section-end\"><\/span><\/h3>\n<p>\nThe unit circle is a circle with a radius of 1 that is centered at the origin of a coordinate plane. It is commonly used in trigonometry to determine the values of trigonometric functions at various angles.<\/p>\n<h3><span class=\"ez-toc-section\" id=\"3_How_can_we_find_the_exact_value_of_cos_105\"><\/span>3. How can we find the exact value of cos 105?<span class=\"ez-toc-section-end\"><\/span><\/h3>\n<p>\nTo find the exact value of cos 105, we can use the angle sum formula for cosine. This formula states that cos(A + B) = cos A * cos B &#8211; sin A * sin B. In this case, we&#8217;ll use the angle A as 60 degrees and angle B as 45 degrees.<\/p>\n<h3><span class=\"ez-toc-section\" id=\"4_Why_do_we_split_cos_105_into_cos_60_and_cos_45\"><\/span>4. Why do we split cos 105 into cos 60 and cos 45?<span class=\"ez-toc-section-end\"><\/span><\/h3>\n<p>\nBy splitting cos 105 into cos 60 and cos 45, we can simplify the calculation since the trigonometric values for these angles are well-known.<\/p>\n<h3><span class=\"ez-toc-section\" id=\"5_What_is_the_value_of_cos_60\"><\/span>5. What is the value of cos 60?<span class=\"ez-toc-section-end\"><\/span><\/h3>\n<p>\nThe value of cos 60 (cosine of 60 degrees) is 0.5. This is a readily available value on the unit circle.<\/p>\n<h3><span class=\"ez-toc-section\" id=\"6_What_is_the_value_of_cos_45\"><\/span>6. What is the value of cos 45?<span class=\"ez-toc-section-end\"><\/span><\/h3>\n<p>\nThe value of cos 45 (cosine of 45 degrees) is (\u221a2)\/2, which is also a common trigonometric value.<\/p>\n<h3><span class=\"ez-toc-section\" id=\"7_How_do_we_use_the_angle_sum_formula_to_find_cos_105\"><\/span>7. How do we use the angle sum formula to find cos 105?<span class=\"ez-toc-section-end\"><\/span><\/h3>\n<p>\nWe can rewrite cos 105 as cos (60 + 45) and then apply the angle sum formula to get the exact value.<\/p>\n<h3><span class=\"ez-toc-section\" id=\"8_What_are_the_trigonometric_values_for_sin_60_and_sin_45\"><\/span>8. What are the trigonometric values for sin 60 and sin 45?<span class=\"ez-toc-section-end\"><\/span><\/h3>\n<p>\nThe value of sin 60 (sine of 60 degrees) is (\u221a3)\/2, and the value of sin 45 (sine of 45 degrees) is (\u221a2)\/2.<\/p>\n<h3><span class=\"ez-toc-section\" id=\"9_How_do_we_evaluate_the_product_cos_60_cos_45\"><\/span>9. How do we evaluate the product cos 60 * cos 45?<span class=\"ez-toc-section-end\"><\/span><\/h3>\n<p>\nTo evaluate the product cos 60 * cos 45, we simply multiply the values obtained for each angle. Thus, (0.5) * (\u221a2)\/2 = (\u221a2)\/4.<\/p>\n<h3><span class=\"ez-toc-section\" id=\"10_How_do_we_evaluate_the_product_sin_60_sin_45\"><\/span>10. How do we evaluate the product sin 60 * sin 45?<span class=\"ez-toc-section-end\"><\/span><\/h3>\n<p>\nTo evaluate the product sin 60 * sin 45, we multiply the sine values obtained for each angle. This results in (\u221a3)\/2 * (\u221a2)\/2 = (\u221a6)\/4.<\/p>\n<h3><span class=\"ez-toc-section\" id=\"11_What_is_the_value_of_cos_105\"><\/span>11. What is the value of cos 105?<span class=\"ez-toc-section-end\"><\/span><\/h3>\n<p>\nThe exact value of cos 105 is obtained by plugging the values of cos 60, cos 45, sin 60, and sin 45 into the angle sum formula. Substituting the known values, we have cos 105 = cos 60 * cos 45 &#8211; sin 60 * sin 45 = (0.5)(\u221a2)\/2 &#8211; (\u221a3)\/2 * (\u221a2)\/2 = (\u221a2)\/4 &#8211; (\u221a6)\/4.<\/p>\n<h3><span class=\"ez-toc-section\" id=\"12_Can_we_simplify_%E2%88%9A24_%E2%80%93_%E2%88%9A64_further\"><\/span>12. Can we simplify (\u221a2)\/4 &#8211; (\u221a6)\/4 further?<span class=\"ez-toc-section-end\"><\/span><\/h3>\n<p>\nYes, we can simplify (\u221a2)\/4 &#8211; (\u221a6)\/4 further by combining the terms with the same denominator. This simplifies to (\u221a2 &#8211; \u221a6)\/4.<\/p>\n<p>In conclusion, the exact value of cos 105 is (\u221a2 &#8211; \u221a6)\/4. By applying the angle sum formula and utilizing the trigonometric values of cos 60 and cos 45, we can obtain the precise value of this trigonometric function.<\/p>\n","protected":false},"excerpt":{"rendered":"<p>**What is the exact value of cos 105?** When it comes to evaluating trigonometric functions, especially those of angles that are not commonly found on the unit circle, it can be a bit tricky. In this case, we are interested in finding the exact value of cos 105. To determine the value of cos 105, &#8230; <\/p>\n<p class=\"read-more-container\"><a title=\"What is the exact value of cos 105?\" class=\"read-more button\" href=\"https:\/\/namso-gen.co\/blog\/what-is-the-exact-value-of-cos-105\/#more-228022\">Read more<span class=\"screen-reader-text\">What is the exact value of cos 105?<\/span><\/a><\/p>\n","protected":false},"author":57,"featured_media":107420,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[86279],"tags":[],"class_list":["post-228022","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>What is the exact value of cos 105?<\/title>\n<meta name=\"description\" content=\"**What is the exact value of cos 105?** When it comes to evaluating trigonometric functions, especially those of angles that are not commonly found on the\" \/>\n<meta name=\"robots\" content=\"index, follow, max-snippet:-1, max-image-preview:large, max-video-preview:-1\" \/>\n<link rel=\"canonical\" href=\"https:\/\/namso-gen.co\/blog\/what-is-the-exact-value-of-cos-105\/\" \/>\n<meta property=\"og:locale\" content=\"en_US\" \/>\n<meta property=\"og:type\" content=\"article\" \/>\n<meta property=\"og:title\" content=\"What is the exact value of cos 105?\" \/>\n<meta property=\"og:description\" content=\"**What is the exact value of cos 105?** When it comes to evaluating trigonometric functions, especially those of angles that are not commonly found on the\" \/>\n<meta property=\"og:url\" content=\"https:\/\/namso-gen.co\/blog\/what-is-the-exact-value-of-cos-105\/\" \/>\n<meta property=\"og:site_name\" content=\"Namso Gen Blog - 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