{"id":665116,"date":"2023-07-19T13:07:34","date_gmt":"2023-07-19T07:37:34","guid":{"rendered":"https:\/\/infinitylearn.com\/surge\/?p=665116"},"modified":"2025-06-03T15:27:55","modified_gmt":"2025-06-03T09:57:55","slug":"trigonometry-formulas","status":"publish","type":"post","link":"https:\/\/infinitylearn.com\/surge\/articles\/trigonometry-formulas\/","title":{"rendered":"Trigonometry Formulas"},"content":{"rendered":"<div id=\"ez-toc-container\" class=\"ez-toc-v2_0_37 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\" style=\"display: none;\"><label for=\"item\" aria-label=\"Table of Content\"><span style=\"display: flex;align-items: center;width: 35px;height: 30px;justify-content: center;\"><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><\/label><input type=\"checkbox\" id=\"item\"><\/a><\/span><\/div>\n<nav><ul class='ez-toc-list ez-toc-list-level-1' style='display:block'><li class='ez-toc-page-1 ez-toc-heading-level-2'><a class=\"ez-toc-link ez-toc-heading-1\" href=\"https:\/\/infinitylearn.com\/surge\/articles\/trigonometry-formulas\/#List_of_Important_Trigonometry_Formulas\" title=\"List of Important Trigonometry Formulas\">List of Important Trigonometry Formulas<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-2'><a class=\"ez-toc-link ez-toc-heading-2\" href=\"https:\/\/infinitylearn.com\/surge\/articles\/trigonometry-formulas\/#Basic_Trigonometric_Ratios\" title=\" \nBasic Trigonometric Ratios\"> \nBasic Trigonometric Ratios<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-2'><a class=\"ez-toc-link ez-toc-heading-3\" href=\"https:\/\/infinitylearn.com\/surge\/articles\/trigonometry-formulas\/#Trigonometric_Identities\" title=\"Trigonometric Identities\">Trigonometric Identities<\/a><ul class='ez-toc-list-level-3'><li class='ez-toc-heading-level-3'><a class=\"ez-toc-link ez-toc-heading-4\" href=\"https:\/\/infinitylearn.com\/surge\/articles\/trigonometry-formulas\/#Trigonometry_Identities\" title=\"Trigonometry Identities\">Trigonometry Identities<\/a><ul class='ez-toc-list-level-4'><li class='ez-toc-heading-level-4'><a class=\"ez-toc-link ez-toc-heading-5\" href=\"https:\/\/infinitylearn.com\/surge\/articles\/trigonometry-formulas\/#Tangent_and_Cotangent_Identities\" title=\"Tangent and Cotangent Identities\">Tangent and Cotangent Identities<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-4'><a class=\"ez-toc-link ez-toc-heading-6\" href=\"https:\/\/infinitylearn.com\/surge\/articles\/trigonometry-formulas\/#Reciprocal_Identities\" title=\"Reciprocal Identities\">Reciprocal Identities<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-4'><a class=\"ez-toc-link ez-toc-heading-7\" href=\"https:\/\/infinitylearn.com\/surge\/articles\/trigonometry-formulas\/#Pythagorean_Identities\" title=\"Pythagorean Identities\">Pythagorean Identities<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-4'><a class=\"ez-toc-link ez-toc-heading-8\" href=\"https:\/\/infinitylearn.com\/surge\/articles\/trigonometry-formulas\/#Even_and_Odd_Angle_Formulas\" title=\"Even and Odd Angle Formulas\">Even and Odd Angle Formulas<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-4'><a class=\"ez-toc-link ez-toc-heading-9\" href=\"https:\/\/infinitylearn.com\/surge\/articles\/trigonometry-formulas\/#Co-function_Formulas\" title=\"Co-function Formulas\">Co-function Formulas<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-4'><a class=\"ez-toc-link ez-toc-heading-10\" href=\"https:\/\/infinitylearn.com\/surge\/articles\/trigonometry-formulas\/#Double_Angle_Formulas\" title=\"Double Angle Formulas\">Double Angle Formulas<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-4'><a class=\"ez-toc-link ez-toc-heading-11\" href=\"https:\/\/infinitylearn.com\/surge\/articles\/trigonometry-formulas\/#Half_Angle_Formulas\" title=\"Half Angle Formulas\">Half Angle Formulas<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-4'><a class=\"ez-toc-link ez-toc-heading-12\" href=\"https:\/\/infinitylearn.com\/surge\/articles\/trigonometry-formulas\/#Thrice_of_Angle_Formulas\" title=\"Thrice of Angle Formulas\">Thrice of Angle Formulas<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-4'><a class=\"ez-toc-link ez-toc-heading-13\" href=\"https:\/\/infinitylearn.com\/surge\/articles\/trigonometry-formulas\/#Product_to_Sum_Formulas\" title=\"Product to Sum Formulas\">Product to Sum Formulas<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-4'><a class=\"ez-toc-link ez-toc-heading-14\" href=\"https:\/\/infinitylearn.com\/surge\/articles\/trigonometry-formulas\/#Sum_to_Product_Formulas\" title=\"Sum to Product Formulas\">Sum to Product Formulas<\/a><\/li><\/ul><\/li><li class='ez-toc-page-1 ez-toc-heading-level-3'><a class=\"ez-toc-link ez-toc-heading-15\" href=\"https:\/\/infinitylearn.com\/surge\/articles\/trigonometry-formulas\/#Trigonometry_table\" title=\"Trigonometry table\">Trigonometry table<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-3'><a class=\"ez-toc-link ez-toc-heading-16\" href=\"https:\/\/infinitylearn.com\/surge\/articles\/trigonometry-formulas\/#Inverse_Trigonometric_Functions\" title=\"Inverse Trigonometric Functions\">Inverse Trigonometric Functions<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-3'><a class=\"ez-toc-link ez-toc-heading-17\" href=\"https:\/\/infinitylearn.com\/surge\/articles\/trigonometry-formulas\/#Signs_of_Trigonometric_Ratios\" title=\"Signs of Trigonometric Ratios\">Signs of Trigonometric Ratios<\/a><\/li><\/ul><\/li><li class='ez-toc-page-1 ez-toc-heading-level-2'><a class=\"ez-toc-link ez-toc-heading-18\" href=\"https:\/\/infinitylearn.com\/surge\/articles\/trigonometry-formulas\/#FAQs_on_Trigonometric_Formulas\" title=\"FAQs on Trigonometric Formulas\">FAQs on Trigonometric Formulas<\/a><ul class='ez-toc-list-level-3'><li class='ez-toc-heading-level-3'><a class=\"ez-toc-link ez-toc-heading-19\" href=\"https:\/\/infinitylearn.com\/surge\/articles\/trigonometry-formulas\/#What_is_the_basic_formula_for_trigonometry\" title=\"What is the basic formula for trigonometry\">What is the basic formula for trigonometry<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-3'><a class=\"ez-toc-link ez-toc-heading-20\" href=\"https:\/\/infinitylearn.com\/surge\/articles\/trigonometry-formulas\/#What_are_the_7_formula_of_trigonometry\" title=\"What are the 7 formula of trigonometry?\">What are the 7 formula of trigonometry?<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-3'><a class=\"ez-toc-link ez-toc-heading-21\" href=\"https:\/\/infinitylearn.com\/surge\/articles\/trigonometry-formulas\/#What_is_15_trigonometry_formula\" title=\"What is 15 trigonometry formula?\">What is 15 trigonometry formula?<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-3'><a class=\"ez-toc-link ez-toc-heading-22\" href=\"https:\/\/infinitylearn.com\/surge\/articles\/trigonometry-formulas\/#What_is_the_trigonometry_formula_for_Class_11\" title=\"What is the trigonometry formula for Class 11?\">What is the trigonometry formula for Class 11?<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-3'><a class=\"ez-toc-link ez-toc-heading-23\" href=\"https:\/\/infinitylearn.com\/surge\/articles\/trigonometry-formulas\/#Who_is_the_father_of_trigonometry\" title=\"Who is the father of trigonometry?\">Who is the father of trigonometry?<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-3'><a class=\"ez-toc-link ez-toc-heading-24\" href=\"https:\/\/infinitylearn.com\/surge\/articles\/trigonometry-formulas\/#Who_is_the_mother_of_trigonometry\" title=\"Who is the mother of trigonometry?\">Who is the mother of trigonometry?<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-3'><a class=\"ez-toc-link ez-toc-heading-25\" href=\"https:\/\/infinitylearn.com\/surge\/articles\/trigonometry-formulas\/#What_is_theta_angle\" title=\"What is theta angle?\">What is theta angle?<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-3'><a class=\"ez-toc-link ez-toc-heading-26\" href=\"https:\/\/infinitylearn.com\/surge\/articles\/trigonometry-formulas\/#What_are_the_4_types_of_trigonometry\" title=\"What are the 4 types of trigonometry?\">What are the 4 types of trigonometry?<\/a><\/li><\/ul><\/li><\/ul><\/nav><\/div>\n<p>Trigonometry formulas are essential mathematical tools that deal with the connections between triangle angles and sides. These formulas, which include sine, cosine, tangent, and their inverses, allow us to handle a variety of real-world distance, height, and angle issues. Understanding and navigating the world around us is made easier by mastering trigonometric formulae.<\/p>\n<h2><span class=\"ez-toc-section\" id=\"List_of_Important_Trigonometry_Formulas\"><\/span>List of Important Trigonometry Formulas<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p>Let&#8217;s explore trigonometry formulas. Imagine you have a right-angled triangle. This triangle has an angle, which we&#8217;ll call \u03b8, a longest side called the hypotenuse, a side that&#8217;s right next to \u03b8 called the adjacent side, and another side that&#8217;s across from \u03b8, which we&#8217;ll call the opposite side.<\/p>\n<h2><span class=\"ez-toc-section\" id=\"Basic_Trigonometric_Ratios\"><\/span><img loading=\"lazy\" class=\"alignnone wp-image-686884 size-large\" src=\"https:\/\/infinitylearn.com\/surge\/wp-content\/uploads\/2023\/07\/trigo-1024x891.png\" alt=\"Trigonometry Formulas\" width=\"640\" height=\"557\" srcset=\"https:\/\/infinitylearn.com\/surge\/wp-content\/uploads\/2023\/07\/trigo-1024x891.png 1024w, https:\/\/infinitylearn.com\/surge\/wp-content\/uploads\/2023\/07\/trigo-300x261.png 300w, https:\/\/infinitylearn.com\/surge\/wp-content\/uploads\/2023\/07\/trigo-768x668.png 768w, https:\/\/infinitylearn.com\/surge\/wp-content\/uploads\/2023\/07\/trigo.png 1379w\" sizes=\"(max-width: 640px) 100vw, 640px\" \/><br \/>\nBasic Trigonometric Ratios<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<ul>\n<li>sin\u03b8 = Opposite side \/ Hypotenuse<\/li>\n<li>cos\u03b8 = Adjacent side \/ Hypotenuse<\/li>\n<li>tan\u03b8 = Opposite side \/ Adjacent Side<\/li>\n<li>sec\u03b8 = Hypotenuse \/ Adjacent side<\/li>\n<li>cosec\u03b8 = Hypotenuse \/ Opposite side<\/li>\n<li>cot\u03b8 = Adjacent Side \/ Opposite side<\/li>\n<\/ul>\n<h2><span class=\"ez-toc-section\" id=\"Trigonometric_Identities\"><\/span>Trigonometric Identities<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p><a href=\"https:\/\/infinitylearn.com\/surge\/articles\/trigonometric-identity\/\"><strong>Trigonometric identities<\/strong><\/a> are special equations that connect various trigonometric functions like sine, cosine, and tangent. They help simplify expressions and solve trigonometric problems.<\/p>\n<p>Reciprocal identities<\/p>\n<ul>\n<li>sin\u03b8 = 1\/cosec\u03b8<\/li>\n<li>cosec\u03b8 = 1\/sin\u03b8<\/li>\n<li>cos\u03b8 = 1\/sec\u03b8<\/li>\n<li>sec\u03b8 = 1\/cos\u03b8<\/li>\n<li>tan\u03b8 = 1\/cot\u03b8<\/li>\n<li>cot\u03b8 = 1\/tan\u03b8<\/li>\n<\/ul>\n<p><a href=\"https:\/\/infinitylearn.com\/surge\/articles\/math-articles\"><button class=\"btn btn-dark mx-2 my-2 px-4\" style=\"border-radius: 50px;\" type=\"button\">Math Articles<\/button><\/a> <a href=\"https:\/\/infinitylearn.com\/surge\/formulas\/math-formulas\"><button class=\"btn btn-dark mx-2 my-2 px-4\" style=\"border-radius: 50px;\" type=\"button\">Math Formulas<\/button><\/a> <a href=\"https:\/\/infinitylearn.com\/surge\/articles\/triviality\/\"><button class=\"btn btn-dark mx-2 my-2 px-4\" style=\"border-radius: 50px;\" type=\"button\">Triviality<\/button><\/a><\/p>\n<h3><span class=\"ez-toc-section\" id=\"Trigonometry_Identities\"><\/span>Trigonometry Identities<span class=\"ez-toc-section-end\"><\/span><\/h3>\n<h4><span class=\"ez-toc-section\" id=\"Tangent_and_Cotangent_Identities\"><\/span>Tangent and Cotangent Identities<span class=\"ez-toc-section-end\"><\/span><\/h4>\n<ul>\n<li>tan\u03b8 = sin \u03b8 \/ cos \u03b8<\/li>\n<li>cot\u03b8 = cos \u03b8 \/ sin \u03b8<\/li>\n<\/ul>\n<h4><span class=\"ez-toc-section\" id=\"Reciprocal_Identities\"><\/span>Reciprocal Identities<span class=\"ez-toc-section-end\"><\/span><\/h4>\n<ul>\n<li>sin\u03b8 = 1\/cosec\u03b8<\/li>\n<li>cosec\u03b8 = 1\/sin\u03b8<\/li>\n<li>cos\u03b8 = 1\/sec\u03b8<\/li>\n<li>sec\u03b8 = 1\/cos\u03b8<\/li>\n<li>tan\u03b8 = 1\/cot\u03b8<\/li>\n<li>cot\u03b8 = 1\/tan\u03b8<\/li>\n<\/ul>\n<h4><span class=\"ez-toc-section\" id=\"Pythagorean_Identities\"><\/span>Pythagorean Identities<span class=\"ez-toc-section-end\"><\/span><\/h4>\n<ul>\n<li>sin2\u03b8 + cos2\u03b8 = 1<\/li>\n<li>1 + tan2\u03b8 = sec2\u03b8<\/li>\n<li>1 + cot2\u03b8 = cosec2\u03b8<\/li>\n<\/ul>\n<h4><span class=\"ez-toc-section\" id=\"Even_and_Odd_Angle_Formulas\"><\/span>Even and Odd Angle Formulas<span class=\"ez-toc-section-end\"><\/span><\/h4>\n<ul>\n<li>sin(-\u03b8) = -sin\u03b8<\/li>\n<li>cos(-\u03b8) = cos\u03b8<\/li>\n<li>tan(-\u03b8) = -tan\u03b8<\/li>\n<li>cot(-\u03b8) = -cot\u03b8<\/li>\n<li>sec(-\u03b8) = sec\u03b8<\/li>\n<li>cosec(-\u03b8) = -cosec\u03b8<\/li>\n<\/ul>\n<h4><span class=\"ez-toc-section\" id=\"Co-function_Formulas\"><\/span>Co-function Formulas<span class=\"ez-toc-section-end\"><\/span><\/h4>\n<ul>\n<li>sin(900-\u03b8) = cos\u03b8<\/li>\n<li>cos(900-\u03b8) = sin\u03b8<\/li>\n<li>tan(900-\u03b8) = cot\u03b8<\/li>\n<li>cot(900-\u03b8) = tan\u03b8<\/li>\n<li>sec(900-\u03b8) = cosec\u03b8<\/li>\n<li>cosec(900-\u03b8) = sec\u03b8<\/li>\n<\/ul>\n<h4><span class=\"ez-toc-section\" id=\"Double_Angle_Formulas\"><\/span>Double Angle Formulas<span class=\"ez-toc-section-end\"><\/span><\/h4>\n<ul>\n<li>sin2\u03b8 = 2 sin\u03b8 cos\u03b8<\/li>\n<li>cos2\u03b8 = 1 \u2013 2sin2\u03b8<\/li>\n<li>tan2\u03b8 = 2 tan\u03b8 \/ 1-tan2\u03b8<\/li>\n<\/ul>\n<h4><span class=\"ez-toc-section\" id=\"Half_Angle_Formulas\"><\/span>Half Angle Formulas<span class=\"ez-toc-section-end\"><\/span><\/h4>\n<ul>\n<li>sin\u03b8 = \u00b1\u221a1-cos2\u03b8\/2<\/li>\n<li>cos\u03b8 = \u00b1\u221a1+cos2\u03b8\/2<\/li>\n<li>tan\u03b8 = \u00b1\u221a1+cos2\u03b8\/1-cos2\u03b8<\/li>\n<\/ul>\n<h4><span class=\"ez-toc-section\" id=\"Thrice_of_Angle_Formulas\"><\/span>Thrice of Angle Formulas<span class=\"ez-toc-section-end\"><\/span><\/h4>\n<ul>\n<li>sin3\u03b8 = 3sin\u03b8 \u2013 4 sin3\u03b8<\/li>\n<li>Cos 3\u03b8 = 4cos3\u03b8 \u2013 3 cos\u03b8<\/li>\n<li>Tan 3\u03b8 = 3tan\u03b8 &#8211; tan3\u03b8\/ 1- 3tan2\u03b8<\/li>\n<li>Cot 3\u03b8 = cot3\u03b8 &#8211; 3cot\u03b8\/3cot2\u03b8 &#8211; 1<\/li>\n<\/ul>\n<h4><span class=\"ez-toc-section\" id=\"Product_to_Sum_Formulas\"><\/span>Product to Sum Formulas<span class=\"ez-toc-section-end\"><\/span><\/h4>\n<ul>\n<li>Sin A Sin B = 1\/2 [Cos (A-B) \u2013 Cos (A+B)]<\/li>\n<li>Cos A Cos B = 1\/2 [Cos (A-B) + Cos (A+B)]<\/li>\n<li>Sin A Cos B = 1\/2 [Sin (A+B) + Sin (A-B)]<\/li>\n<li>Cos A Sin B = 1\/2 [Sin (A+B) \u2013 Sin (A-B)]<\/li>\n<\/ul>\n<h4><span class=\"ez-toc-section\" id=\"Sum_to_Product_Formulas\"><\/span>Sum to Product Formulas<span class=\"ez-toc-section-end\"><\/span><\/h4>\n<ul>\n<li>Sin A + Sin B = 2 sin (A+B)\/2 cos (A-B)\/2<\/li>\n<li>Sin A &#8211; Sin B = 2 sin (A+B)\/2 sin (A-B)\/2<\/li>\n<li>Cos A + Cos B = 2 cos (A+B)\/2 cos (A-B)\/2<\/li>\n<li>Cos A &#8211; Cos B = 2 cos (A+B)\/2 cos (A-B)\/2<\/li>\n<\/ul>\n<h3><span class=\"ez-toc-section\" id=\"Trigonometry_table\"><\/span>Trigonometry table<span class=\"ez-toc-section-end\"><\/span><\/h3>\n<p>The table below contains trigonometric formulas for angles that are often utilised in problem solving.<\/p>\n<div class=\"table-responsive\">\n<table class=\"table table-bordered table-striped\" cellspacing=\"0\" cellpadding=\"5\">\n<tbody>\n<tr style=\"background-color: #89cff0; color: black;\">\n<td><strong>Degrees<\/strong><\/td>\n<td><strong>0\u00b0<\/strong><\/td>\n<td><strong>30\u00b0<\/strong><\/td>\n<td><strong>45\u00b0<\/strong><\/td>\n<td><strong>60\u00b0<\/strong><\/td>\n<td><strong>90\u00b0<\/strong><\/td>\n<td><strong>180\u00b0<\/strong><\/td>\n<td><strong>270\u00b0<\/strong><\/td>\n<td><strong>360\u00b0<\/strong><\/td>\n<\/tr>\n<tr style=\"background-color: #89cff0; color: black;\">\n<td><strong>Radians<\/strong><\/td>\n<td><strong>0<\/strong><\/td>\n<td><strong>\u03c0\/6<\/strong><\/td>\n<td><strong>\u03c0\/4<\/strong><\/td>\n<td><strong>\u03c0\/3<\/strong><\/td>\n<td><strong>\u03c0\/2<\/strong><\/td>\n<td><strong>\u03c0<\/strong><\/td>\n<td><strong>3\u03c0\/2<\/strong><\/td>\n<td><strong>2\u03c0<\/strong><\/td>\n<\/tr>\n<tr>\n<td style=\"background-color: #89cff0; color: black;\"><strong>Sin \u03b8<\/strong><\/td>\n<td>0<\/td>\n<td>1\/2<\/td>\n<td>1\/\u221a2<\/td>\n<td>\u221a3\/2<\/td>\n<td>1<\/td>\n<td>0<\/td>\n<td>-1<\/td>\n<td>0<\/td>\n<\/tr>\n<tr>\n<td style=\"background-color: #89cff0; color: black;\"><strong>Cos \u03b8<\/strong><\/td>\n<td>1<\/td>\n<td>\u221a3\/2<\/td>\n<td>1\/\u221a2<\/td>\n<td>1\/2<\/td>\n<td>0<\/td>\n<td>-1<\/td>\n<td>0<\/td>\n<td>1<\/td>\n<\/tr>\n<tr>\n<td style=\"background-color: #89cff0; color: black;\"><strong>Tan \u03b8<\/strong><\/td>\n<td>0<\/td>\n<td>1\/\u221a3<\/td>\n<td>1<\/td>\n<td>\u221a3<\/td>\n<td>\u221e<\/td>\n<td>0<\/td>\n<td>\u221e<\/td>\n<td>0<\/td>\n<\/tr>\n<tr>\n<td style=\"background-color: #89cff0; color: black;\"><strong>Cot \u03b8<\/strong><\/td>\n<td>\u221e<\/td>\n<td>\u221a3<\/td>\n<td>1<\/td>\n<td>1\/\u221a3<\/td>\n<td>0<\/td>\n<td>\u221e<\/td>\n<td>0<\/td>\n<td>\u221e<\/td>\n<\/tr>\n<tr>\n<td style=\"background-color: #89cff0; color: black;\"><strong>Sec \u03b8<\/strong><\/td>\n<td>1<\/td>\n<td>2\/\u221a3<\/td>\n<td>\u221a2<\/td>\n<td>2<\/td>\n<td>\u221e<\/td>\n<td>-1<\/td>\n<td>\u221e<\/td>\n<td>1<\/td>\n<\/tr>\n<tr>\n<td style=\"background-color: #89cff0; color: black;\"><strong>Cosec \u03b8<\/strong><\/td>\n<td>\u221e<\/td>\n<td>2<\/td>\n<td>\u221a2<\/td>\n<td>2\/\u221a3<\/td>\n<td>1<\/td>\n<td>\u221e<\/td>\n<td>-1<\/td>\n<td>\u221e<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<\/div>\n<h3><span class=\"ez-toc-section\" id=\"Inverse_Trigonometric_Functions\"><\/span>Inverse Trigonometric Functions<span class=\"ez-toc-section-end\"><\/span><\/h3>\n<p>If Sin \u03b8 = x, then \u03b8 = sin-1 x = arcsin(x)<\/p>\n<p>Similarly,<\/p>\n<ul>\n<li>\u03b8 = cos-1x = arccos(x)<\/li>\n<li>\u03b8 = tan-1 x = arctan(x)<\/li>\n<\/ul>\n<p>Also, the inverse properties could be defined as;<\/p>\n<ul>\n<li>sin<sup>-1<\/sup>(sin \u03b8) = \u03b8<\/li>\n<li>cos<sup>-1<\/sup>(cos \u03b8) = \u03b8<\/li>\n<li>tan<sup>-1<\/sup>(tan \u03b8) = \u03b8<\/li>\n<\/ul>\n<h3><span class=\"ez-toc-section\" id=\"Signs_of_Trigonometric_Ratios\"><\/span>Signs of Trigonometric Ratios<span class=\"ez-toc-section-end\"><\/span><\/h3>\n<ul>\n<li>All Six trigonometric ratios are positive in the first quadrant<\/li>\n<li>Only are positive and the remaining all are negative in the second quadrant.<\/li>\n<li>Only are positive and the remaining all are negative in the third quadrant.<\/li>\n<li>Only are positive and the remaining all are negative in the fourth quadrant.<\/li>\n<\/ul>\n<h2><span class=\"ez-toc-section\" id=\"FAQs_on_Trigonometric_Formulas\"><\/span>FAQs on <span class=\"TextRun SCXW234976528 BCX0\" lang=\"EN-IN\" xml:lang=\"EN-IN\" data-contrast=\"none\"><span class=\"NormalTextRun SCXW234976528 BCX0\" data-ccp-parastyle=\"heading 2\">Trigonometric Formulas<\/span><\/span><span class=\"ez-toc-section-end\"><\/span><\/h2>\n\t\t<section class=\"sc_fs_faq sc_card \">\n\t\t\t<div>\n\t\t\t\t<h3><span class=\"ez-toc-section\" id=\"What_is_the_basic_formula_for_trigonometry\"><\/span>What is the basic formula for trigonometry<span class=\"ez-toc-section-end\"><\/span><\/h3>\t\t\t\t<div>\n\t\t\t\t\t\t\t\t\t\t<p>\n\t\t\t\t\t\tThe basic formula in trigonometry relates the angles and sides of a right-angled triangle, such as sine, cosine, and tangent.\t\t\t\t\t<\/p>\n\t\t\t\t<\/div>\n\t\t\t<\/div>\n\t\t<\/section>\n\t\t\t\t<section class=\"sc_fs_faq sc_card \">\n\t\t\t<div>\n\t\t\t\t<h3><span class=\"ez-toc-section\" id=\"What_are_the_7_formula_of_trigonometry\"><\/span>What are the 7 formula of trigonometry?<span class=\"ez-toc-section-end\"><\/span><\/h3>\t\t\t\t<div>\n\t\t\t\t\t\t\t\t\t\t<p>\n\t\t\t\t\t\tThere are 7 fundamental trigonometric formulas, including sine, cosine, tangent, cosecant, secant, cotangent, and the Pythagorean theorem.\t\t\t\t\t<\/p>\n\t\t\t\t<\/div>\n\t\t\t<\/div>\n\t\t<\/section>\n\t\t\t\t<section class=\"sc_fs_faq sc_card \">\n\t\t\t<div>\n\t\t\t\t<h3><span class=\"ez-toc-section\" id=\"What_is_15_trigonometry_formula\"><\/span>What is 15 trigonometry formula?<span class=\"ez-toc-section-end\"><\/span><\/h3>\t\t\t\t<div>\n\t\t\t\t\t\t\t\t\t\t<p>\n\t\t\t\t\t\tThere is no standard 15 trigonometry formula. The core trigonometric formulas are usually limited to the fundamental 7.\t\t\t\t\t<\/p>\n\t\t\t\t<\/div>\n\t\t\t<\/div>\n\t\t<\/section>\n\t\t\t\t<section class=\"sc_fs_faq sc_card \">\n\t\t\t<div>\n\t\t\t\t<h3><span class=\"ez-toc-section\" id=\"What_is_the_trigonometry_formula_for_Class_11\"><\/span>What is the trigonometry formula for Class 11?<span class=\"ez-toc-section-end\"><\/span><\/h3>\t\t\t\t<div>\n\t\t\t\t\t\t\t\t\t\t<p>\n\t\t\t\t\t\tTrigonometry formulas for Class 11 cover the basics, including sine, cosine, tangent, and their inverses, as well as trigonometric identities.\t\t\t\t\t<\/p>\n\t\t\t\t<\/div>\n\t\t\t<\/div>\n\t\t<\/section>\n\t\t\t\t<section class=\"sc_fs_faq sc_card \">\n\t\t\t<div>\n\t\t\t\t<h3><span class=\"ez-toc-section\" id=\"Who_is_the_father_of_trigonometry\"><\/span>Who is the father of trigonometry?<span class=\"ez-toc-section-end\"><\/span><\/h3>\t\t\t\t<div>\n\t\t\t\t\t\t\t\t\t\t<p>\n\t\t\t\t\t\tThe father of trigonometry is considered to be Hipparchus.\t\t\t\t\t<\/p>\n\t\t\t\t<\/div>\n\t\t\t<\/div>\n\t\t<\/section>\n\t\t\t\t<section class=\"sc_fs_faq sc_card \">\n\t\t\t<div>\n\t\t\t\t<h3><span class=\"ez-toc-section\" id=\"Who_is_the_mother_of_trigonometry\"><\/span>Who is the mother of trigonometry?<span class=\"ez-toc-section-end\"><\/span><\/h3>\t\t\t\t<div>\n\t\t\t\t\t\t\t\t\t\t<p>\n\t\t\t\t\t\tThere isn't a widely recognized mother of trigonometry as it is a collective field of mathematics.\t\t\t\t\t<\/p>\n\t\t\t\t<\/div>\n\t\t\t<\/div>\n\t\t<\/section>\n\t\t\t\t<section class=\"sc_fs_faq sc_card \">\n\t\t\t<div>\n\t\t\t\t<h3><span class=\"ez-toc-section\" id=\"What_is_theta_angle\"><\/span>What is theta angle?<span class=\"ez-toc-section-end\"><\/span><\/h3>\t\t\t\t<div>\n\t\t\t\t\t\t\t\t\t\t<p>\n\t\t\t\t\t\tTheta (\u03b8) is a symbol used in trigonometry to represent an angle.\t\t\t\t\t<\/p>\n\t\t\t\t<\/div>\n\t\t\t<\/div>\n\t\t<\/section>\n\t\t\t\t<section class=\"sc_fs_faq sc_card \">\n\t\t\t<div>\n\t\t\t\t<h3><span class=\"ez-toc-section\" id=\"What_are_the_4_types_of_trigonometry\"><\/span>What are the 4 types of trigonometry?<span class=\"ez-toc-section-end\"><\/span><\/h3>\t\t\t\t<div>\n\t\t\t\t\t\t\t\t\t\t<p>\n\t\t\t\t\t\tThe four main types of trigonometry are plane trigonometry, spherical trigonometry, hyperbolic trigonometry, and analytic trigonometry.\t\t\t\t\t<\/p>\n\t\t\t\t<\/div>\n\t\t\t<\/div>\n\t\t<\/section>\n\t\t\n<script type=\"application\/ld+json\">\n\t{\n\t\t\"@context\": \"https:\/\/schema.org\",\n\t\t\"@type\": \"FAQPage\",\n\t\t\"mainEntity\": [\n\t\t\t\t\t{\n\t\t\t\t\"@type\": \"Question\",\n\t\t\t\t\"name\": \"What is the basic formula for trigonometry\",\n\t\t\t\t\"acceptedAnswer\": {\n\t\t\t\t\t\"@type\": \"Answer\",\n\t\t\t\t\t\"text\": \"The basic formula in trigonometry relates the angles and sides of a right-angled triangle, such as sine, cosine, and tangent.\"\n\t\t\t\t\t\t\t\t\t}\n\t\t\t}\n\t\t\t,\t\t\t\t{\n\t\t\t\t\"@type\": \"Question\",\n\t\t\t\t\"name\": \"What are the 7 formula of trigonometry?\",\n\t\t\t\t\"acceptedAnswer\": {\n\t\t\t\t\t\"@type\": \"Answer\",\n\t\t\t\t\t\"text\": \"There are 7 fundamental trigonometric formulas, including sine, cosine, tangent, cosecant, secant, cotangent, and the Pythagorean theorem.\"\n\t\t\t\t\t\t\t\t\t}\n\t\t\t}\n\t\t\t,\t\t\t\t{\n\t\t\t\t\"@type\": \"Question\",\n\t\t\t\t\"name\": \"What is 15 trigonometry formula?\",\n\t\t\t\t\"acceptedAnswer\": {\n\t\t\t\t\t\"@type\": \"Answer\",\n\t\t\t\t\t\"text\": \"There is no standard 15 trigonometry formula. 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These formulas, which include [&hellip;]<\/p>\n","protected":false},"author":53,"featured_media":0,"comment_status":"closed","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"_yoast_wpseo_focuskw":"Trigonometry Formulas","_yoast_wpseo_title":"Trigonometry Formulas, Table & Identities","_yoast_wpseo_metadesc":"Trigonometry Formulas are mathematical equations used to solve problems involving angles and triangles, such as sine, cosine, tangent, and Pythagorean theorem.","custom_permalink":"articles\/trigonometry-formulas\/"},"categories":[8442,8443],"tags":[],"table_tags":[],"acf":[],"yoast_head":"<!-- This site is optimized with the Yoast SEO plugin v17.9 - https:\/\/yoast.com\/wordpress\/plugins\/seo\/ -->\n<title>Trigonometry Formulas, Table &amp; Identities<\/title>\n<meta name=\"description\" content=\"Trigonometry Formulas are mathematical equations used to solve problems involving angles and triangles, such as sine, cosine, tangent, and Pythagorean 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