{"id":201173,"date":"2023-12-20T03:11:16","date_gmt":"2023-12-20T03:11:16","guid":{"rendered":"https:\/\/namso-gen.co\/blog\/how-to-get-exact-value-of-trigonometric-functions\/"},"modified":"2023-12-20T03:11:16","modified_gmt":"2023-12-20T03:11:16","slug":"how-to-get-exact-value-of-trigonometric-functions","status":"publish","type":"post","link":"https:\/\/namso-gen.co\/blog\/how-to-get-exact-value-of-trigonometric-functions\/","title":{"rendered":"How to get exact value of trigonometric functions?"},"content":{"rendered":"<p>Trigonometric functions are essential in mathematics and are used to relate the angles of a triangle to the lengths of its sides. In many cases, we need to find the exact value of these functions for specific angles. So, how can we go about getting the exact value of trigonometric functions?<\/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-get-exact-value-of-trigonometric-functions\/#How_to_get_exact_value_of_trigonometric_functions\" title=\"How to get exact value of trigonometric functions?\">How to get exact value of trigonometric functions?<\/a><ul class='ez-toc-list-level-3' ><li class='ez-toc-heading-level-3'><a class=\"ez-toc-link ez-toc-heading-2\" href=\"https:\/\/namso-gen.co\/blog\/how-to-get-exact-value-of-trigonometric-functions\/#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-3\" href=\"https:\/\/namso-gen.co\/blog\/how-to-get-exact-value-of-trigonometric-functions\/#1_What_are_the_basic_trigonometric_functions\" title=\"1. What are the basic trigonometric functions?\">1. What are the basic trigonometric functions?<\/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-get-exact-value-of-trigonometric-functions\/#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-5\" href=\"https:\/\/namso-gen.co\/blog\/how-to-get-exact-value-of-trigonometric-functions\/#3_How_can_trigonometric_identities_help_in_finding_exact_values\" title=\"3. How can trigonometric identities help in finding exact values?\">3. How can trigonometric identities help in finding exact values?<\/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-get-exact-value-of-trigonometric-functions\/#4_How_do_special_right_triangles_help_in_finding_exact_values\" title=\"4. How do special right triangles help in finding exact values?\">4. How do special right triangles help in finding exact values?<\/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-get-exact-value-of-trigonometric-functions\/#5_How_can_we_determine_the_reference_angle_for_a_given_angle\" title=\"5. How can we determine the reference angle for a given angle?\">5. How can we determine the reference angle for a given angle?<\/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-get-exact-value-of-trigonometric-functions\/#6_What_is_the_relationship_between_sine_and_cosine_functions\" title=\"6. What is the relationship between sine and cosine functions?\">6. What is the relationship between sine and cosine functions?<\/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\/how-to-get-exact-value-of-trigonometric-functions\/#7_How_can_we_use_the_double_angle_formula_to_find_exact_values\" title=\"7. How can we use the double angle formula to find exact values?\">7. How can we use the double angle formula to find exact values?<\/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\/how-to-get-exact-value-of-trigonometric-functions\/#8_What_is_the_period_of_trigonometric_functions\" title=\"8. What is the period of trigonometric functions?\">8. What is the period of trigonometric functions?<\/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\/how-to-get-exact-value-of-trigonometric-functions\/#9_How_do_we_find_the_reciprocal_trigonometric_functions\" title=\"9. How do we find the reciprocal trigonometric functions?\">9. How do we find the reciprocal trigonometric functions?<\/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-get-exact-value-of-trigonometric-functions\/#10_How_can_we_use_the_sum_and_difference_formulas_to_find_exact_values\" title=\"10. How can we use the sum and difference formulas to find exact values?\">10. How can we use the sum and difference formulas to find exact values?<\/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-get-exact-value-of-trigonometric-functions\/#11_What_is_the_relationship_between_sine_and_cosine_functions_in_terms_of_phase_shift\" title=\"11. What is the relationship between sine and cosine functions in terms of phase shift?\">11. What is the relationship between sine and cosine functions in terms of phase shift?<\/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-get-exact-value-of-trigonometric-functions\/#12_How_can_we_use_the_periodicity_of_trigonometric_functions_to_find_exact_values\" title=\"12. How can we use the periodicity of trigonometric functions to find exact values?\">12. How can we use the periodicity of trigonometric functions to find exact values?<\/a><\/li><\/ul><\/li><\/ul><\/nav><\/div>\n<h2><span class=\"ez-toc-section\" id=\"How_to_get_exact_value_of_trigonometric_functions\"><\/span>How to get exact value of trigonometric functions?<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p>\nTo get the exact value of trigonometric functions for a specific angle, we need to use the properties of special right triangles, trigonometric identities, and the unit circle.<\/p>\n<p>Trigonometric functions such as sine, cosine, and tangent are ratios of the sides of a right triangle. By using the Pythagorean theorem and the definitions of these functions, we can determine the exact values for common angles.<\/p>\n<p>For example, the sine of 30 degrees is equal to 1\/2, the cosine of 45 degrees is equal to \u221a2\/2, and the tangent of 60 degrees is equal to \u221a3.<\/p>\n<p>Additionally, the unit circle provides a way to determine the values of trigonometric functions for any angle. By knowing the coordinates of points on the unit circle, we can find the exact values of sine, cosine, and tangent for any angle.<\/p>\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_are_the_basic_trigonometric_functions\"><\/span>1. What are the basic trigonometric functions?<span class=\"ez-toc-section-end\"><\/span><\/h3>\n<p>\nThe basic trigonometric functions are sine, cosine, and tangent, which are defined as ratios of the sides of a right triangle.<\/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 centered at the origin of a Cartesian plane. It is used to define trigonometric functions for any angle.<\/p>\n<h3><span class=\"ez-toc-section\" id=\"3_How_can_trigonometric_identities_help_in_finding_exact_values\"><\/span>3. How can trigonometric identities help in finding exact values?<span class=\"ez-toc-section-end\"><\/span><\/h3>\n<p>\nTrigonometric identities provide relationships between trigonometric functions that can be used to simplify expressions and find exact values.<\/p>\n<h3><span class=\"ez-toc-section\" id=\"4_How_do_special_right_triangles_help_in_finding_exact_values\"><\/span>4. How do special right triangles help in finding exact values?<span class=\"ez-toc-section-end\"><\/span><\/h3>\n<p>\nSpecial right triangles, such as the 45-45-90 and 30-60-90 triangles, have specific ratios of side lengths that can be used to find exact values of trigonometric functions.<\/p>\n<h3><span class=\"ez-toc-section\" id=\"5_How_can_we_determine_the_reference_angle_for_a_given_angle\"><\/span>5. How can we determine the reference angle for a given angle?<span class=\"ez-toc-section-end\"><\/span><\/h3>\n<p>\nThe reference angle for a given angle is the acute angle formed by the terminal side of the angle and the x-axis. It is useful in finding the exact values of trigonometric functions using the unit circle.<\/p>\n<h3><span class=\"ez-toc-section\" id=\"6_What_is_the_relationship_between_sine_and_cosine_functions\"><\/span>6. What is the relationship between sine and cosine functions?<span class=\"ez-toc-section-end\"><\/span><\/h3>\n<p>\nThe sine and cosine functions are related by the Pythagorean identity, sin^2\u03b8 + cos^2\u03b8 = 1. This relationship can be used to find exact values of trigonometric functions.<\/p>\n<h3><span class=\"ez-toc-section\" id=\"7_How_can_we_use_the_double_angle_formula_to_find_exact_values\"><\/span>7. How can we use the double angle formula to find exact values?<span class=\"ez-toc-section-end\"><\/span><\/h3>\n<p>\nThe double angle formula relates the trigonometric functions of an angle to the trigonometric functions of twice that angle. It can be used to find exact values for certain angles.<\/p>\n<h3><span class=\"ez-toc-section\" id=\"8_What_is_the_period_of_trigonometric_functions\"><\/span>8. What is the period of trigonometric functions?<span class=\"ez-toc-section-end\"><\/span><\/h3>\n<p>\nThe period of a trigonometric function is the smallest positive value of x for which the function repeats its values. For sine and cosine functions, the period is 2\u03c0.<\/p>\n<h3><span class=\"ez-toc-section\" id=\"9_How_do_we_find_the_reciprocal_trigonometric_functions\"><\/span>9. How do we find the reciprocal trigonometric functions?<span class=\"ez-toc-section-end\"><\/span><\/h3>\n<p>\nThe reciprocal trigonometric functions, cosecant, secant, and cotangent, are the reciprocals of sine, cosine, and tangent, respectively. They can be found by taking the reciprocal of the corresponding trigonometric function.<\/p>\n<h3><span class=\"ez-toc-section\" id=\"10_How_can_we_use_the_sum_and_difference_formulas_to_find_exact_values\"><\/span>10. How can we use the sum and difference formulas to find exact values?<span class=\"ez-toc-section-end\"><\/span><\/h3>\n<p>\nThe sum and difference formulas relate the trigonometric functions of the sum or difference of two angles to the trigonometric functions of the individual angles. They can be used to find exact values for certain angles.<\/p>\n<h3><span class=\"ez-toc-section\" id=\"11_What_is_the_relationship_between_sine_and_cosine_functions_in_terms_of_phase_shift\"><\/span>11. What is the relationship between sine and cosine functions in terms of phase shift?<span class=\"ez-toc-section-end\"><\/span><\/h3>\n<p>\nThe sine and cosine functions have a phase shift of \u03c0\/2, meaning that the sine function leads the cosine function by \u03c0\/2 radians. This relationship can be useful in analyzing periodic functions.<\/p>\n<h3><span class=\"ez-toc-section\" id=\"12_How_can_we_use_the_periodicity_of_trigonometric_functions_to_find_exact_values\"><\/span>12. How can we use the periodicity of trigonometric functions to find exact values?<span class=\"ez-toc-section-end\"><\/span><\/h3>\n<p>\nThe periodicity of trigonometric functions can be used to find the exact values of trigonometric functions for angles outside the standard range by adding or subtracting multiples of the period.<\/p>\n","protected":false},"excerpt":{"rendered":"<p>Trigonometric functions are essential in mathematics and are used to relate the angles of a triangle to the lengths of its sides. In many cases, we need to find the exact value of these functions for specific angles. So, how can we go about getting the exact value of trigonometric functions? How to get exact &#8230; <\/p>\n<p class=\"read-more-container\"><a title=\"How to get exact value of trigonometric functions?\" class=\"read-more button\" href=\"https:\/\/namso-gen.co\/blog\/how-to-get-exact-value-of-trigonometric-functions\/#more-201173\">Read more<span class=\"screen-reader-text\">How to get exact value of trigonometric functions?<\/span><\/a><\/p>\n","protected":false},"author":51,"featured_media":107420,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[86279],"tags":[],"class_list":["post-201173","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 get exact value of trigonometric functions?<\/title>\n<meta name=\"description\" content=\"Trigonometric functions are essential in mathematics and are used to relate the angles of a triangle to the lengths of its sides. 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