{"id":26212,"date":"2023-03-12T16:02:27","date_gmt":"2023-03-12T16:02:27","guid":{"rendered":"https:\/\/www.splashlearn.com\/math-vocabulary\/?page_id=26212"},"modified":"2023-11-15T07:50:56","modified_gmt":"2023-11-15T07:50:56","slug":"reciprocal-identities-in-trigonometry","status":"publish","type":"post","link":"https:\/\/www.splashlearn.com\/math-vocabulary\/reciprocal-identities","title":{"rendered":"Reciprocal Identities in Trigonometry"},"content":{"rendered":"<div class=\"aioseo-breadcrumbs\"><span class=\"aioseo-breadcrumb\">\n\tMath-Vocabulary\n<\/span><\/div>\n\n<div class=\"ub_table-of-contents\" data-showtext=\"show\" data-hidetext=\"hide\" data-scrolltype=\"auto\" id=\"ub_table-of-contents-b5513343-cb60-43e8-82e1-4567c91d9f9f\" data-initiallyhideonmobile=\"false\"\n                    data-initiallyshow=\"true\"><div class=\"ub_table-of-contents-extra-container\"><div class=\"ub_table-of-contents-container ub_table-of-contents-1-column \"><ul><li><a href=https:\/\/www.splashlearn.com\/math-vocabulary\/reciprocal-identities#0-what-are-trigonometric-reciprocal-identities-introduction>What Are Trigonometric Reciprocal Identities? Introduction<\/a><\/li><li><a href=https:\/\/www.splashlearn.com\/math-vocabulary\/reciprocal-identities#2-proof-of-reciprocal-identities>Proof of Reciprocal Identities<\/a><\/li><li><a href=https:\/\/www.splashlearn.com\/math-vocabulary\/reciprocal-identities#3-relationship-between-reciprocal-identities>Relationship between Reciprocal Identities<\/a><\/li><li><a href=https:\/\/www.splashlearn.com\/math-vocabulary\/reciprocal-identities#5-solved-examples-on-reciprocal-identities>Solved Examples on Reciprocal Identities<\/a><\/li><li><a href=https:\/\/www.splashlearn.com\/math-vocabulary\/reciprocal-identities#6-practice-problems-on-reciprocal-identities>Practice Problems on Reciprocal Identities<\/a><\/li><li><a href=https:\/\/www.splashlearn.com\/math-vocabulary\/reciprocal-identities#7-frequently-asked-questions-on-reciprocal-identities>Frequently Asked Questions on Reciprocal Identities<\/a><\/li><\/ul><\/div><\/div><\/div>\n\n\n<h2 class=\"wp-block-heading eplus-wrapper\" id=\"0-what-are-trigonometric-reciprocal-identities-introduction\">What Are Trigonometric Reciprocal Identities? Introduction<\/h2>\n\n\n\n<p class=\"eplus-wrapper\">The six trigonometric ratios are sine, cosine, tangent, cotangent, secant, cosecant, out of which the three standard trigonometric ratios are sine, cosine, and tangent. The six trigonometric ratios can be grouped in pairs as reciprocals. The reciprocal identities are the reciprocals of these six trigonometric ratios. Note that reciprocal identities are not the same as inverse trigonometric functions.<\/p>\n\n\n\n<p class=\"eplus-wrapper\">Reciprocal identities are the reciprocals of the six fundamental trigonometric functions (sine, cosine, tangent, secant, cosecant, and cotangent).&nbsp;<\/p>\n\n\n\n<p class=\"eplus-wrapper\">We know that the reciprocal of a fraction $\\frac{a}{b}$ is given by $\\frac{b}{a}$. It is obtained by interchanging the values of numerator and denominator. Similarly, we can find the reciprocal of each trigonometric ratio using their definitions.<\/p>\n\n\n\n<p class=\"eplus-wrapper\">Example of reciprocal identity: The reciprocal of the sine ratio is cosecant.&nbsp;<\/p>\n\n\n\n<h2 class=\"wp-block-heading eplus-wrapper\" id=\"1-reciprocal-identities-formulas\">Reciprocal Identities Formulas<\/h2>\n\n\n\n<p class=\"eplus-wrapper\">Reciprocal identities are used to simplify calculations in various trigonometry problems. The formulas for the six major reciprocal identities are as follows:<\/p>\n\n\n\n<ul class=\"eplus-wrapper wp-block-list\">\n<li class=\"eplus-wrapper\"><strong>sin x <\/strong>$= \\frac{1}{cosec\\; x}$<\/li>\n\n\n\n<li class=\"eplus-wrapper\"><strong>cos x <\/strong>$= \\frac{1}{sec\\; x}$<\/li>\n\n\n\n<li class=\"eplus-wrapper\"><strong>tan x <\/strong>$= \\frac{1}{cot\\; x}$<\/li>\n\n\n\n<li class=\"eplus-wrapper\"><strong>cot x <\/strong>$= \\frac{1}{tan\\; x}$<\/li>\n\n\n\n<li class=\"eplus-wrapper\"><strong>sec x <\/strong>$= \\frac{1}{cos\\; x}$<\/li>\n\n\n\n<li class=\"eplus-wrapper\"><strong>cosec x<\/strong> $= \\frac{1}{sin\\; x}$<\/li>\n<\/ul>\n\n\n\n<h2 class=\"wp-block-heading eplus-wrapper\" id=\"2-proof-of-reciprocal-identities\">Proof of Reciprocal Identities<\/h2>\n\n\n\n<p class=\"eplus-wrapper\">In geometry, trigonometry is a branch of mathematics that studies the relationship between the sides and angles of a right-angled triangle. Consider a right triangle.<\/p>\n\n\n\n<figure class=\"wp-block-image size-full eplus-wrapper\"><img loading=\"lazy\" decoding=\"async\" width=\"620\" height=\"317\" src=\"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2023\/11\/adjacent-side-opposite-side-of-an-angle-in-a-right-triangle.png\" alt=\"Adjacent side, opposite side of an angle in a right triangle\" class=\"wp-image-35699\" title=\"Adjacent side, opposite side of an angle in a right triangle\" srcset=\"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2023\/11\/adjacent-side-opposite-side-of-an-angle-in-a-right-triangle.png 620w, https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2023\/11\/adjacent-side-opposite-side-of-an-angle-in-a-right-triangle-300x153.png 300w\" sizes=\"auto, (max-width: 620px) 100vw, 620px\" \/><\/figure>\n\n\n\n<p class=\"eplus-wrapper\">Let\u2019s understand the definition of each trigonometric ratio.<\/p>\n\n\n\n<ul class=\"eplus-wrapper wp-block-list\">\n<li class=\"eplus-wrapper\">$sin\\; \\theta = \\frac{Opposite\\; Side}{Hypotenuse}$<br>$cosec\\; \\theta = \\frac{Hypotenuse}{Opposite\\; Side}$<br>sine and cosecant are reciprocals.<br>Thus, $\\frac{1}{sin\\; \\theta} = cosec\\; \\theta$&nbsp; and $\\frac{1}{cosec\\; \\theta} = sin\\; \\theta$<\/li>\n<\/ul>\n\n\n\n<ul class=\"eplus-wrapper wp-block-list\">\n<li class=\"eplus-wrapper\">$cos\\; \\theta = \\frac{Adjacent\\; Side}{Hypotenuse}$<br>$sec\\; \\theta = \\frac{Hypotenuse}{Adjacent\\; Side}$<br>cosine and secant are reciprocals.<br>Thus, $\\frac{1}{cos\\; \\theta} = sec\\; \\theta$&nbsp; and $\\frac{1}{sec\\; \\theta} = cos\\; \\theta$<\/li>\n<\/ul>\n\n\n\n<ul class=\"eplus-wrapper wp-block-list\">\n<li class=\"eplus-wrapper\">$tan\\; \\theta = \\frac{Opposite\\; Side}{Adjacent\\; Side}$<br>$cot\\; \\theta = \\frac{Adjacent\\; Side}{Opposite\\; Side}$<br>tangent and cotangent are reciprocals.<br>Thus, $\\frac{1}{tan\\; \\theta} = cot\\; \\theta$&nbsp; and $\\frac{1}{cot\\; \\theta} = tan\\; \\theta$<\/li>\n<\/ul>\n\n\n\n<p class=\"eplus-wrapper\"><strong>In summary:<\/strong><\/p>\n\n\n\n<ul class=\"eplus-wrapper wp-block-list\">\n<li class=\"eplus-wrapper\">sin $\\theta$ is the reciprocal of cosec $\\theta$.<\/li>\n\n\n\n<li class=\"eplus-wrapper\">cosec $\\theta$ is the reciprocal of sin $\\theta$.<\/li>\n\n\n\n<li class=\"eplus-wrapper\">cos $\\theta$ is the reciprocal of sec $\\theta$.<\/li>\n\n\n\n<li class=\"eplus-wrapper\">sec $\\theta$ is the reciprocal of cos $\\theta$.<\/li>\n\n\n\n<li class=\"eplus-wrapper\">tan $\\theta$ is the reciprocal of cot $\\theta$.<\/li>\n\n\n\n<li class=\"eplus-wrapper\">cot $\\theta$ is the reciprocal of tan $\\theta$.<\/li>\n<\/ul>\n\n\n\n<h2 class=\"wp-block-heading eplus-wrapper\" id=\"3-relationship-between-reciprocal-identities\">Relationship between Reciprocal Identities<\/h2>\n\n\n\n<p class=\"eplus-wrapper\">We know that any number multiplied with its reciprocal results in 1. Similarly, the product of a trigonometric ratio and its reciprocal is one.&nbsp;<\/p>\n\n\n\n<ul class=\"eplus-wrapper wp-block-list\">\n<li class=\"eplus-wrapper\">$sin\\; \\theta \\times  csc\\; \\theta = 1$<\/li>\n\n\n\n<li class=\"eplus-wrapper\">$cos\\; \\theta \\times sec\\; \\theta = 1$<\/li>\n\n\n\n<li class=\"eplus-wrapper\">$tan\\; \\theta \\times cot\\; \\theta = 1$<\/li>\n<\/ul>\n\n\n\n<p class=\"eplus-wrapper\"><strong>Note:<\/strong><\/p>\n\n\n\n<p class=\"eplus-wrapper\">&nbsp;$tan\\; \\theta = \\frac{sin\\; \\theta}{cos\\; \\theta}$<\/p>\n\n\n\n<p class=\"eplus-wrapper\">$cot\\; \\theta = \\frac{cos\\; \\theta}{sin\\; \\theta}$<\/p>\n\n\n\n<h2 class=\"wp-block-heading eplus-wrapper\" id=\"4-conclusion\">Conclusion<\/h2>\n\n\n\n<p class=\"eplus-wrapper\">Reciprocal identities are the reciprocals of the six fundamental trigonometric functions (sine, cosine, tangent, secant, cosecant, and cotangent). In this article, we explored different reciprocal identities, their formulas, and proof. Let\u2019s solve a few examples and practice problems.<\/p>\n\n\n\n<h2 class=\"wp-block-heading eplus-wrapper\" id=\"5-solved-examples-on-reciprocal-identities\">Solved Examples on Reciprocal Identities<\/h2>\n\n\n\n<p class=\"eplus-wrapper\"><strong>1. With the use of a reciprocal identity, determine the expression&#8217;s value.<\/strong><\/p>\n\n\n\n<p class=\"eplus-wrapper\">$\\frac{sin\\; \\theta}{cos\\; \\theta} \\times sec\\; \\theta \\times csc\\; \\theta$<\/p>\n\n\n\n<p class=\"eplus-wrapper\"><strong>Solution:<\/strong><\/p>\n\n\n\n<p class=\"eplus-wrapper\">We know that,<\/p>\n\n\n\n<p class=\"eplus-wrapper\">$csc\\; \\theta = \\frac{1}{sin\\; \\theta}$ and $sec\\; \\theta = \\frac{1}{cos\\; \\theta}$<\/p>\n\n\n\n<p class=\"eplus-wrapper\">Substituting these values,&nbsp;<\/p>\n\n\n\n<p class=\"eplus-wrapper\">$\\frac{sin\\;\\theta}{cos\\;\\theta} \\times sec\\;\\theta \\times csc\\;\\theta = \\frac{sin\\;\\theta}{cos\\;\\theta} \\times \\frac{1}{cos\\;\\theta} \\times \\frac{1}{sin\\;\\theta}$<\/p>\n\n\n\n<p class=\"eplus-wrapper\">$= \\frac{1}{cos\\;\\theta} \\times \\frac{1}{cos\\;\\theta}$<\/p>\n\n\n\n<p class=\"eplus-wrapper\">$= \\frac{1}{cos^{2}\\theta}$<\/p>\n\n\n\n<p class=\"eplus-wrapper\">$= sec^{2}\\theta$<\/p>\n\n\n\n<p class=\"eplus-wrapper\"><strong>2. If sin x <\/strong>$=\\frac{1}{2}$<strong> and cos x <\/strong>$= \\frac{\\sqrt{3}}{2}$<strong>, find all the other trigonometric ratios.<\/strong><\/p>\n\n\n\n<p class=\"eplus-wrapper\"><strong>Solution:<\/strong><\/p>\n\n\n\n<p class=\"eplus-wrapper\">sin x $= \\frac{1}{2}$<\/p>\n\n\n\n<p class=\"eplus-wrapper\">cos x $= \\frac{\\sqrt{3}}{2}$<\/p>\n\n\n\n<p class=\"eplus-wrapper\">tan x $= \\frac{sin\\;\\theta}{cos\\;\\theta} = \\frac{\\frac{1}{2}}{\\frac{\\sqrt{3}}{2}} = \\frac{1}{\\sqrt{3}}$<\/p>\n\n\n\n<p class=\"eplus-wrapper\">cosec x $= \\frac{1}{sin\\; x} = 2$<\/p>\n\n\n\n<p class=\"eplus-wrapper\">sec x $= \\frac{1}{cos\\; x} = \\frac{2}{sqrt{3}}$<\/p>\n\n\n\n<p class=\"eplus-wrapper\"><strong>3. For <\/strong>$\\theta = 90^{\\circ}$<strong>, sin <\/strong>$\\theta = 1$<strong> and cos <\/strong>$\\theta = 0$<strong>. Find cosec<\/strong> $\\theta$<strong> and sec <\/strong>$\\theta$<strong>.<\/strong><\/p>\n\n\n\n<p class=\"eplus-wrapper\"><strong>Solution:<\/strong><\/p>\n\n\n\n<p class=\"eplus-wrapper\">$sin\\; \\theta = 1,\\; cos\\; \\theta = 0$<\/p>\n\n\n\n<p class=\"eplus-wrapper\">$cosec\\;\\theta = \\frac{1}{sin\\;\\theta}$ and$sec\\;\\theta = \\frac{1}{cos\\;\\theta}$<\/p>\n\n\n\n<p class=\"eplus-wrapper\">$cosec\\;\\theta = \\frac{1}{1}$ and $sec\\;\\theta = \\frac{1}{0}$<\/p>\n\n\n\n<p class=\"eplus-wrapper\">$cosec\\;\\theta = 1$ and $sec\\;\\theta = Not\\; defined$<\/p>\n\n\n\n<h2 class=\"wp-block-heading eplus-wrapper\" id=\"6-practice-problems-on-reciprocal-identities\">Practice Problems on Reciprocal Identities<\/h2>\n\n\n\n<p class=\"eplus-wrapper\"><div class=\"spq_wrapper\"><h2 style=\"display:none;\">Reciprocal Identities in Trigonometry<\/h2><p style=\"display:none;\">Attend this quiz & Test your knowledge.<\/p><div class=\"spq_question_wrapper\" data-answer=\"3\"><span class=\"spq_question_header\"><span class=\"sqp_question_number\">1<\/span><h3 class=\"sqp_question_text\">What is the reciprocal of $cos\\;\\theta$ ?<\/h3><\/span><div class=\"spq_answer_block\" data-value=\"0\">$sin\\;\\theta$<\/div><div class=\"spq_answer_block\" data-value=\"1\">$cos\\;\\theta$<\/div><div class=\"spq_answer_block\" data-value=\"2\">$tan\\;\\theta$<\/div><div class=\"spq_answer_block\" data-value=\"3\">$sec\\;\\theta$<\/div><div class=\"sqp_question_hint\"><div class=\"sqp_question_hint__header\"><span class=\"spq_correct\">Correct<\/span><span class=\"spq_incorrect\">Incorrect<\/span><\/div><div class=\"sqp_question_hint__content\"><span>Correct answer is: $sec\\;\\theta$<br\/>$sec\\;\\theta$ is the reciprocal of $cos\\;\\theta$.<\/span><\/div><\/div><\/div><div class=\"spq_question_wrapper\" data-answer=\"1\"><span class=\"spq_question_header\"><span class=\"sqp_question_number\">2<\/span><h3 class=\"sqp_question_text\">What is the value of $sec\\;\\theta$  if $cos\\;\\theta  = \\frac{1}{\\sqrt{2}}$?<\/h3><\/span><div class=\"spq_answer_block\" data-value=\"0\">$\\frac{1}{\\sqrt{2}}$<\/div><div class=\"spq_answer_block\" data-value=\"1\">$\\sqrt{2}$<\/div><div class=\"spq_answer_block\" data-value=\"2\">$\\frac{1}{2}$<\/div><div class=\"spq_answer_block\" data-value=\"3\">$1$<\/div><div class=\"sqp_question_hint\"><div class=\"sqp_question_hint__header\"><span class=\"spq_correct\">Correct<\/span><span class=\"spq_incorrect\">Incorrect<\/span><\/div><div class=\"sqp_question_hint__content\"><span>Correct answer is: $\\sqrt{2}$<br\/>$sec\\;x = \\frac{1}{cos\\;x}$<br>\r\nThus, $sec\\;\\theta = \\frac{1}{cos\\;\\theta} = \\sqrt{2}$<\/span><\/div><\/div><\/div><div class=\"spq_question_wrapper\" data-answer=\"2\"><span class=\"spq_question_header\"><span class=\"sqp_question_number\">3<\/span><h3 class=\"sqp_question_text\">sin x  ________ $= 1$<\/h3><\/span><div class=\"spq_answer_block\" data-value=\"0\">cos x<\/div><div class=\"spq_answer_block\" data-value=\"1\">tan x<\/div><div class=\"spq_answer_block\" data-value=\"2\">cosec x<\/div><div class=\"spq_answer_block\" data-value=\"3\">sec x<\/div><div class=\"sqp_question_hint\"><div class=\"sqp_question_hint__header\"><span class=\"spq_correct\">Correct<\/span><span class=\"spq_incorrect\">Incorrect<\/span><\/div><div class=\"sqp_question_hint__content\"><span>Correct answer is: cosec x<br\/>sin x  cosec x $= 1$<br>\r\nsin x is the reciprocal of cosec x.<\/span><\/div><\/div><\/div><div class=\"spq_question_wrapper\" data-answer=\"2\"><span class=\"spq_question_header\"><span class=\"sqp_question_number\">4<\/span><h3 class=\"sqp_question_text\">What is the reciprocal identity of cot $\\theta$?<\/h3><\/span><div class=\"spq_answer_block\" data-value=\"0\">$sin\\;\\theta$<\/div><div class=\"spq_answer_block\" data-value=\"1\">$cos\\;\\theta$<\/div><div class=\"spq_answer_block\" data-value=\"2\">$tan\\;\\theta$<\/div><div class=\"spq_answer_block\" data-value=\"3\">$sec\\;\\theta$<\/div><div class=\"sqp_question_hint\"><div class=\"sqp_question_hint__header\"><span class=\"spq_correct\">Correct<\/span><span class=\"spq_incorrect\">Incorrect<\/span><\/div><div class=\"sqp_question_hint__content\"><span>Correct answer is: $tan\\;\\theta$<br\/>$cot\\;\\theta = \\frac{1}{tan\\;\\theta}$ <\/span><\/div><\/div><\/div><\/div>  <script type=\"application\/ld+json\">{\n        \"@context\": \"https:\/\/schema.org\/\", \n        \"@type\": \"Quiz\", \n        \"typicalAgeRange\": \"3-11\",\n        \"educationalLevel\":  \"beginner\",\n        \"assesses\" : \"Attend this quiz & Test your knowledge.\",\n        \"educationalAlignment\": [\n              {\n                \"@type\": \"AlignmentObject\",\n                \"alignmentType\": \"educationalSubject\",\n                \"targetName\": \"Math\"\n              }] ,\n        \"name\": \"Reciprocal Identities in Trigonometry\",        \n        \"about\": {\n                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\"text\/html\",\n                                \"text\": \"tan x\",\n                                \"comment\": {\n                                    \"@type\": \"Comment\",\n                                    \"text\": \"sin x  cosec x $$= 1$$<br>\r\nsin x is the reciprocal of cosec x.\"\n                                    }\n                                }, {\n                                \"@type\": \"Answer\",\n                                \"position\": 3,\n                                \"encodingFormat\": \"text\/html\",\n                                \"text\": \"sec x\",\n                                \"comment\": {\n                                    \"@type\": \"Comment\",\n                                    \"text\": \"sin x  cosec x $$= 1$$<br>\r\nsin x is the reciprocal of cosec x.\"\n                                    }\n                                }],\n                    \"acceptedAnswer\": {\n                      \"@type\": \"Answer\",\n                      \"position\": 2,\n                      \"encodingFormat\": \"text\/html\",\n                      \"text\": \"cosec x\",\n                      \"comment\": {\n                          \"@type\": \"Comment\",\n                          \"text\": \"sin x  cosec x $$= 1$$<br>\r\nsin x is the reciprocal of cosec x.\"\n                        },\n                      \"answerExplanation\": {\n                        \"@type\": \"Comment\",\n                        \"text\": \"sin x  cosec x $$= 1$$<br>\r\nsin x is the reciprocal of cosec x.\"\n                      }\n                    } \n\n                    },{\n                    \"@type\": \"Question\",   \n                    \"eduQuestionType\": \"Multiple choice\",\n                    \"learningResourceType\": \"Practice problem\",\n                    \"name\": \"What is the reciprocal identity of cot $$\\\\theta$$?\",\n                    \"text\": \"What is the reciprocal identity of cot $$\\\\theta$$?\",\n                    \"comment\": {\n                      \"@type\": \"Comment\",\n                      \"text\": \"$$cot\\\\;\\\\theta = \\\\frac{1}{tan\\\\;\\\\theta}$$ \"\n                    },\n                    \"encodingFormat\": \"text\/html\",\n                    \"suggestedAnswer\": [ {\n                                \"@type\": \"Answer\",\n                                \"position\": 0,\n                                \"encodingFormat\": \"text\/html\",\n                                \"text\": \"$$sin\\\\;\\\\theta$$\",\n                                \"comment\": {\n                                    \"@type\": \"Comment\",\n                                    \"text\": \"$$cot\\\\;\\\\theta = \\\\frac{1}{tan\\\\;\\\\theta}$$ \"\n                                    }\n                                }, {\n                                \"@type\": \"Answer\",\n                                \"position\": 1,\n                                \"encodingFormat\": \"text\/html\",\n                                \"text\": \"$$cos\\\\;\\\\theta$$\",\n                                \"comment\": {\n                                    \"@type\": \"Comment\",\n                                    \"text\": \"$$cot\\\\;\\\\theta = \\\\frac{1}{tan\\\\;\\\\theta}$$ \"\n                                    }\n                                }, {\n                                \"@type\": \"Answer\",\n                                \"position\": 3,\n                                \"encodingFormat\": \"text\/html\",\n                                \"text\": \"$$sec\\\\;\\\\theta$$\",\n                                \"comment\": {\n                                    \"@type\": \"Comment\",\n                                    \"text\": \"$$cot\\\\;\\\\theta = \\\\frac{1}{tan\\\\;\\\\theta}$$ \"\n                                    }\n                                }],\n                    \"acceptedAnswer\": {\n                      \"@type\": \"Answer\",\n                      \"position\": 2,\n                      \"encodingFormat\": \"text\/html\",\n                      \"text\": \"$$tan\\\\;\\\\theta$$\",\n                      \"comment\": {\n                          \"@type\": \"Comment\",\n                          \"text\": \"$$cot\\\\;\\\\theta = \\\\frac{1}{tan\\\\;\\\\theta}$$ \"\n                        },\n                      \"answerExplanation\": {\n                        \"@type\": \"Comment\",\n                        \"text\": \"$$cot\\\\;\\\\theta = \\\\frac{1}{tan\\\\;\\\\theta}$$ \"\n                      }\n                    } \n\n                    }]}<\/script><\/p>\n\n\n\n<h2 class=\"wp-block-heading eplus-wrapper\" id=\"7-frequently-asked-questions-on-reciprocal-identities\">Frequently Asked Questions on Reciprocal Identities<\/h2>\n\n\n<div class=\"wp-block-ub-content-toggle\" id=\"ub-content-toggle-ee25c04c-2e17-4cae-8af9-4ebdd3a7526f\" data-mobilecollapse=\"true\" data-desktopcollapse=\"true\">\n<div class=\"wp-block-ub-content-toggle-accordion\">\n                <div class=\"wp-block-ub-content-toggle-accordion-title-wrap\" aria-expanded=\"false\" aria-controls=\"ub-content-toggle-panel-0-ee25c04c-2e17-4cae-8af9-4ebdd3a7526f\" tabindex=\"0\">\n                    <p class=\"wp-block-ub-content-toggle-accordion-title ub-content-toggle-title-ee25c04c-2e17-4cae-8af9-4ebdd3a7526f\"><strong>Can the denominator be 0 in case of the trigonometric reciprocal identities?<\/strong><\/p><div class=\"wp-block-ub-content-toggle-accordion-toggle-wrap right\"><span class=\"wp-block-ub-content-toggle-accordion-state-indicator wp-block-ub-chevron-down\"><\/span>\n                    <\/div><\/div><div role=\"region\" class=\"wp-block-ub-content-toggle-accordion-content-wrap ub-hide\" id=\"ub-content-toggle-panel-0-ee25c04c-2e17-4cae-8af9-4ebdd3a7526f\">\n\n<p class=\"eplus-wrapper\">Yes. However, such a division is not defined. Consider an example:<\/p>\n\n\n\n<p class=\"eplus-wrapper\">$tan 90^{\\circ} = 0$<\/p>\n\n\n\n<p class=\"eplus-wrapper\">Thus,&nbsp; cot&nbsp; $90^{\\circ}$ will be 1 divided by 0, which is not defined.<\/p>\n\n<\/div><\/div>\n\n<div class=\"wp-block-ub-content-toggle-accordion\">\n                <div class=\"wp-block-ub-content-toggle-accordion-title-wrap\" aria-expanded=\"false\" aria-controls=\"ub-content-toggle-panel-1-ee25c04c-2e17-4cae-8af9-4ebdd3a7526f\" tabindex=\"0\">\n                    <p class=\"wp-block-ub-content-toggle-accordion-title ub-content-toggle-title-ee25c04c-2e17-4cae-8af9-4ebdd3a7526f\"><strong>What are the 6 trigonometric ratios?<\/strong><\/p><div class=\"wp-block-ub-content-toggle-accordion-toggle-wrap right\"><span class=\"wp-block-ub-content-toggle-accordion-state-indicator wp-block-ub-chevron-down\"><\/span>\n                    <\/div><\/div><div role=\"region\" class=\"wp-block-ub-content-toggle-accordion-content-wrap ub-hide\" id=\"ub-content-toggle-panel-1-ee25c04c-2e17-4cae-8af9-4ebdd3a7526f\">\n\n<p class=\"eplus-wrapper\">Six trigonometric ratios: sine, cosine, tangent, cotangent, secant, and cosecant.<\/p>\n\n<\/div><\/div>\n\n<div class=\"wp-block-ub-content-toggle-accordion\">\n                <div class=\"wp-block-ub-content-toggle-accordion-title-wrap\" aria-expanded=\"false\" aria-controls=\"ub-content-toggle-panel-2-ee25c04c-2e17-4cae-8af9-4ebdd3a7526f\" tabindex=\"0\">\n                    <p class=\"wp-block-ub-content-toggle-accordion-title ub-content-toggle-title-ee25c04c-2e17-4cae-8af9-4ebdd3a7526f\"><strong>What are the applications of trigonometry in real life?<\/strong><\/p><div class=\"wp-block-ub-content-toggle-accordion-toggle-wrap right\"><span class=\"wp-block-ub-content-toggle-accordion-state-indicator wp-block-ub-chevron-down\"><\/span>\n                    <\/div><\/div><div role=\"region\" class=\"wp-block-ub-content-toggle-accordion-content-wrap ub-hide\" id=\"ub-content-toggle-panel-2-ee25c04c-2e17-4cae-8af9-4ebdd3a7526f\">\n\n<p class=\"eplus-wrapper\">Trigonometry has many applications in the fields such as engineering and aviation, where calculations of height and distance are involved.<\/p>\n\n<\/div><\/div>\n\n<div class=\"wp-block-ub-content-toggle-accordion\">\n                <div class=\"wp-block-ub-content-toggle-accordion-title-wrap\" aria-expanded=\"false\" aria-controls=\"ub-content-toggle-panel-3-ee25c04c-2e17-4cae-8af9-4ebdd3a7526f\" tabindex=\"0\">\n                    <p class=\"wp-block-ub-content-toggle-accordion-title ub-content-toggle-title-ee25c04c-2e17-4cae-8af9-4ebdd3a7526f\"><strong>What is the difference between <\/strong>$sin(x^{2})$<strong> and <\/strong>$sin^{2}(x)$<strong>?<\/strong><\/p><div class=\"wp-block-ub-content-toggle-accordion-toggle-wrap right\"><span class=\"wp-block-ub-content-toggle-accordion-state-indicator wp-block-ub-chevron-down\"><\/span>\n                    <\/div><\/div><div role=\"region\" class=\"wp-block-ub-content-toggle-accordion-content-wrap ub-hide\" id=\"ub-content-toggle-panel-3-ee25c04c-2e17-4cae-8af9-4ebdd3a7526f\">\n\n<p class=\"eplus-wrapper\">$sin(x^{2})$ means to square the value of x first and then apply the sine function.$sin^{2}(x)$ simply means to square the value of sin(x).<\/p>\n\n<\/div><\/div>\n<\/div>","protected":false},"excerpt":{"rendered":"<p>What Are Trigonometric Reciprocal Identities? Introduction The six trigonometric ratios are sine, cosine, tangent, cotangent, secant, cosecant, out of which the three standard trigonometric ratios are sine, cosine, and tangent. The six trigonometric ratios can be grouped in pairs as reciprocals. The reciprocal identities are the reciprocals of these six trigonometric ratios. Note that reciprocal &#8230; <a title=\"Reciprocal Identities in Trigonometry\" class=\"read-more\" href=\"https:\/\/www.splashlearn.com\/math-vocabulary\/reciprocal-identities\" aria-label=\"More on Reciprocal Identities in Trigonometry\">Read more<\/a><\/p>\n","protected":false},"author":2,"featured_media":0,"comment_status":"closed","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"ub_ctt_via":"","footnotes":""},"categories":[1],"tags":[],"class_list":["post-26212","post","type-post","status-publish","format-standard","hentry","category-all"],"featured_image_src":null,"author_info":{"display_name":"Mithun Jhawar","author_link":"https:\/\/www.splashlearn.com\/math-vocabulary\/author\/mithun-jhawarsplashlearn-com\/"},"acf":[],"aioseo_notices":[],"_links":{"self":[{"href":"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-json\/wp\/v2\/posts\/26212","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-json\/wp\/v2\/users\/2"}],"replies":[{"embeddable":true,"href":"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-json\/wp\/v2\/comments?post=26212"}],"version-history":[{"count":20,"href":"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-json\/wp\/v2\/posts\/26212\/revisions"}],"predecessor-version":[{"id":35700,"href":"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-json\/wp\/v2\/posts\/26212\/revisions\/35700"}],"wp:attachment":[{"href":"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-json\/wp\/v2\/media?parent=26212"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-json\/wp\/v2\/categories?post=26212"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-json\/wp\/v2\/tags?post=26212"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}