{"id":6585,"date":"2026-07-13T13:56:14","date_gmt":"2026-07-13T18:56:14","guid":{"rendered":"https:\/\/www.eastcentral.edu\/learning-center\/?page_id=6585"},"modified":"2026-07-13T13:56:33","modified_gmt":"2026-07-13T18:56:33","slug":"pythagorean-identities","status":"publish","type":"page","link":"https:\/\/www.eastcentral.edu\/learning-center\/pythagorean-identities\/","title":{"rendered":"Pythagorean Identities"},"content":{"rendered":"

*There are three so-called \u201cPythagorean Identities\u201d that can be used to simplify expressions containing trigonometric\u00a0functions. The three Pythagorean identities are:<\/p>\n

sin2<\/sup>x + cos2<\/sup>x = 1

1 + cot2<\/sup>x = csc2<\/sup>x

tan2<\/sup>x + 1 = sec2<\/sup>x<\/p>\n

*These identities can be used to determine function values.
Example:<\/strong> If the cot x = \u221a3 <\/span> 2 <\/span> <\/span>, then what is the value of csc x if the angle is in Quadrant 3?<\/p>\n

Using the second Pythagorean identity, we substitute the given value for cot x.<\/p>\n\n\n

\n\n1 +\n\n(\n\n\n \n \u221a3\n <\/span>\n \n 2\n <\/span>\n<\/span>\n\n)\n\n2<\/sup>\n\n = \n\ncsc2<\/sup>x\n\n

\n\n1 +\n\n\n \n 3\n <\/span>\n \n 4\n <\/span>\n<\/span>\n\n = \n\ncsc2<\/sup>x\n\n

\n\n\n \n 7\n <\/span>\n \n 4\n <\/span>\n<\/span>\n\n = \n\ncsc2<\/sup>x\n\n

\n\n\n \n \u2212\u221a7\n <\/span>\n \n 2\n <\/span>\n<\/span>\n\n = \n\ncsc x\n\n    
\n\n\n(The csc function is negative in quadrant 3.)\n<\/span>\n\n<\/div>\n\n\n
\n
\"Â鶹Éç<\/a>
For more help, contact The Learning Center<\/figcaption><\/figure>\n<\/div>","protected":false},"excerpt":{"rendered":"

*There are three so-called \u201cPythagorean Identities\u201d that can be used to simplify expressions containing trigonometric\u00a0functions. The three Pythagorean identities are: sin2x + cos2x = 1 1 + cot2x = csc2x tan2x + 1 = sec2x *These identities can be used to determine function values. Example: If the cot x = \u221a3 2 , then what […]<\/p>\n","protected":false},"author":12,"featured_media":0,"parent":0,"menu_order":0,"comment_status":"closed","ping_status":"closed","template":"","meta":{"_eb_attr":"","footnotes":""},"class_list":["post-6585","page","type-page","status-publish","hentry"],"yoast_head":"\nPythagorean Identities - Learning Center<\/title>\n<meta name=\"robots\" content=\"index, follow, max-snippet:-1, max-image-preview:large, max-video-preview:-1\" \/>\n<link rel=\"canonical\" href=\"https:\/\/www.eastcentral.edu\/learning-center\/pythagorean-identities\/\" \/>\n<meta property=\"og:locale\" content=\"en_US\" \/>\n<meta property=\"og:type\" content=\"article\" \/>\n<meta property=\"og:title\" content=\"Pythagorean Identities - Learning Center\" \/>\n<meta property=\"og:description\" content=\"*There are three so-called \u201cPythagorean Identities\u201d that can be used to simplify expressions containing trigonometric\u00a0functions. The three Pythagorean identities are: sin2x + cos2x = 1 1 + cot2x = csc2x tan2x + 1 = sec2x *These identities can be used to determine function values. Example: If the cot x = \u221a3 2 , then what […]\" \/>\n<meta property=\"og:url\" content=\"https:\/\/www.eastcentral.edu\/learning-center\/pythagorean-identities\/\" \/>\n<meta property=\"og:site_name\" content=\"Learning Center\" \/>\n<meta property=\"article:modified_time\" content=\"2026-07-13T18:56:33+00:00\" \/>\n<meta property=\"og:image\" content=\"https:\/\/www.eastcentral.edu\/learning-center\/wp-content\/uploads\/sites\/27\/2025\/05\/image.jpeg\" \/>\n\t<meta property=\"og:image:width\" content=\"602\" \/>\n\t<meta property=\"og:image:height\" content=\"455\" \/>\n\t<meta property=\"og:image:type\" content=\"image\/jpeg\" \/>\n<meta name=\"twitter:card\" content=\"summary_large_image\" \/>\n<meta name=\"twitter:label1\" content=\"Est. reading time\" \/>\n\t<meta name=\"twitter:data1\" content=\"1 minute\" \/>\n<script type=\"application\/ld+json\" class=\"yoast-schema-graph\">{\"@context\":\"https:\\\/\\\/schema.org\",\"@graph\":[{\"@type\":\"WebPage\",\"@id\":\"https:\\\/\\\/www.eastcentral.edu\\\/learning-center\\\/pythagorean-identities\\\/\",\"url\":\"https:\\\/\\\/www.eastcentral.edu\\\/learning-center\\\/pythagorean-identities\\\/\",\"name\":\"Pythagorean Identities - Learning Center\",\"isPartOf\":{\"@id\":\"https:\\\/\\\/www.eastcentral.edu\\\/learning-center\\\/#website\"},\"primaryImageOfPage\":{\"@id\":\"https:\\\/\\\/www.eastcentral.edu\\\/learning-center\\\/pythagorean-identities\\\/#primaryimage\"},\"image\":{\"@id\":\"https:\\\/\\\/www.eastcentral.edu\\\/learning-center\\\/pythagorean-identities\\\/#primaryimage\"},\"thumbnailUrl\":\"https:\\\/\\\/www.eastcentral.edu\\\/learning-center\\\/wp-content\\\/uploads\\\/sites\\\/27\\\/2025\\\/05\\\/image.jpeg\",\"datePublished\":\"2026-07-13T18:56:14+00:00\",\"dateModified\":\"2026-07-13T18:56:33+00:00\",\"breadcrumb\":{\"@id\":\"https:\\\/\\\/www.eastcentral.edu\\\/learning-center\\\/pythagorean-identities\\\/#breadcrumb\"},\"inLanguage\":\"en-US\",\"potentialAction\":[{\"@type\":\"ReadAction\",\"target\":[\"https:\\\/\\\/www.eastcentral.edu\\\/learning-center\\\/pythagorean-identities\\\/\"]}]},{\"@type\":\"ImageObject\",\"inLanguage\":\"en-US\",\"@id\":\"https:\\\/\\\/www.eastcentral.edu\\\/learning-center\\\/pythagorean-identities\\\/#primaryimage\",\"url\":\"https:\\\/\\\/www.eastcentral.edu\\\/learning-center\\\/wp-content\\\/uploads\\\/sites\\\/27\\\/2025\\\/05\\\/image.jpeg\",\"contentUrl\":\"https:\\\/\\\/www.eastcentral.edu\\\/learning-center\\\/wp-content\\\/uploads\\\/sites\\\/27\\\/2025\\\/05\\\/image.jpeg\",\"width\":602,\"height\":455,\"caption\":\"Â鶹Éç Learning Center Logo\"},{\"@type\":\"BreadcrumbList\",\"@id\":\"https:\\\/\\\/www.eastcentral.edu\\\/learning-center\\\/pythagorean-identities\\\/#breadcrumb\",\"itemListElement\":[{\"@type\":\"ListItem\",\"position\":1,\"name\":\"Home\",\"item\":\"https:\\\/\\\/www.eastcentral.edu\\\/learning-center\\\/\"},{\"@type\":\"ListItem\",\"position\":2,\"name\":\"Pythagorean Identities\"}]},{\"@type\":\"WebSite\",\"@id\":\"https:\\\/\\\/www.eastcentral.edu\\\/learning-center\\\/#website\",\"url\":\"https:\\\/\\\/www.eastcentral.edu\\\/learning-center\\\/\",\"name\":\"Learning Center\",\"description\":\"\",\"potentialAction\":[{\"@type\":\"SearchAction\",\"target\":{\"@type\":\"EntryPoint\",\"urlTemplate\":\"https:\\\/\\\/www.eastcentral.edu\\\/learning-center\\\/?s={search_term_string}\"},\"query-input\":{\"@type\":\"PropertyValueSpecification\",\"valueRequired\":true,\"valueName\":\"search_term_string\"}}],\"inLanguage\":\"en-US\"}]}<\/script>\n<!-- \/ Yoast SEO plugin. -->","yoast_head_json":{"title":"Pythagorean Identities - Learning Center","robots":{"index":"index","follow":"follow","max-snippet":"max-snippet:-1","max-image-preview":"max-image-preview:large","max-video-preview":"max-video-preview:-1"},"canonical":"https:\/\/www.eastcentral.edu\/learning-center\/pythagorean-identities\/","og_locale":"en_US","og_type":"article","og_title":"Pythagorean Identities - Learning Center","og_description":"*There are three so-called \u201cPythagorean Identities\u201d that can be used to simplify expressions containing trigonometric\u00a0functions. 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