{"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
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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":""},"yst_prominent_words":[],"class_list":["post-6585","page","type-page","status-publish","hentry"],"_links":{"self":[{"href":"https:\/\/www.eastcentral.edu\/learning-center\/wp-json\/wp\/v2\/pages\/6585","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/www.eastcentral.edu\/learning-center\/wp-json\/wp\/v2\/pages"}],"about":[{"href":"https:\/\/www.eastcentral.edu\/learning-center\/wp-json\/wp\/v2\/types\/page"}],"author":[{"embeddable":true,"href":"https:\/\/www.eastcentral.edu\/learning-center\/wp-json\/wp\/v2\/users\/12"}],"replies":[{"embeddable":true,"href":"https:\/\/www.eastcentral.edu\/learning-center\/wp-json\/wp\/v2\/comments?post=6585"}],"version-history":[{"count":1,"href":"https:\/\/www.eastcentral.edu\/learning-center\/wp-json\/wp\/v2\/pages\/6585\/revisions"}],"predecessor-version":[{"id":6586,"href":"https:\/\/www.eastcentral.edu\/learning-center\/wp-json\/wp\/v2\/pages\/6585\/revisions\/6586"}],"wp:attachment":[{"href":"https:\/\/www.eastcentral.edu\/learning-center\/wp-json\/wp\/v2\/media?parent=6585"}],"wp:term":[{"taxonomy":"yst_prominent_words","embeddable":true,"href":"https:\/\/www.eastcentral.edu\/learning-center\/wp-json\/wp\/v2\/yst_prominent_words?post=6585"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}