{"id":1963,"date":"2023-12-08T14:37:41","date_gmt":"2023-12-08T14:37:41","guid":{"rendered":"https:\/\/ced.fst-usmba.ac.ma\/p\/mjaga\/?page_id=1963"},"modified":"2023-12-11T13:53:04","modified_gmt":"2023-12-11T13:53:04","slug":"how-to-motivate-and-remember-the-law-of-cosines-the-law-of-sinesand-the-law-of-tangents-and-the-connections-between-these-laws","status":"publish","type":"page","link":"https:\/\/ced.fst-usmba.ac.ma\/p\/mjaga\/how-to-motivate-and-remember-the-law-of-cosines-the-law-of-sinesand-the-law-of-tangents-and-the-connections-between-these-laws\/","title":{"rendered":"How to Motivate and Remember the Law of Cosines, the Law of Sinesand the Law of Tangents and the Connections Between these Laws"},"content":{"rendered":"\n
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Moroccan Journal of Algebra and Geometry with Applications<\/strong><\/p>\n\n\n\n

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How to Motivate and Remember the Law of Cosines, the Law of Sines
and the Law of Tangents and the Connections Between these Laws<\/strong><\/p>\n<\/div>\n<\/div>\n\n\n\n

David E. Dobbs <\/strong><\/i>
Department of Mathematics, University of Tennessee, Knoxville, Tennessee 37996-1320, USA.<\/p>\n\n\n\n

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Pages 174-208 | Received 10 February 2023, Accepted 20 April 2023, Published 11 December 2023 <\/span><\/p>\n\n\n\n

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Abstract<\/span><\/strong><\/p>\n\n\n\n

Instructors could use various portions of this note as enrichment material in the trigonometric part of a Precalculus course. This note has both pedagogic aspects and theoretical aspects. We give practical advice for instructors seeking ways to motivate the statements of the Law of Cosines and the Law of Sines and ways to help their students to remember those statements in order to work appropriate problems. We also discuss the somewhat less familiar Law of Tangents, including a couple of applications of this law in which the author was involved. We provide some theoretical connections among these three trigonometric laws, giving precise senses in which these three laws are equivalent, with each of these laws leading to an equational characterization of the concept of a triangle in Euclidean geometry.<\/p>\n\n\n\n

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Keywords<\/strong>:<\/span>  Law of Sines, Law of Cosines, Law of Tangents, SAS, ASA, SSS, inequality, similar triangles, Mollweide equations, Euclidean geometry. <\/p>\n\n\n\n

MSC numbers<\/strong>:<\/span> Primary 51-02; Secondary 33B10, 51N20.<\/p>\n\n\n\n

Downloads:<\/strong> Full-text PDF<\/a> <\/p>\n<\/div>\n\n\n\n

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MJAGA_Vol2_Issue2-174-208<\/a>\n

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Moroccan Journal of Algebra and Geometry with Applications Latest articles How to Motivate and Remember the Law of Cosines, the Law of Sines and the Law of Tangents and the Connections Between these Laws David E. Dobbs  Department of Mathematics, University of Tennessee, Knoxville, Tennessee 37996-1320, USA. Pages 174-208 | Received 10 February 2023, Accepted Read More<\/a><\/p>\n","protected":false},"author":1,"featured_media":0,"parent":0,"menu_order":0,"comment_status":"closed","ping_status":"closed","template":"template-page-builder.php","meta":{"footnotes":""},"class_list":["post-1963","page","type-page","status-publish","hentry","entry"],"_links":{"self":[{"href":"https:\/\/ced.fst-usmba.ac.ma\/p\/mjaga\/wp-json\/wp\/v2\/pages\/1963","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/ced.fst-usmba.ac.ma\/p\/mjaga\/wp-json\/wp\/v2\/pages"}],"about":[{"href":"https:\/\/ced.fst-usmba.ac.ma\/p\/mjaga\/wp-json\/wp\/v2\/types\/page"}],"author":[{"embeddable":true,"href":"https:\/\/ced.fst-usmba.ac.ma\/p\/mjaga\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/ced.fst-usmba.ac.ma\/p\/mjaga\/wp-json\/wp\/v2\/comments?post=1963"}],"version-history":[{"count":8,"href":"https:\/\/ced.fst-usmba.ac.ma\/p\/mjaga\/wp-json\/wp\/v2\/pages\/1963\/revisions"}],"predecessor-version":[{"id":2221,"href":"https:\/\/ced.fst-usmba.ac.ma\/p\/mjaga\/wp-json\/wp\/v2\/pages\/1963\/revisions\/2221"}],"wp:attachment":[{"href":"https:\/\/ced.fst-usmba.ac.ma\/p\/mjaga\/wp-json\/wp\/v2\/media?parent=1963"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}