{"id":1899,"date":"2024-07-01T13:11:27","date_gmt":"2024-07-01T10:11:27","guid":{"rendered":"https:\/\/cedra.academy\/?p=1899"},"modified":"2024-07-02T14:01:41","modified_gmt":"2024-07-02T11:01:41","slug":"teorema-sinusurilor-si-teorema-cosinusului","status":"publish","type":"post","link":"https:\/\/cedra.academy\/?p=1899","title":{"rendered":"Teorema sinusurilor \u015fi teorema cosinusului"},"content":{"rendered":"\n<p>Calculul lungimii unui segment \u0219i a m\u0103surii unui unghi \u00een geometrie se realizeaz\u0103 adesea folosind teorema sinusurilor \u0219i teorema cosinusului, dou\u0103 instrumente fundamentale \u00een trigonometrie. Aceste teoreme sunt esen\u021biale pentru rezolvarea triunghiurilor, fie ele dreptunghice sau oblice.<\/p>\n\n\n\n<h3 class=\"wp-block-heading\">Teorema sinusurilor<\/h3>\n\n\n\n<p>Teorema sinusurilor afirm\u0103 c\u0103, \u00eentr-un triunghi, raportul dintre lungimea unei laturi \u0219i sinusul unghiului opus este constant pentru toate cele trei laturi \u0219i unghiuri ale triunghiului. Matematic, aceasta este exprimat\u0103 astfel:<br>[\\frac{a}{\\sin A} = \\frac{b}{\\sin B} = \\frac{c}{\\sin C} = 2R] unde (a), (b) \u0219i (c) sunt lungimile laturilor triunghiului, (A), (B) \u0219i (C) sunt m\u0103surile unghiurilor opuse acestor laturi, iar (R) este raza cercului circumscris triunghiului. Aceast\u0103 teorem\u0103 este util\u0103 pentru determinarea lungimilor laturilor necunoscute sau a m\u0103surilor unghiurilor \u00eentr-un triunghi, atunci c\u00e2nd sunt cunoscute suficiente date ini\u021biale.<\/p>\n\n\n\n<h3 class=\"wp-block-heading\">Teorema cosinusului<\/h3>\n\n\n\n<p>Teorema cosinusului, cunoscut\u0103 \u0219i ca teorema lui Pitagora generalizat\u0103, este utilizat\u0103 pentru a calcula lungimea unei laturi a unui triunghi atunci c\u00e2nd sunt cunoscute lungimile celorlalte dou\u0103 laturi \u0219i m\u0103sura unghiului dintre ele. Aceasta se exprim\u0103 prin:<br>[ c^2 = a^2 + b^2 &#8211; 2ab \\cos C ], unde (a) \u0219i (b) sunt lungimile celor dou\u0103 laturi cunoscute, (C) este unghiul dintre aceste laturi, iar (c) este lungimea laturii opuse unghiului (C). Teorema cosinusului este deosebit de util\u0103 \u00een triunghiurile oblice, unde unghiurile nu sunt neap\u0103rat de 90 de grade.<\/p>\n\n\n\n<p>Prin utilizarea teoremei sinusurilor \u0219i a teoremei cosinusului, se pot rezolva probleme complexe de geometrie plan\u0103. Aceste teoreme ofer\u0103 metode precise pentru determinarea lungimilor \u0219i unghiurilor necunoscute, facilit\u00e2nd astfel \u00een\u021belegerea \u0219i aplicarea conceptelor geometrice \u00een diverse domenii, de la arhitectur\u0103 \u0219i inginerie p\u00e2n\u0103 la astronomie \u0219i fizic\u0103.<\/p>\n\n\n\n<div class=\"wp-block-file\"><a id=\"wp-block-file--media-f3ca82cc-20ca-4ba9-bb8f-376c6585fa8c\" href=\"https:\/\/cedra.academy\/wp-content\/uploads\/2024\/07\/5-Teorema-sinusurilor-si-teorema-cosinusului.pptx\">PPRX  Teorema sinusurilor \u015fi teorema cosinusului    <\/a><a href=\"https:\/\/cedra.academy\/wp-content\/uploads\/2024\/07\/5-Teorema-sinusurilor-si-teorema-cosinusului.pptx\" class=\"wp-block-file__button wp-element-button\" download aria-describedby=\"wp-block-file--media-f3ca82cc-20ca-4ba9-bb8f-376c6585fa8c\">Descarc\u0103<\/a><\/div>\n\n\n\n<figure class=\"wp-block-image size-large\"><img decoding=\"async\" loading=\"lazy\" width=\"1024\" height=\"891\" src=\"https:\/\/cedra.academy\/wp-content\/uploads\/2024\/07\/5a-Teorema-sinusurilor-si-teorema-cosinusului-1024x891.jpg\" alt=\"\" class=\"wp-image-1902\" srcset=\"https:\/\/cedra.academy\/wp-content\/uploads\/2024\/07\/5a-Teorema-sinusurilor-si-teorema-cosinusului-1024x891.jpg 1024w, https:\/\/cedra.academy\/wp-content\/uploads\/2024\/07\/5a-Teorema-sinusurilor-si-teorema-cosinusului-300x261.jpg 300w, https:\/\/cedra.academy\/wp-content\/uploads\/2024\/07\/5a-Teorema-sinusurilor-si-teorema-cosinusului-768x668.jpg 768w, https:\/\/cedra.academy\/wp-content\/uploads\/2024\/07\/5a-Teorema-sinusurilor-si-teorema-cosinusului-1536x1337.jpg 1536w, https:\/\/cedra.academy\/wp-content\/uploads\/2024\/07\/5a-Teorema-sinusurilor-si-teorema-cosinusului.jpg 1848w\" sizes=\"(max-width: 1024px) 100vw, 1024px\" \/><\/figure>\n","protected":false},"excerpt":{"rendered":"<p>Calculul lungimii unui segment \u0219i a m\u0103surii unui unghi \u00een geometrie se realizeaz\u0103 adesea folosind teorema sinusurilor \u0219i teorema cosinusului, dou\u0103 instrumente fundamentale \u00een trigonometrie. Aceste teoreme sunt esen\u021biale pentru [&hellip;]<\/p>\n","protected":false},"author":1,"featured_media":1900,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[13,10],"tags":[],"_links":{"self":[{"href":"https:\/\/cedra.academy\/index.php?rest_route=\/wp\/v2\/posts\/1899"}],"collection":[{"href":"https:\/\/cedra.academy\/index.php?rest_route=\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/cedra.academy\/index.php?rest_route=\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/cedra.academy\/index.php?rest_route=\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/cedra.academy\/index.php?rest_route=%2Fwp%2Fv2%2Fcomments&post=1899"}],"version-history":[{"count":3,"href":"https:\/\/cedra.academy\/index.php?rest_route=\/wp\/v2\/posts\/1899\/revisions"}],"predecessor-version":[{"id":1905,"href":"https:\/\/cedra.academy\/index.php?rest_route=\/wp\/v2\/posts\/1899\/revisions\/1905"}],"wp:featuredmedia":[{"embeddable":true,"href":"https:\/\/cedra.academy\/index.php?rest_route=\/wp\/v2\/media\/1900"}],"wp:attachment":[{"href":"https:\/\/cedra.academy\/index.php?rest_route=%2Fwp%2Fv2%2Fmedia&parent=1899"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/cedra.academy\/index.php?rest_route=%2Fwp%2Fv2%2Fcategories&post=1899"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/cedra.academy\/index.php?rest_route=%2Fwp%2Fv2%2Ftags&post=1899"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}