{"id":8398,"date":"2012-04-16T19:21:40","date_gmt":"2012-04-16T18:21:40","guid":{"rendered":"https:\/\/www.acasinhadamatematica.pt\/?p=8398"},"modified":"2021-12-30T01:14:20","modified_gmt":"2021-12-30T01:14:20","slug":"a-partir-da-formula","status":"publish","type":"post","link":"https:\/\/www.acasinhadamatematica.pt\/?p=8398","title":{"rendered":"A partir da f\u00f3rmula"},"content":{"rendered":"<p><ul id='GTTabs_ul_8398' class='GTTabs' style='display:none'>\n<li id='GTTabs_li_0_8398' class='GTTabs_curr'><a  id=\"8398_0\" onMouseOver=\"GTTabsShowLinks('Enunciado'); return true;\"  onMouseOut=\"GTTabsShowLinks();\"  class='GTTabsLinks'>Enunciado<\/a><\/li>\n<li id='GTTabs_li_1_8398' ><a  id=\"8398_1\" onMouseOver=\"GTTabsShowLinks('Resolu\u00e7\u00e3o'); return true;\"  onMouseOut=\"GTTabsShowLinks();\"  class='GTTabsLinks'>Resolu\u00e7\u00e3o<\/a><\/li>\n<\/ul>\n\n<div class='GTTabs_divs GTTabs_curr_div' id='GTTabs_0_8398'>\n<span class='GTTabs_titles'><b>Enunciado<\/b><\/span><\/p>\n<p>A partir da f\u00f3rmula $$\\operatorname{sen} \\left( {\\alpha\u00a0 + \\beta } \\right) = \\operatorname{sen} \\alpha \\cos \\beta\u00a0 + \\cos \\alpha \\operatorname{sen} \\beta $$ encontre uma f\u00f3rmula para:<\/p>\n<ol>\n<li>$\\operatorname{sen} \\left( {\\alpha\u00a0 &#8211; \\beta } \\right)$<\/li>\n<li>$\\operatorname{sen} \\left( {2\\alpha } \\right)$<\/li>\n<\/ol>\n<p><div class='GTTabsNavigation' style='display:none'><span class='GTTabs_nav_next'><a href='#GTTabs_ul_8398' onClick='GTTabs_show(1,8398)'>Resolu\u00e7\u00e3o &gt;&gt;<\/a><\/span><\/div><\/div>\n\n<div class='GTTabs_divs' id='GTTabs_1_8398'>\n<span class='GTTabs_titles'><b>Resolu\u00e7\u00e3o<\/b><\/span><!--more--><\/p>\n<blockquote>\n<p>$$\\operatorname{sen} \\left( {\\alpha\u00a0 + \\beta } \\right) = \\operatorname{sen} \\alpha \\cos \\beta\u00a0 + \\cos \\alpha \\operatorname{sen} \\beta $$<\/p>\n<\/blockquote>\n<ol>\n<li>\u00a0Ora, $$\\begin{array}{*{20}{l}}<br \/>\n{\\operatorname{sen} \\left( {\\alpha\u00a0 &#8211; \\beta } \\right)}&amp; = &amp;{\\operatorname{sen} \\left( {\\alpha\u00a0 + ( &#8211; \\beta )} \\right)} \\\\<br \/>\n{}&amp; = &amp;{\\operatorname{sen} \\alpha \\cos \\left( { &#8211; \\beta } \\right) + \\cos \\alpha \\operatorname{sen} \\left( { &#8211; \\beta } \\right)} \\\\<br \/>\n{}&amp; = &amp;{\\operatorname{sen} \\alpha \\cos \\beta\u00a0 &#8211; \\cos \\alpha \\operatorname{sen} \\beta }<br \/>\n\\end{array}$$<br \/>\nLogo, $\\operatorname{sen} \\left( {\\alpha\u00a0 &#8211; \\beta } \\right) = \\operatorname{sen} \\alpha \\cos \\beta\u00a0 &#8211; \\cos \\alpha \\operatorname{sen} \\beta $.<br \/>\n\u00ad<\/li>\n<li>Ora, $$\\begin{array}{*{20}{l}}<br \/>\n{\\operatorname{sen} \\left( {2\\alpha } \\right)}&amp; = &amp;{\\operatorname{sen} \\left( {\\alpha\u00a0 + \\alpha } \\right)} \\\\<br \/>\n{}&amp; = &amp;{\\operatorname{sen} \\alpha \\cos \\alpha\u00a0 + \\cos \\alpha \\operatorname{sen} \\alpha } \\\\<br \/>\n{}&amp; = &amp;{2\\operatorname{sen} \\alpha \\cos \\alpha }<br \/>\n\\end{array}$$<br \/>\nLogo, $\\operatorname{sen} \\left( {2\\alpha } \\right) = 2\\operatorname{sen} \\alpha \\cos \\alpha $.<br \/>\n\u00ad<\/li>\n<\/ol>\n<blockquote>\n<p>$$\\operatorname{sen} \\left( {\\alpha\u00a0 &#8211; \\beta } \\right) = \\operatorname{sen} \\alpha \\cos \\beta\u00a0 &#8211; \\cos \\alpha \\operatorname{sen} \\beta $$<\/p>\n<\/blockquote>\n<blockquote>\n<p>$$\\operatorname{sen} \\left( {2\\alpha } \\right) = 2\\operatorname{sen} \\alpha \\cos \\alpha $$<\/p>\n<\/blockquote>\n<div class='GTTabsNavigation' style='display:none'><span class='GTTabs_nav_prev'><a href='#GTTabs_ul_8398' onClick='GTTabs_show(0,8398)'>&lt;&lt; Enunciado<\/a><\/span><\/div><\/div>\n\n","protected":false},"excerpt":{"rendered":"<p>Enunciado Resolu\u00e7\u00e3o Enunciado A partir da f\u00f3rmula $$\\operatorname{sen} \\left( {\\alpha\u00a0 + \\beta } \\right) = \\operatorname{sen} \\alpha \\cos \\beta\u00a0 + \\cos \\alpha \\operatorname{sen} \\beta $$ encontre uma f\u00f3rmula para: $\\operatorname{sen} \\left( {\\alpha\u00a0 &#8211; \\beta&#46;&#46;&#46;<\/p>\n","protected":false},"author":1,"featured_media":19179,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"_jetpack_memberships_contains_paid_content":false,"footnotes":""},"categories":[226,97,295],"tags":[427,301],"series":[],"class_list":["post-8398","post","type-post","status-publish","format-standard","has-post-thumbnail","hentry","category-12--ano","category-aplicando","category-funcoes-seno-co-seno-e-tangente","tag-12-o-ano","tag-formulas-trigonometricas"],"views":1878,"jetpack_featured_media_url":"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2021\/12\/Mat70.png","jetpack_sharing_enabled":true,"jetpack_likes_enabled":true,"_links":{"self":[{"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=\/wp\/v2\/posts\/8398","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=%2Fwp%2Fv2%2Fcomments&post=8398"}],"version-history":[{"count":0,"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=\/wp\/v2\/posts\/8398\/revisions"}],"wp:featuredmedia":[{"embeddable":true,"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=\/wp\/v2\/media\/19179"}],"wp:attachment":[{"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=%2Fwp%2Fv2%2Fmedia&parent=8398"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=%2Fwp%2Fv2%2Fcategories&post=8398"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=%2Fwp%2Fv2%2Ftags&post=8398"},{"taxonomy":"series","embeddable":true,"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=%2Fwp%2Fv2%2Fseries&post=8398"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}