{"id":14124,"date":"2018-03-12T01:04:55","date_gmt":"2018-03-12T01:04:55","guid":{"rendered":"https:\/\/www.acasinhadamatematica.pt\/?p=14124"},"modified":"2022-01-11T10:39:36","modified_gmt":"2022-01-11T10:39:36","slug":"verifica-se-existe-pelo-menos-um-angulo-agudo","status":"publish","type":"post","link":"https:\/\/www.acasinhadamatematica.pt\/?p=14124","title":{"rendered":"Verifica se existe pelo menos um \u00e2ngulo agudo"},"content":{"rendered":"<p><ul id='GTTabs_ul_14124' class='GTTabs' style='display:none'>\n<li id='GTTabs_li_0_14124' class='GTTabs_curr'><a  id=\"14124_0\" onMouseOver=\"GTTabsShowLinks('Enunciado'); return true;\"  onMouseOut=\"GTTabsShowLinks();\"  class='GTTabsLinks'>Enunciado<\/a><\/li>\n<li id='GTTabs_li_1_14124' ><a  id=\"14124_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_14124'>\n<span class='GTTabs_titles'><b>Enunciado<\/b><\/span><\/p>\n<p>Verifica, justificando, se existe pelo menos um \u00e2ngulo agudo de amplitude\u00a0\u03b1 para o qual:<\/p>\n<ol>\n<li>\\({\\mathop{\\rm sen}\\nolimits} \\alpha = 1,4\\);<\/li>\n<li>\\({\\mathop{\\rm sen}\\nolimits} \\alpha = 0,6\\) e\u00a0\\({\\mathop{\\rm tg}\\nolimits} \\alpha = 0,75\\);<\/li>\n<li>\\(\\cos \\alpha = &#8211; 1\\)<\/li>\n<\/ol>\n<p><div class='GTTabsNavigation' style='display:none'><span class='GTTabs_nav_next'><a href='#GTTabs_ul_14124' onClick='GTTabs_show(1,14124)'>Resolu\u00e7\u00e3o &gt;&gt;<\/a><\/span><\/div><\/div>\n\n<div class='GTTabs_divs' id='GTTabs_1_14124'>\n<span class='GTTabs_titles'><b>Resolu\u00e7\u00e3o<\/b><\/span><!--more--><\/p>\n<p>Verifica, justificando, se existe pelo menos um \u00e2ngulo agudo de amplitude\u00a0\u03b1 para o qual:<\/p>\n<ol>\n<li>\\({\\mathop{\\rm sen}\\nolimits} \\alpha = 1,4\\);<br \/>\n<span style=\"color: #0000ff;\">N\u00e3o existe, pois\u00a0\\(0 &lt; {\\mathop{\\rm sen}\\nolimits} \\alpha &lt; 1\\) para\u00a0\\(\\alpha \\in \\left] {0^\\circ ,\\;90^\\circ } \\right[\\).<br \/>\n\u00ad<br \/>\n<\/span><\/li>\n<li>\\({\\mathop{\\rm sen}\\nolimits} \\alpha = 0,6\\) e\u00a0\\({\\mathop{\\rm tg}\\nolimits} \\alpha = 0,75\\);<br \/>\n<span style=\"color: #0000ff;\">Se\u00a0\\(\\alpha \\in \\left] {0^\\circ ,\\;90^\\circ } \\right[\\), ent\u00e3o \\(\\cos \\alpha = \\sqrt {1 &#8211; {{{\\mathop{\\rm sen}\\nolimits} }^2}\\alpha } = \\sqrt {1 &#8211; {{0,6}^2}} = \\sqrt {0,64} = 0,8\\), pela F\u00f3rmula Fundamental da Trigonometria. Assim, vem:\u00a0\\({\\mathop{\\rm tg}\\nolimits} \\alpha = \\frac{{{\\mathop{\\rm sen}\\nolimits} \\alpha }}{{\\cos \\alpha }} = \\frac{{0,6}}{{0,8}} = \\frac{6}{8} = \\frac{3}{4} = 0,75\\).<\/span><br \/>\n<span style=\"color: #0000ff;\">Portanto, existe um \u00e2ngulo agudo que satisfaz a condi\u00e7\u00e3o dada.<br \/>\n\u00ad<br \/>\n<\/span><\/li>\n<li>\\(\\cos \\alpha = &#8211; 1\\)<br \/>\n<span style=\"color: #0000ff;\">N\u00e3o existe, pois\u00a0\\(0 &lt; \\cos \\alpha &lt; 1\\) para\u00a0\\(\\alpha \\in \\left] {0^\\circ ,\\;90^\\circ } \\right[\\).<\/span><\/li>\n<\/ol>\n<div class='GTTabsNavigation' style='display:none'><span class='GTTabs_nav_prev'><a href='#GTTabs_ul_14124' onClick='GTTabs_show(0,14124)'>&lt;&lt; Enunciado<\/a><\/span><\/div><\/div>\n\n","protected":false},"excerpt":{"rendered":"<p>Enunciado Resolu\u00e7\u00e3o Enunciado Verifica, justificando, se existe pelo menos um \u00e2ngulo agudo de amplitude\u00a0\u03b1 para o qual: \\({\\mathop{\\rm sen}\\nolimits} \\alpha = 1,4\\); \\({\\mathop{\\rm sen}\\nolimits} \\alpha = 0,6\\) e\u00a0\\({\\mathop{\\rm tg}\\nolimits} \\alpha = 0,75\\); \\(\\cos \\alpha&#46;&#46;&#46;<\/p>\n","protected":false},"author":1,"featured_media":14110,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"_jetpack_memberships_contains_paid_content":false,"footnotes":""},"categories":[213,97,489],"tags":[491,493,490,492],"series":[],"class_list":["post-14124","post","type-post","status-publish","format-standard","has-post-thumbnail","hentry","category-9--ano","category-aplicando","category-trigonometria-9--ano","tag-cosseno","tag-razao-trigonometrica","tag-seno","tag-tangente"],"views":1805,"jetpack_featured_media_url":"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2018\/03\/Mat52.png","jetpack_sharing_enabled":true,"jetpack_likes_enabled":true,"_links":{"self":[{"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=\/wp\/v2\/posts\/14124","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=14124"}],"version-history":[{"count":0,"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=\/wp\/v2\/posts\/14124\/revisions"}],"wp:featuredmedia":[{"embeddable":true,"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=\/wp\/v2\/media\/14110"}],"wp:attachment":[{"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=%2Fwp%2Fv2%2Fmedia&parent=14124"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=%2Fwp%2Fv2%2Fcategories&post=14124"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=%2Fwp%2Fv2%2Ftags&post=14124"},{"taxonomy":"series","embeddable":true,"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=%2Fwp%2Fv2%2Fseries&post=14124"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}