{"id":14050,"date":"2018-03-11T12:57:07","date_gmt":"2018-03-11T12:57:07","guid":{"rendered":"https:\/\/www.acasinhadamatematica.pt\/?p=14050"},"modified":"2022-01-11T10:33:49","modified_gmt":"2022-01-11T10:33:49","slug":"sem-calcular-o-valor-de-%ce%b1","status":"publish","type":"post","link":"https:\/\/www.acasinhadamatematica.pt\/?p=14050","title":{"rendered":"Sem calcular o valor de \u03b1"},"content":{"rendered":"<p><ul id='GTTabs_ul_14050' class='GTTabs' style='display:none'>\n<li id='GTTabs_li_0_14050' class='GTTabs_curr'><a  id=\"14050_0\" onMouseOver=\"GTTabsShowLinks('Enunciado'); return true;\"  onMouseOut=\"GTTabsShowLinks();\"  class='GTTabsLinks'>Enunciado<\/a><\/li>\n<li id='GTTabs_li_1_14050' ><a  id=\"14050_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_14050'>\n<span class='GTTabs_titles'><b>Enunciado<\/b><\/span><\/p>\n<p>Sem calcular o valor de\u00a0\u03b1, determina \\(\\cos \\alpha \\) e \\({{\\mathop{\\rm tg}\\nolimits} \\alpha }\\), sabendo que \\({\\mathop{\\rm sen}\\nolimits} \\alpha = 0,36\\) e\u00a0\u03b1 \u00e9 a amplitude de um \u00e2ngulo agudo. Apresenta os valores arredondados \u00e0s cent\u00e9simas.<\/p>\n<p><div class='GTTabsNavigation' style='display:none'><span class='GTTabs_nav_next'><a href='#GTTabs_ul_14050' onClick='GTTabs_show(1,14050)'>Resolu\u00e7\u00e3o &gt;&gt;<\/a><\/span><\/div><\/div>\n\n<div class='GTTabs_divs' id='GTTabs_1_14050'>\n<span class='GTTabs_titles'><b>Resolu\u00e7\u00e3o<\/b><\/span><!--more--><\/p>\n<blockquote>\n<p>F\u00f3rmula Fundamental da Trigonometria\u00a0\\[{{\\mathop{\\rm sen}\\nolimits} ^2}\\alpha + {\\cos ^2}\\alpha = 1\\] qualquer que seja o \u00e2ngulo de amplitude\u00a0\\(\\alpha \\).<\/p>\n<\/blockquote>\n<p>Utilizando a F\u00f3rmula Fundamental da Trigonometria, vem:<\/p>\n<p>\\[\\begin{array}{*{20}{l}}{{{0,36}^2} + {{\\cos }^2}\\alpha = 1}&amp; \\Leftrightarrow &amp;{{{\\cos }^2}\\alpha = 1 &#8211; {{0,36}^2}}\\\\{}&amp; \\Leftrightarrow &amp;{{{\\cos }^2}\\alpha = 0,8704}\\end{array}\\]<\/p>\n<p>Como \\(\\cos \\alpha &gt; 0\\), ent\u00e3o\u00a0\\(\\cos \\alpha = \\sqrt {0,8704} \\approx 0,93\\).<\/p>\n<p>E\u00a0\\({\\mathop{\\rm tg}\\nolimits} \\alpha = \\frac{{{\\mathop{\\rm sen}\\nolimits} \\alpha }}{{\\cos \\alpha }} = \\frac{{0,36}}{{\\sqrt {0,8704} }} \\approx 0,39\\).<\/p><\/p>\n<div class='GTTabsNavigation' style='display:none'><span class='GTTabs_nav_prev'><a href='#GTTabs_ul_14050' onClick='GTTabs_show(0,14050)'>&lt;&lt; Enunciado<\/a><\/span><\/div><\/div>\n\n","protected":false},"excerpt":{"rendered":"<p>Enunciado Resolu\u00e7\u00e3o Enunciado Sem calcular o valor de\u00a0\u03b1, determina \\(\\cos \\alpha \\) e \\({{\\mathop{\\rm tg}\\nolimits} \\alpha }\\), sabendo que \\({\\mathop{\\rm sen}\\nolimits} \\alpha = 0,36\\) e\u00a0\u03b1 \u00e9 a amplitude de um \u00e2ngulo agudo. Apresenta os&#46;&#46;&#46;<\/p>\n","protected":false},"author":1,"featured_media":14081,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"_jetpack_memberships_contains_paid_content":false,"footnotes":""},"categories":[213,97,489],"tags":[426,491,493,490,492],"series":[],"class_list":["post-14050","post","type-post","status-publish","format-standard","has-post-thumbnail","hentry","category-9--ano","category-aplicando","category-trigonometria-9--ano","tag-9-o-ano","tag-cosseno","tag-razao-trigonometrica","tag-seno","tag-tangente"],"views":1747,"jetpack_featured_media_url":"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2018\/03\/Mat26.png","jetpack_sharing_enabled":true,"jetpack_likes_enabled":true,"_links":{"self":[{"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=\/wp\/v2\/posts\/14050","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=14050"}],"version-history":[{"count":0,"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=\/wp\/v2\/posts\/14050\/revisions"}],"wp:featuredmedia":[{"embeddable":true,"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=\/wp\/v2\/media\/14081"}],"wp:attachment":[{"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=%2Fwp%2Fv2%2Fmedia&parent=14050"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=%2Fwp%2Fv2%2Fcategories&post=14050"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=%2Fwp%2Fv2%2Ftags&post=14050"},{"taxonomy":"series","embeddable":true,"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=%2Fwp%2Fv2%2Fseries&post=14050"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}