{"id":14210,"date":"2018-03-30T23:41:50","date_gmt":"2018-03-30T22:41:50","guid":{"rendered":"https:\/\/www.acasinhadamatematica.pt\/?p=14210"},"modified":"2022-01-11T11:41:34","modified_gmt":"2022-01-11T11:41:34","slug":"sabendo-que-mathoprm-sennolimits-alpha-frac13","status":"publish","type":"post","link":"https:\/\/www.acasinhadamatematica.pt\/?p=14210","title":{"rendered":"Sabendo que \\({\\mathop{\\rm sen}\\nolimits} \\alpha  = \\frac{1}{3}\\)"},"content":{"rendered":"<p><ul id='GTTabs_ul_14210' class='GTTabs' style='display:none'>\n<li id='GTTabs_li_0_14210' class='GTTabs_curr'><a  id=\"14210_0\" onMouseOver=\"GTTabsShowLinks('Enunciado'); return true;\"  onMouseOut=\"GTTabsShowLinks();\"  class='GTTabsLinks'>Enunciado<\/a><\/li>\n<li id='GTTabs_li_1_14210' ><a  id=\"14210_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_14210'>\n<span class='GTTabs_titles'><b>Enunciado<\/b><\/span><\/p>\n<p>Sabendo que \\({\\mathop{\\rm sen}\\nolimits} \\alpha = \\frac{1}{3}\\), qual \u00e9 o valor de\u00a0\\({\\cos \\alpha }\\) e de \\({\\mathop{\\rm tg}\\nolimits} \\alpha \\)?<\/p>\n<p><div class='GTTabsNavigation' style='display:none'><span class='GTTabs_nav_next'><a href='#GTTabs_ul_14210' onClick='GTTabs_show(1,14210)'>Resolu\u00e7\u00e3o &gt;&gt;<\/a><\/span><\/div><\/div>\n\n<div class='GTTabs_divs' id='GTTabs_1_14210'>\n<span class='GTTabs_titles'><b>Resolu\u00e7\u00e3o<\/b><\/span><!--more--><\/p>\n<p>Aplicando a F\u00f3rmula Fundamental da Trigonometria, vem:<\/p>\n<p>\\[\\begin{array}{*{20}{l}}{{{\\left( {\\frac{1}{3}} \\right)}^2} + {{\\cos }^2}\\alpha = 1}&amp; \\Leftrightarrow &amp;{{{\\cos }^2}\\alpha = 1 &#8211; \\frac{1}{9}}\\\\{}&amp; \\Leftrightarrow &amp;{{{\\cos }^2}\\alpha = \\frac{8}{9}}\\end{array}\\]<\/p>\n<p>Como \\(\\alpha \\in \\left] {0^\\circ ,\\;90^\\circ } \\right[\\), ent\u00e3o\u00a0\\(\\cos \\alpha &gt; 0\\).<\/p>\n<p>Logo,\u00a0\\(\\cos \\alpha = + \\sqrt {\\frac{8}{9}} = \\frac{{\\sqrt 8 }}{3} = \\frac{{2\\sqrt 2 }}{3}\\).<\/p>\n<p>E, finalmente,\u00a0\\({\\mathop{\\rm tg}\\nolimits} \\alpha = \\frac{{{\\mathop{\\rm sen}\\nolimits} \\alpha }}{{\\cos \\alpha }} = \\frac{{\\frac{1}{3}}}{{\\frac{{2\\sqrt 2 }}{3}}} = \\frac{1}{3} \\times \\frac{3}{{2\\sqrt 2 }} \\times \\frac{{\\sqrt 2 }}{{\\sqrt 2 }} = \\frac{{\\sqrt 2 }}{4}\\).<\/p><\/p>\n<div class='GTTabsNavigation' style='display:none'><span class='GTTabs_nav_prev'><a href='#GTTabs_ul_14210' onClick='GTTabs_show(0,14210)'>&lt;&lt; Enunciado<\/a><\/span><\/div><\/div>\n\n","protected":false},"excerpt":{"rendered":"<p>Enunciado Resolu\u00e7\u00e3o Enunciado Sabendo que \\({\\mathop{\\rm sen}\\nolimits} \\alpha = \\frac{1}{3}\\), qual \u00e9 o valor de\u00a0\\({\\cos \\alpha }\\) e de \\({\\mathop{\\rm tg}\\nolimits} \\alpha \\)? Resolu\u00e7\u00e3o &gt;&gt; Resolu\u00e7\u00e3o &lt;&lt; Enunciado<\/p>\n","protected":false},"author":1,"featured_media":14114,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"_jetpack_memberships_contains_paid_content":false,"footnotes":""},"categories":[213,97,489],"tags":[426,491,490,492],"series":[],"class_list":["post-14210","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-seno","tag-tangente"],"views":3441,"jetpack_featured_media_url":"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2018\/03\/Mat56.png","jetpack_sharing_enabled":true,"jetpack_likes_enabled":true,"_links":{"self":[{"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=\/wp\/v2\/posts\/14210","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=14210"}],"version-history":[{"count":0,"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=\/wp\/v2\/posts\/14210\/revisions"}],"wp:attachment":[{"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=%2Fwp%2Fv2%2Fmedia&parent=14210"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=%2Fwp%2Fv2%2Fcategories&post=14210"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=%2Fwp%2Fv2%2Ftags&post=14210"},{"taxonomy":"series","embeddable":true,"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=%2Fwp%2Fv2%2Fseries&post=14210"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}