{"id":8666,"date":"2012-04-23T00:51:28","date_gmt":"2012-04-22T23:51:28","guid":{"rendered":"https:\/\/www.acasinhadamatematica.pt\/?p=8666"},"modified":"2022-01-14T01:24:29","modified_gmt":"2022-01-14T01:24:29","slug":"dada-a-funcao-f","status":"publish","type":"post","link":"https:\/\/www.acasinhadamatematica.pt\/?p=8666","title":{"rendered":"Dada a fun\u00e7\u00e3o $f$"},"content":{"rendered":"<p><ul id='GTTabs_ul_8666' class='GTTabs' style='display:none'>\n<li id='GTTabs_li_0_8666' class='GTTabs_curr'><a  id=\"8666_0\" onMouseOver=\"GTTabsShowLinks('Enunciado'); return true;\"  onMouseOut=\"GTTabsShowLinks();\"  class='GTTabsLinks'>Enunciado<\/a><\/li>\n<li id='GTTabs_li_1_8666' ><a  id=\"8666_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_8666'>\n<span class='GTTabs_titles'><b>Enunciado<\/b><\/span><\/p>\n<p>Dada a fun\u00e7\u00e3o $f$ tal que $$f(x) = \\sqrt 3 \\operatorname{sen} x + \\cos x$$<\/p>\n<ol>\n<li>Encontre $a$ e $\\alpha $ de modo que $$f(x) = a\\operatorname{sen} \\left( {x + \\alpha } \\right)$$<\/li>\n<li>Resolva a equa\u00e7\u00e3o $f(x) = 1$.<\/li>\n<\/ol>\n<p><div class='GTTabsNavigation' style='display:none'><span class='GTTabs_nav_next'><a href='#GTTabs_ul_8666' onClick='GTTabs_show(1,8666)'>Resolu\u00e7\u00e3o &gt;&gt;<\/a><\/span><\/div><\/div>\n\n<div class='GTTabs_divs' id='GTTabs_1_8666'>\n<span class='GTTabs_titles'><b>Resolu\u00e7\u00e3o<\/b><\/span><!--more--><\/p>\n<blockquote>\n<p>Dada a fun\u00e7\u00e3o $f$ tal que $$f(x) = \\sqrt 3 \\operatorname{sen} x + \\cos x$$<\/p>\n<\/blockquote>\n<p>\u00ad<\/p>\n<ol>\n<li>Ora,<br \/>\n$$\\begin{array}{*{20}{l}}<br \/>\n{f(x)}&amp; = &amp;{2 \\times \\left( {\\frac{{\\sqrt 3 }}{2}\\operatorname{sen} x + \\frac{1}{2}\\cos x} \\right)} \\\\<br \/>\n{}&amp; = &amp;{2 \\times \\left( {\\operatorname{sen} x \\times \\cos \\left( {\\frac{\\pi }{6}} \\right) + \\cos x \\times \\operatorname{sen} \\left( {\\frac{\\pi }{6}} \\right)} \\right)} \\\\<br \/>\n{}&amp; = &amp;{2\\operatorname{sen} \\left( {x + \\frac{\\pi }{6}} \\right)}<br \/>\n\\end{array}$$<br \/>\nLogo, $a = 2$ e $\\alpha\u00a0 = \\frac{\\pi }{6}$.<br \/>\n\u00ad<\/li>\n<li>Ora,<br \/>\n$$\\begin{array}{*{20}{l}}<br \/>\n{f(x) = 1}&amp; \\Leftrightarrow &amp;{2\\operatorname{sen} \\left( {x + \\frac{\\pi }{6}} \\right) = 1} \\\\<br \/>\n{}&amp; \\Leftrightarrow &amp;{\\operatorname{sen} \\left( {x + \\frac{\\pi }{6}} \\right) = \\frac{1}{2}} \\\\<br \/>\n{}&amp; \\Leftrightarrow &amp;{\\begin{array}{*{20}{l}}<br \/>\n{x + \\frac{\\pi }{6} = \\frac{\\pi }{6} + 2k\\pi }&amp; \\vee &amp;{x + \\frac{\\pi }{6} = \\pi\u00a0 &#8211; \\frac{\\pi }{6} + 2k\\pi ,k \\in \\mathbb{Z}}<br \/>\n\\end{array}} \\\\<br \/>\n{}&amp; \\Leftrightarrow &amp;{\\begin{array}{*{20}{l}}<br \/>\n{x = 2k\\pi }&amp; \\vee &amp;{x = \\frac{{2\\pi }}{3} + 2k\\pi ,k \\in \\mathbb{Z}}<br \/>\n\\end{array}}<br \/>\n\\end{array}$$<\/li>\n<\/ol>\n<div class='GTTabsNavigation' style='display:none'><span class='GTTabs_nav_prev'><a href='#GTTabs_ul_8666' onClick='GTTabs_show(0,8666)'>&lt;&lt; Enunciado<\/a><\/span><\/div><\/div>\n\n","protected":false},"excerpt":{"rendered":"<p>Enunciado Resolu\u00e7\u00e3o Enunciado Dada a fun\u00e7\u00e3o $f$ tal que $$f(x) = \\sqrt 3 \\operatorname{sen} x + \\cos x$$ Encontre $a$ e $\\alpha $ de modo que $$f(x) = a\\operatorname{sen} \\left( {x + \\alpha }&#46;&#46;&#46;<\/p>\n","protected":false},"author":1,"featured_media":14113,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"_jetpack_memberships_contains_paid_content":false,"footnotes":""},"categories":[226,97,295],"tags":[427,307],"series":[],"class_list":["post-8666","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-funcoes-trigonometricas"],"views":2286,"jetpack_featured_media_url":"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2018\/03\/Mat55.png","jetpack_sharing_enabled":true,"jetpack_likes_enabled":true,"_links":{"self":[{"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=\/wp\/v2\/posts\/8666","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=8666"}],"version-history":[{"count":0,"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=\/wp\/v2\/posts\/8666\/revisions"}],"wp:featuredmedia":[{"embeddable":true,"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=\/wp\/v2\/media\/14113"}],"wp:attachment":[{"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=%2Fwp%2Fv2%2Fmedia&parent=8666"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=%2Fwp%2Fv2%2Fcategories&post=8666"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=%2Fwp%2Fv2%2Ftags&post=8666"},{"taxonomy":"series","embeddable":true,"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=%2Fwp%2Fv2%2Fseries&post=8666"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}