{"id":8423,"date":"2012-04-16T21:39:41","date_gmt":"2012-04-16T20:39:41","guid":{"rendered":"https:\/\/www.acasinhadamatematica.pt\/?p=8423"},"modified":"2021-12-30T01:27:59","modified_gmt":"2021-12-30T01:27:59","slug":"mostre-que-as-funcoes-sao-identicas","status":"publish","type":"post","link":"https:\/\/www.acasinhadamatematica.pt\/?p=8423","title":{"rendered":"Mostre que as fun\u00e7\u00f5es s\u00e3o id\u00eanticas"},"content":{"rendered":"<p><ul id='GTTabs_ul_8423' class='GTTabs' style='display:none'>\n<li id='GTTabs_li_0_8423' class='GTTabs_curr'><a  id=\"8423_0\" onMouseOver=\"GTTabsShowLinks('Enunciado'); return true;\"  onMouseOut=\"GTTabsShowLinks();\"  class='GTTabsLinks'>Enunciado<\/a><\/li>\n<li id='GTTabs_li_1_8423' ><a  id=\"8423_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_8423'>\n<span class='GTTabs_titles'><b>Enunciado<\/b><\/span><\/p>\n<p>Mostre que a fun\u00e7\u00e3o $x \\to f(x) = 2\\cos \\left( {4x + 3\\pi } \\right)$ \u00e9 id\u00eantica \u00e0 fun\u00e7\u00e3o $x \\to g(x) = 2\\operatorname{sen} \\left( {4x &#8211; \\frac{\\pi }{2}} \\right)$.<\/p>\n<p><div class='GTTabsNavigation' style='display:none'><span class='GTTabs_nav_next'><a href='#GTTabs_ul_8423' onClick='GTTabs_show(1,8423)'>Resolu\u00e7\u00e3o &gt;&gt;<\/a><\/span><\/div><\/div>\n\n<div class='GTTabs_divs' id='GTTabs_1_8423'>\n<span class='GTTabs_titles'><b>Resolu\u00e7\u00e3o<\/b><\/span><!--more--><\/p>\n<p>Ora, $$\\begin{array}{*{20}{l}} \u00a0 {f(x)}&amp; = &amp;{2\\cos \\left( {4x + 3\\pi } \\right)} \\\\ \u00a0 {}&amp; = &amp;{2\\cos \\left( {4x + \\pi } \\right)} \\\\ \u00a0 {}&amp; = &amp;{ &#8211; 2\\cos \\left( {4x} \\right)} \\\\ \u00a0 {}&amp; = &amp;{ &#8211; 2\\operatorname{sen} \\left( {\\frac{\\pi }{2} &#8211; 4x} \\right)} \\\\ \u00a0 {}&amp; = &amp;{2\\operatorname{sen} \\left( {4x &#8211; \\frac{\\pi }{2}} \\right)} \\\\ \u00a0 {}&amp; = &amp;{g(x)} \\end{array}$$ Como ${D_f} = {D_g} = \\mathbb{R}$ e $f(x) = g(x),\\forall x \\in \\mathbb{R}$, ent\u00e3o as fun\u00e7\u00f5es $f$ e $g$ s\u00e3o id\u00eanticas.<\/p><\/p>\n<div class='GTTabsNavigation' style='display:none'><span class='GTTabs_nav_prev'><a href='#GTTabs_ul_8423' onClick='GTTabs_show(0,8423)'>&lt;&lt; Enunciado<\/a><\/span><\/div><\/div>\n\n","protected":false},"excerpt":{"rendered":"<p>Enunciado Resolu\u00e7\u00e3o Enunciado Mostre que a fun\u00e7\u00e3o $x \\to f(x) = 2\\cos \\left( {4x + 3\\pi } \\right)$ \u00e9 id\u00eantica \u00e0 fun\u00e7\u00e3o $x \\to g(x) = 2\\operatorname{sen} \\left( {4x &#8211; \\frac{\\pi }{2}} \\right)$. Resolu\u00e7\u00e3o&#46;&#46;&#46;<\/p>\n","protected":false},"author":1,"featured_media":14083,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"_jetpack_memberships_contains_paid_content":false,"footnotes":""},"categories":[226,97,295],"tags":[427,299,296],"series":[],"class_list":["post-8423","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-funcao-co-seno","tag-funcao-seno"],"views":2945,"jetpack_featured_media_url":"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2018\/03\/Mat28.png","jetpack_sharing_enabled":true,"jetpack_likes_enabled":true,"_links":{"self":[{"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=\/wp\/v2\/posts\/8423","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=8423"}],"version-history":[{"count":0,"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=\/wp\/v2\/posts\/8423\/revisions"}],"wp:featuredmedia":[{"embeddable":true,"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=\/wp\/v2\/media\/14083"}],"wp:attachment":[{"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=%2Fwp%2Fv2%2Fmedia&parent=8423"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=%2Fwp%2Fv2%2Fcategories&post=8423"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=%2Fwp%2Fv2%2Ftags&post=8423"},{"taxonomy":"series","embeddable":true,"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=%2Fwp%2Fv2%2Fseries&post=8423"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}