{"id":8382,"date":"2012-04-16T15:29:02","date_gmt":"2012-04-16T14:29:02","guid":{"rendered":"https:\/\/www.acasinhadamatematica.pt\/?p=8382"},"modified":"2021-12-30T01:07:47","modified_gmt":"2021-12-30T01:07:47","slug":"qual-e-o-periodo-positivo-minimo","status":"publish","type":"post","link":"https:\/\/www.acasinhadamatematica.pt\/?p=8382","title":{"rendered":"Qual \u00e9 o per\u00edodo positivo m\u00ednimo?"},"content":{"rendered":"<p><ul id='GTTabs_ul_8382' class='GTTabs' style='display:none'>\n<li id='GTTabs_li_0_8382' class='GTTabs_curr'><a  id=\"8382_0\" onMouseOver=\"GTTabsShowLinks('Enunciado'); return true;\"  onMouseOut=\"GTTabsShowLinks();\"  class='GTTabsLinks'>Enunciado<\/a><\/li>\n<li id='GTTabs_li_1_8382' ><a  id=\"8382_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_8382'>\n<span class='GTTabs_titles'><b>Enunciado<\/b><\/span> Qual \u00e9 o per\u00edodo positivo m\u00ednimo de cada uma das fun\u00e7\u00f5es?<\/p>\n<ol>\n<li>$f:x \\to \\operatorname{tg} \\left( {3x} \\right)$<\/li>\n<li>$g:x \\to \\operatorname{tg} \\left( {\\frac{x}{4}} \\right)$<\/li>\n<li>$h:x \\to 2 + 3\\operatorname{tg} \\left( {\\frac{x}{{10}}} \\right)$<\/li>\n<\/ol>\n<p><div class='GTTabsNavigation' style='display:none'><span class='GTTabs_nav_next'><a href='#GTTabs_ul_8382' onClick='GTTabs_show(1,8382)'>Resolu\u00e7\u00e3o &gt;&gt;<\/a><\/span><\/div><\/div>\n\n<div class='GTTabs_divs' id='GTTabs_1_8382'>\n<span class='GTTabs_titles'><b>Resolu\u00e7\u00e3o<\/b><\/span><!--more--><\/p>\n<ol>\n<li>O per\u00edodo positivo m\u00ednimo da fun\u00e7\u00e3o $x \\to \\operatorname{tg} x$ \u00e9 $\\pi $. Ora, $3x = \\pi\u00a0 \\Leftrightarrow x = \\frac{\\pi }{3}$.<br \/>\nLogo, o per\u00edodo positivo m\u00ednimo da fun\u00e7\u00e3o\u00a0$f:x \\to \\operatorname{tg} \\left( {3x} \\right)$ \u00e9 $\\frac{\\pi }{3}$.<br \/>\n\u00ad<\/li>\n<li>O per\u00edodo positivo m\u00ednimo da fun\u00e7\u00e3o $x \\to \\operatorname{tg} x$ \u00e9 $\\pi $. Ora, $\\frac{x}{4} = \\pi\u00a0 \\Leftrightarrow x = 4\\pi $.<br \/>\nLogo, o per\u00edodo positivo m\u00ednimo da fun\u00e7\u00e3o\u00a0$g:x \\to \\operatorname{tg} \\left( {\\frac{x}{4}} \\right)$ \u00e9 $4\\pi $.<br \/>\n\u00ad<\/li>\n<li>O per\u00edodo positivo m\u00ednimo da fun\u00e7\u00e3o $x \\to \\operatorname{tg} x$ \u00e9 $\\pi $. Ora, $\\frac{x}{{10}} = \\pi\u00a0 \\Leftrightarrow x = 10\\pi $.<br \/>\nLogo, o per\u00edodo positivo m\u00ednimo da fun\u00e7\u00e3o\u00a0$h:x \\to 2 + 3\\operatorname{tg} \\left( {\\frac{x}{{10}}} \\right)$ \u00e9 $10\\pi $.<\/li>\n<\/ol>\n<div class='GTTabsNavigation' style='display:none'><span class='GTTabs_nav_prev'><a href='#GTTabs_ul_8382' onClick='GTTabs_show(0,8382)'>&lt;&lt; Enunciado<\/a><\/span><\/div><\/div>\n\n","protected":false},"excerpt":{"rendered":"<p>Enunciado Resolu\u00e7\u00e3o Enunciado Qual \u00e9 o per\u00edodo positivo m\u00ednimo de cada uma das fun\u00e7\u00f5es? $f:x \\to \\operatorname{tg} \\left( {3x} \\right)$ $g:x \\to \\operatorname{tg} \\left( {\\frac{x}{4}} \\right)$ $h:x \\to 2 + 3\\operatorname{tg} \\left( {\\frac{x}{{10}}} \\right)$&#46;&#46;&#46;<\/p>\n","protected":false},"author":1,"featured_media":19181,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"_jetpack_memberships_contains_paid_content":false,"footnotes":""},"categories":[226,97,295],"tags":[427,297],"series":[],"class_list":["post-8382","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-periodo-positivo-minimo"],"views":15778,"jetpack_featured_media_url":"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2021\/12\/Mat72.png","jetpack_sharing_enabled":true,"jetpack_likes_enabled":true,"_links":{"self":[{"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=\/wp\/v2\/posts\/8382","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=8382"}],"version-history":[{"count":0,"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=\/wp\/v2\/posts\/8382\/revisions"}],"wp:featuredmedia":[{"embeddable":true,"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=\/wp\/v2\/media\/19181"}],"wp:attachment":[{"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=%2Fwp%2Fv2%2Fmedia&parent=8382"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=%2Fwp%2Fv2%2Fcategories&post=8382"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=%2Fwp%2Fv2%2Ftags&post=8382"},{"taxonomy":"series","embeddable":true,"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=%2Fwp%2Fv2%2Fseries&post=8382"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}