{"id":3809,"date":"2010-10-08T23:30:40","date_gmt":"2010-10-08T22:30:40","guid":{"rendered":"https:\/\/www.acasinhadamatematica.pt\/?p=3809"},"modified":"2022-01-13T14:36:08","modified_gmt":"2022-01-13T14:36:08","slug":"rascunho-5","status":"publish","type":"post","link":"https:\/\/www.acasinhadamatematica.pt\/?p=3809","title":{"rendered":"Sabe-se que&#8230;"},"content":{"rendered":"<p><ul id='GTTabs_ul_3809' class='GTTabs' style='display:none'>\n<li id='GTTabs_li_0_3809' class='GTTabs_curr'><a  id=\"3809_0\" onMouseOver=\"GTTabsShowLinks('Enunciado'); return true;\"  onMouseOut=\"GTTabsShowLinks();\"  class='GTTabsLinks'>Enunciado<\/a><\/li>\n<li id='GTTabs_li_1_3809' ><a  id=\"3809_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_3809'>\n<span class='GTTabs_titles'><b>Enunciado<\/b><\/span><\/p>\n<p>Sabe-se que $\\cos \\alpha =\\frac{1}{3}$.<\/p>\n<ol>\n<li>Determine o valor exato de $sen\\,\\alpha $ e de $tg\\,\\alpha $, sabendo que $-\\frac{\\pi }{2}&lt;\\alpha &lt;0$.<\/li>\n<li>Determine o valor exato de $sen\\,\\alpha $ e de $tg\\,\\alpha $, sabendo que $\\frac{3\\pi }{2}&lt;\\alpha &lt;2\\pi $.<\/li>\n<\/ol>\n<p><div class='GTTabsNavigation' style='display:none'><span class='GTTabs_nav_next'><a href='#GTTabs_ul_3809' onClick='GTTabs_show(1,3809)'>Resolu\u00e7\u00e3o &gt;&gt;<\/a><\/span><\/div><\/div>\n\n<div class='GTTabs_divs' id='GTTabs_1_3809'>\n<span class='GTTabs_titles'><b>Resolu\u00e7\u00e3o<\/b><\/span><!--more--><\/p>\n<ol>\n<li>Considerando que $se{{n}^{2}}\\alpha +{{\\cos }^{2}}\\alpha =1$ (FFT) e sabendo que $-\\frac{\\pi }{2}&lt;\\alpha &lt;0$, ent\u00e3o:<br \/>\n\\[\\begin{array}{*{35}{l}}<br \/>\nsen\\,\\alpha\u00a0 &amp; = &amp; -\\sqrt{1-{{\\left( \\frac{1}{3} \\right)}^{2}}}\\ \\ \\ \\text{(note que um\u00a0 }\\!\\!\\hat{\\mathrm{a}}\\!\\!\\text{ ngulo do 4 }\\!\\!{}^\\text{o}\\!\\!\\text{\u00a0 Q tem seno negativo)}\u00a0 \\\\<br \/>\n{} &amp; = &amp; -\\sqrt{\\frac{8}{9}}\u00a0 \\\\<br \/>\n{} &amp; = &amp; -\\frac{2\\sqrt{2}}{3}\u00a0 \\\\<br \/>\n\\end{array}\\]<br \/>\ne<br \/>\n\\[tg\\,\\alpha =\\frac{sen\\,\\alpha }{\\cos \\alpha }=\\frac{-\\frac{2\\sqrt{2}}{3}}{\\frac{1}{3}}=-2\\sqrt{2}\\]<br \/>\n\u00ad<\/li>\n<li>Considerando que $se{{n}^{2}}\\alpha +{{\\cos }^{2}}\\alpha =1$ (FFT) e sabendo que $\\frac{3\\pi }{2}&lt;\\alpha &lt;2\\pi $, ent\u00e3o:<br \/>\n\\[\\begin{array}{*{35}{l}}<br \/>\nsen\\,\\alpha\u00a0 &amp; = &amp; -\\sqrt{1-{{\\left( \\frac{1}{3} \\right)}^{2}}}\\ \\ \\ \\text{(note que um\u00a0 }\\!\\!\\hat{\\mathrm{a}}\\!\\!\\text{ ngulo do 4 }\\!\\!{}^\\text{o}\\!\\!\\text{\u00a0 Q tem seno negativo)}\u00a0 \\\\<br \/>\n{} &amp; = &amp; -\\sqrt{\\frac{8}{9}}\u00a0 \\\\<br \/>\n{} &amp; = &amp; -\\frac{2\\sqrt{2}}{3}\u00a0 \\\\<br \/>\n\\end{array}\\]<br \/>\ne<br \/>\n\\[tg\\,\\alpha =\\frac{sen\\,\\alpha }{\\cos \\alpha }=\\frac{-\\frac{2\\sqrt{2}}{3}}{\\frac{1}{3}}=-2\\sqrt{2}\\]<\/li>\n<\/ol>\n<div class='GTTabsNavigation' style='display:none'><span class='GTTabs_nav_prev'><a href='#GTTabs_ul_3809' onClick='GTTabs_show(0,3809)'>&lt;&lt; Enunciado<\/a><\/span><\/div><\/div>\n\n","protected":false},"excerpt":{"rendered":"<p>Enunciado Resolu\u00e7\u00e3o Enunciado Sabe-se que $\\cos \\alpha =\\frac{1}{3}$. Determine o valor exato de $sen\\,\\alpha $ e de $tg\\,\\alpha $, sabendo que $-\\frac{\\pi }{2}&lt;\\alpha &lt;0$. Determine o valor exato de $sen\\,\\alpha $ e de $tg\\,\\alpha&#46;&#46;&#46;<\/p>\n","protected":false},"author":1,"featured_media":19469,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"_jetpack_memberships_contains_paid_content":false,"footnotes":""},"categories":[98,97,99],"tags":[422,423],"series":[],"class_list":["post-3809","post","type-post","status-publish","format-standard","has-post-thumbnail","hentry","category-11--ano","category-aplicando","category-trigonometria","tag-11-o-ano","tag-trigonometria"],"views":2038,"jetpack_featured_media_url":"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2021\/12\/Mat133.png","jetpack_sharing_enabled":true,"jetpack_likes_enabled":true,"_links":{"self":[{"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=\/wp\/v2\/posts\/3809","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=3809"}],"version-history":[{"count":0,"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=\/wp\/v2\/posts\/3809\/revisions"}],"wp:featuredmedia":[{"embeddable":true,"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=\/wp\/v2\/media\/19469"}],"wp:attachment":[{"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=%2Fwp%2Fv2%2Fmedia&parent=3809"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=%2Fwp%2Fv2%2Fcategories&post=3809"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=%2Fwp%2Fv2%2Ftags&post=3809"},{"taxonomy":"series","embeddable":true,"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=%2Fwp%2Fv2%2Fseries&post=3809"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}