{"id":4321,"date":"2010-10-19T03:05:55","date_gmt":"2010-10-19T02:05:55","guid":{"rendered":"https:\/\/www.acasinhadamatematica.pt\/?p=4321"},"modified":"2022-01-13T16:26:20","modified_gmt":"2022-01-13T16:26:20","slug":"calcule-o-valor-numerico","status":"publish","type":"post","link":"https:\/\/www.acasinhadamatematica.pt\/?p=4321","title":{"rendered":"Calcule o valor num\u00e9rico"},"content":{"rendered":"<p><ul id='GTTabs_ul_4321' class='GTTabs' style='display:none'>\n<li id='GTTabs_li_0_4321' class='GTTabs_curr'><a  id=\"4321_0\" onMouseOver=\"GTTabsShowLinks('Enunciado'); return true;\"  onMouseOut=\"GTTabsShowLinks();\"  class='GTTabsLinks'>Enunciado<\/a><\/li>\n<li id='GTTabs_li_1_4321' ><a  id=\"4321_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_4321'>\n<span class='GTTabs_titles'><b>Enunciado<\/b><\/span><\/p>\n<ol>\n<li>Se $\\cos (\\alpha -\\frac{\\pi }{2})=\\frac{4}{5}$, calcule o valor num\u00e9rico de $\\begin{matrix}<br \/>\n\\cos (-\\alpha )-\\cos (\\pi +\\alpha ) &amp; \\wedge\u00a0 &amp; \\alpha \\in 1.{}^\\text{o}Q\u00a0 \\\\<br \/>\n\\end{matrix}$.<\/li>\n<li>Determine o valor exato de $tg\\,(-\\alpha )+\\cos (\\alpha -\\frac{\\pi }{2})$, sabendo que $\\begin{matrix}<br \/>\nsen\\,(-\\pi -\\alpha )=\\frac{3}{7} &amp; \\wedge\u00a0 &amp; \\alpha \\in 2.{}^\\text{o}Q\u00a0 \\\\<br \/>\n\\end{matrix}$.<\/li>\n<\/ol>\n<p><div class='GTTabsNavigation' style='display:none'><span class='GTTabs_nav_next'><a href='#GTTabs_ul_4321' onClick='GTTabs_show(1,4321)'>Resolu\u00e7\u00e3o &gt;&gt;<\/a><\/span><\/div><\/div>\n\n<div class='GTTabs_divs' id='GTTabs_1_4321'>\n<span class='GTTabs_titles'><b>Resolu\u00e7\u00e3o<\/b><\/span><!--more--><\/p>\n<ol>\n<li>Ora, $\\cos (-\\alpha )-\\cos (\\pi +\\alpha )=\\cos \\alpha +\\cos \\alpha =2\\cos \\alpha $.<br \/>\nPor outro lado, $\\cos (\\alpha -\\frac{\\pi }{2})=\\frac{4}{5}\\Leftrightarrow \\cos (\\frac{\\pi }{2}-\\alpha )=\\frac{4}{5}\\Leftrightarrow sen\\,\\alpha =\\frac{4}{5}$.<br \/>\nComo $\\alpha \\in 1.{}^\\text{o}Q$, ent\u00e3o $\\cos \\alpha =+\\sqrt{1-{{(\\frac{4}{5})}^{2}}}=\\sqrt{1-\\frac{16}{25}}=\\frac{3}{5}$.<br \/>\nLogo, $\\cos (-\\alpha )-\\cos (\\pi +\\alpha )=2\\times \\frac{3}{5}=\\frac{6}{5}$.<br \/>\n\u00ad<\/li>\n<li>Ora, $tg\\,(-\\alpha )+\\cos (\\alpha -\\frac{\\pi }{2})=-tg\\,\\alpha +\\cos (\\frac{\\pi }{2}-\\alpha )=-tg\\,\\alpha +sen\\,\\alpha $.<br \/>\nPor outro lado, $sen\\,(-\\pi -\\alpha )=\\frac{3}{7}\\Leftrightarrow sen\\,(\\pi +\\alpha )=-\\frac{3}{7}\\Leftrightarrow sen\\,\\alpha =\\frac{3}{7}$.<br \/>\nComo $\\alpha \\in 2.{}^\\text{o}Q$, ent\u00e3o $\\cos \\alpha =-\\sqrt{1-{{(\\frac{3}{7})}^{2}}}=\\sqrt{1-\\frac{9}{49}}=\\frac{2\\sqrt{10}}{7}$.<br \/>\nLogo, \\[\\begin{matrix}<br \/>\ntg\\,(-\\alpha )+\\cos (\\alpha -\\frac{\\pi }{2}) &amp; = &amp; -\\frac{\\frac{3}{7}}{\\frac{2\\sqrt{10}}{7}}+\\frac{3}{7}\u00a0 \\\\<br \/>\n{} &amp; = &amp; \\frac{3}{2\\sqrt{10}}+\\frac{3}{7}\u00a0 \\\\<br \/>\n{} &amp; = &amp; \\frac{3\\sqrt{10}}{20}+\\frac{3}{7}\u00a0 \\\\<br \/>\n{} &amp; = &amp; \\frac{21\\sqrt{10}+60}{140}\u00a0 \\\\<br \/>\n\\end{matrix}\\]<\/li>\n<\/ol>\n<div class='GTTabsNavigation' style='display:none'><span class='GTTabs_nav_prev'><a href='#GTTabs_ul_4321' onClick='GTTabs_show(0,4321)'>&lt;&lt; Enunciado<\/a><\/span><\/div><\/div>\n\n","protected":false},"excerpt":{"rendered":"<p>Enunciado Resolu\u00e7\u00e3o Enunciado Se $\\cos (\\alpha -\\frac{\\pi }{2})=\\frac{4}{5}$, calcule o valor num\u00e9rico de $\\begin{matrix} \\cos (-\\alpha )-\\cos (\\pi +\\alpha ) &amp; \\wedge\u00a0 &amp; \\alpha \\in 1.{}^\\text{o}Q\u00a0 \\\\ \\end{matrix}$. Determine o valor exato 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-4321","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":1869,"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\/4321","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=4321"}],"version-history":[{"count":0,"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=\/wp\/v2\/posts\/4321\/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=4321"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=%2Fwp%2Fv2%2Fcategories&post=4321"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=%2Fwp%2Fv2%2Ftags&post=4321"},{"taxonomy":"series","embeddable":true,"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=%2Fwp%2Fv2%2Fseries&post=4321"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}