{"id":4313,"date":"2010-10-19T02:29:33","date_gmt":"2010-10-19T01:29:33","guid":{"rendered":"https:\/\/www.acasinhadamatematica.pt\/?p=4313"},"modified":"2022-01-13T16:24:53","modified_gmt":"2022-01-13T16:24:53","slug":"calcule-o-valor-exacto","status":"publish","type":"post","link":"https:\/\/www.acasinhadamatematica.pt\/?p=4313","title":{"rendered":"Calcule o valor exato"},"content":{"rendered":"<p><ul id='GTTabs_ul_4313' class='GTTabs' style='display:none'>\n<li id='GTTabs_li_0_4313' class='GTTabs_curr'><a  id=\"4313_0\" onMouseOver=\"GTTabsShowLinks('Enunciado'); return true;\"  onMouseOut=\"GTTabsShowLinks();\"  class='GTTabsLinks'>Enunciado<\/a><\/li>\n<li id='GTTabs_li_1_4313' ><a  id=\"4313_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_4313'>\n<span class='GTTabs_titles'><b>Enunciado<\/b><\/span><\/p>\n<p>Calcule o valor exato de cada uma das express\u00f5es.<\/p>\n<ol>\n<li>$sen\\,\\frac{13\\pi }{3}+\\cos 5\\pi -tg\\,(-7\\pi )+\\cos (-\\frac{23\\pi }{4})$<\/li>\n<li>$se{{n}^{2}}\\,(-\\frac{7\\pi }{4})+{{\\cos }^{2}}(-\\frac{7\\pi }{4})$<\/li>\n<li>$sen\\,\\frac{19\\pi }{3}+\\cos (-3\\pi )-tg\\,(-\\frac{15\\pi }{4})+\\cos (-\\frac{11\\pi }{6})$<\/li>\n<li>$tg\\,\\frac{13\\pi }{4}+\\cos 6\\pi -sen\\,(-\\frac{7\\pi }{2})+\\cos (-\\frac{17\\pi }{3})$<\/li>\n<\/ol>\n<p><div class='GTTabsNavigation' style='display:none'><span class='GTTabs_nav_next'><a href='#GTTabs_ul_4313' onClick='GTTabs_show(1,4313)'>Resolu\u00e7\u00e3o &gt;&gt;<\/a><\/span><\/div><\/div>\n\n<div class='GTTabs_divs' id='GTTabs_1_4313'>\n<span class='GTTabs_titles'><b>Resolu\u00e7\u00e3o<\/b><\/span><!--more--><\/p>\n<ol>\n<li>Ora,<br \/>\n\\[\\begin{array}{*{35}{l}}<br \/>\nsen\\,\\frac{13\\pi }{3}+\\cos 5\\pi -tg\\,(-7\\pi )+\\cos (-\\frac{23\\pi }{4}) &amp; = &amp; sen\\,(4\\pi +\\frac{\\pi }{3})+\\cos (4\\pi +\\pi )-tg\\,(-7\\pi +0)+\\cos (-6\\pi +\\frac{\\pi }{4})\u00a0 \\\\<br \/>\n{} &amp; = &amp; sen\\,\\frac{\\pi }{3}+\\cos \\pi -tg\\,0+\\cos \\frac{\\pi }{4}\u00a0 \\\\<br \/>\n{} &amp; = &amp; \\frac{\\sqrt{3}}{2}-1-0+\\frac{\\sqrt{2}}{2}\u00a0 \\\\<br \/>\n{} &amp; = &amp; \\frac{\\sqrt{3}+\\sqrt{2}-2}{2}\u00a0 \\\\<br \/>\n\\end{array}\\]<\/li>\n<li>Ora,<br \/>\n\\[\\begin{array}{*{35}{l}}<br \/>\nse{{n}^{2}}\\,(-\\frac{7\\pi }{4})+{{\\cos }^{2}}(-\\frac{7\\pi }{4}) &amp; = &amp; se{{n}^{2}}\\,(-2\\pi +\\frac{\\pi }{4})+{{\\cos }^{2}}(-2\\pi +\\frac{\\pi }{4})\u00a0 \\\\<br \/>\n{} &amp; = &amp; se{{n}^{2}}\\,(\\frac{\\pi }{4})+{{\\cos }^{2}}(\\frac{\\pi }{4})\u00a0 \\\\<br \/>\n{} &amp; = &amp; {{\\left( \\frac{\\sqrt{2}}{2} \\right)}^{2}}+{{\\left( \\frac{\\sqrt{2}}{2} \\right)}^{2}}\u00a0 \\\\<br \/>\n{} &amp; = &amp; 1\u00a0 \\\\<br \/>\n\\end{array}\\]<\/li>\n<li>Ora,<br \/>\n\\[\\begin{array}{*{35}{l}}<br \/>\nsen\\,\\frac{19\\pi }{3}+\\cos (-3\\pi )-tg\\,(-\\frac{15\\pi }{4})+\\cos (-\\frac{11\\pi }{6}) &amp; = &amp; sen\\,(6\\pi +\\frac{\\pi }{3})+\\cos (-4\\pi +\\pi )-tg\\,(-4\\pi +\\frac{\\pi }{4})+\\cos (-2\\pi +\\frac{\\pi }{6})\u00a0 \\\\<br \/>\n{} &amp; = &amp; \\frac{\\sqrt{3}}{2}-1-1+\\frac{\\sqrt{3}}{2}\u00a0 \\\\<br \/>\n{} &amp; = &amp; \\sqrt{3}-2\u00a0 \\\\<br \/>\n\\end{array}\\]<\/li>\n<li>Ora,<br \/>\n\\[\\begin{array}{*{35}{l}}<br \/>\ntg\\,\\frac{13\\pi }{4}+\\cos 6\\pi -sen\\,(-\\frac{7\\pi }{2})+\\cos (-\\frac{17\\pi }{3}) &amp; = &amp; tg\\,\\frac{\\pi }{4}+1-sen\\,(-4\\pi +\\frac{\\pi }{2})+\\cos (-6\\pi +\\frac{\\pi }{3})\u00a0 \\\\<br \/>\n{} &amp; = &amp; 1+1-1+\\frac{1}{2}\u00a0 \\\\<br \/>\n{} &amp; = &amp; \\frac{3}{2}\u00a0 \\\\<br \/>\n\\end{array}\\]<\/li>\n<\/ol>\n<div class='GTTabsNavigation' style='display:none'><span class='GTTabs_nav_prev'><a href='#GTTabs_ul_4313' onClick='GTTabs_show(0,4313)'>&lt;&lt; Enunciado<\/a><\/span><\/div><\/div>\n\n","protected":false},"excerpt":{"rendered":"<p>Enunciado Resolu\u00e7\u00e3o Enunciado Calcule o valor exato de cada uma das express\u00f5es. $sen\\,\\frac{13\\pi }{3}+\\cos 5\\pi -tg\\,(-7\\pi )+\\cos (-\\frac{23\\pi }{4})$ $se{{n}^{2}}\\,(-\\frac{7\\pi }{4})+{{\\cos }^{2}}(-\\frac{7\\pi }{4})$ $sen\\,\\frac{19\\pi }{3}+\\cos (-3\\pi )-tg\\,(-\\frac{15\\pi }{4})+\\cos (-\\frac{11\\pi }{6})$ $tg\\,\\frac{13\\pi }{4}+\\cos 6\\pi -sen\\,(-\\frac{7\\pi&#46;&#46;&#46;<\/p>\n","protected":false},"author":1,"featured_media":19462,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"_jetpack_memberships_contains_paid_content":false,"footnotes":""},"categories":[98,97,99],"tags":[424,423],"series":[],"class_list":["post-4313","post","type-post","status-publish","format-standard","has-post-thumbnail","hentry","category-11--ano","category-aplicando","category-trigonometria","tag-8-o-ano","tag-trigonometria"],"views":2532,"jetpack_featured_media_url":"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2021\/12\/Mat126.png","jetpack_sharing_enabled":true,"jetpack_likes_enabled":true,"_links":{"self":[{"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=\/wp\/v2\/posts\/4313","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=4313"}],"version-history":[{"count":0,"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=\/wp\/v2\/posts\/4313\/revisions"}],"wp:attachment":[{"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=%2Fwp%2Fv2%2Fmedia&parent=4313"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=%2Fwp%2Fv2%2Fcategories&post=4313"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=%2Fwp%2Fv2%2Ftags&post=4313"},{"taxonomy":"series","embeddable":true,"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=%2Fwp%2Fv2%2Fseries&post=4313"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}