{"id":457,"date":"2012-11-01T23:18:40","date_gmt":"2012-11-01T14:18:40","guid":{"rendered":"http:\/\/www.roundown.net\/nyushi\/?p=457"},"modified":"2021-10-03T15:55:51","modified_gmt":"2021-10-03T06:55:51","slug":"kbr201002","status":"publish","type":"post","link":"https:\/\/www.roundown.net\/nyushi\/kbr201002\/","title":{"rendered":"\u7b51\u6ce2\u5927\u7406\u7cfb2010\uff1a\u7b2c2\u554f"},"content":{"rendered":"<hr \/>\n<p>\\(3\\) \u3064\u306e\u66f2\u7dda\r\n\\[\\begin{align}\r\nC _ 1 : \\ y & = \\sin x \\quad \\left( 0 \\leqq x \\lt \\frac{\\pi}{2} \\right) \\\\\r\nC _ 2 : \\ y & = \\cos x \\quad \\left( 0 \\leqq x \\lt \\frac{\\pi}{2} \\right) \\\\\r\nC _ 3 : \\ y & = \\tan x \\quad \\left( 0 \\leqq x \\lt \\frac{\\pi}{2} \\right)\r\n\\end{align}\\]\r\n\u306b\u3064\u3044\u3066\u4ee5\u4e0b\u306e\u554f\u3044\u306b\u7b54\u3048\u3088.<\/p>\r\n<ol>\r\n<li><p><strong>(1)<\/strong>\u3000\\(C _ 1\\) \u3068 \\(C _ 2\\) \u306e\u4ea4\u70b9, \\(C _ 2\\) \u3068 \\(C _ 3\\) \u306e\u4ea4\u70b9, \\(C _ 3\\) \u3068 \\(C _ 1\\) \u306e\u4ea4\u70b9\u306e\u305d\u308c\u305e\u308c\u306b\u3064\u3044\u3066 \\(y\\) \u5ea7\u6a19\u3092\u6c42\u3081\u3088.<\/p><\/li>\r\n<li><p><strong>(2)<\/strong>\u3000\\(C _ 1 , C _ 2 , C _ 3\\) \u306b\u3088\u3063\u3066\u56f2\u307e\u308c\u308b\u56f3\u5f62\u306e\u9762\u7a4d\u3092\u6c42\u3081\u3088.<\/p><\/li>\r\n<\/ol>\r\n<hr \/>\r\n<!--more-->\r\n<h4>\u3010 \u89e3 \u7b54 \u3011<\/h4>\r\n<p><strong>(1)<\/strong><\/p>\r\n<ul>\r\n<li><p>\\(C _ 1\\) \u3068 \\(C _ 2\\) \u306e\u4ea4\u70b9\u306b\u3064\u3044\u3066\r\n\\[\\begin{align}\r\n\\sin x & = \\cos x \\\\\r\n\\sqrt{2} \\sin \\left( x -\\dfrac{\\pi}{4} \\right) & = 0 \\\\\r\n\\text{\u2234} \\quad x =\\dfrac{\\pi}{4} &\r\n\\end{align}\\]\r\n\u3057\u305f\u304c\u3063\u3066, \u4ea4\u70b9\u306e \\(y\\) \u5ea7\u6a19\u306f\r\n\\[\r\n\\sin \\dfrac{\\pi}{4} = \\underline{\\dfrac{\\sqrt{2}}{2}}\r\n\\]<\/li>\r\n<li><p>\\(C _ 2\\) \u3068 \\(C _ 3\\) \u306e\u4ea4\u70b9\u306b\u3064\u3044\u3066\r\n\\[\\begin{align}\r\n\\cos x & = \\tan x \\\\\r\n\\cos^2 x -\\sin x & = 0 \\\\\r\n\\sin^2 x +\\sin x -1 & = 0 \\\\\r\n\\text{\u2234} \\quad \\sin x = \\dfrac{\\sqrt{5} -1}{2} &\r\n\\end{align}\\]\r\n\u3053\u3053\u3067, \\(\\sin \\alpha =\\dfrac{\\sqrt{5} -1}{2} \\ \\left( 0 \\lt \\alpha \\lt \\dfrac{\\pi}{2} \\right)\\) \u3068\u304a\u3051\u3070, \u4ea4\u70b9\u306e \\(y\\) \u5ea7\u6a19\u306f\r\n\\[\\begin{align}\r\n\\cos \\alpha & = \\sqrt{1 -\\left( \\dfrac{\\sqrt{5} -1}{2} \\right)^2} \\\\\r\n& = \\underline{\\sqrt{\\dfrac{\\sqrt{5} -1}{2}}}\r\n\\end{align}\\]<\/li>\r\n<li><p>\\(C _ 3\\) \u3068 \\(C _ 1\\) \u306e\u4ea4\u70b9\u306b\u3064\u3044\u3066\r\n\\[\\begin{align}\r\n\\sin x & = \\tan x \\\\\r\n\\sin x \\left( \\cos x -1 \\right) & = 0 \\\\\r\n\\text{\u2234} \\quad x = 0 &\r\n\\end{align}\\]\r\n\u3057\u305f\u304c\u3063\u3066, \u4ea4\u70b9\u306e \\(y\\) \u5ea7\u6a19\u306f\r\n\\[\r\n\\sin 0 = \\underline{0}\r\n\\]<\/li>\r\n<\/ul>\r\n<p><strong>(2)<\/strong><\/p>\r\n<p>\\(C _ 1 , C _ 2 , C _ 3\\) \u306b\u56f2\u307e\u308c\u308b\u90e8\u5206\u306f\u4e0b\u56f3\u659c\u7dda\u90e8\u306e\u3088\u3046\u306b\u306a\u308b.<\/p>\r\n<img decoding=\"async\" src=\"\/\/www.roundown.net\/nyushi\/wp-content\/uploads\/tsukuba_r_2010_02_01.png\" alt=\"\" title=\"tsukuba_r_2010_02_01\" class=\"aligncenter size-full\" \/>\r\n<p>\u3088\u3063\u3066, \u6c42\u3081\u308b\u9762\u7a4d \\(S\\) \u306f\r\n\\[\\begin{align}\r\nS & = \\displaystyle\\int _ 0^{\\alpha} ( \\tan x -\\sin x ) \\, dx +\\displaystyle\\int _ {\\alpha}^{\\frac{\\pi}{4}} ( \\cos x -\\sin x ) \\, dx \\\\\r\n& = \\left[ -\\log ( \\cos x ) \\right] _ 0^{\\alpha} +\\left[ \\sin x \\right] _ {\\alpha}^{\\frac{\\pi}{4}} -\\left[ -\\cos x \\right] _ 0^{\\frac{\\pi}{4}} \\\\\r\n& = \\dfrac{1}{2} \\log \\dfrac{2}{\\sqrt{5}-1} +\\dfrac{\\sqrt{2}}{2} -\\dfrac{\\sqrt{5}-1}{2} +\\dfrac{\\sqrt{2}}{2} -1 \\\\\r\n& = \\underline{\\dfrac{1}{2} \\log \\dfrac{\\sqrt{5}+1}{2} -\\dfrac{\\sqrt{5}+1}{2} +\\sqrt{2}}\r\n\\end{align}\\]\r\n","protected":false},"excerpt":{"rendered":"\\(3\\) \u3064\u306e\u66f2\u7dda \\[\\begin{align} C _ 1 : \\ y &#038; = \\sin x \\quad \\left( 0 \\leqq x \\lt \\frac{\\pi}{2} \\right) \\\\ C _ 2 :  &hellip; <a href=\"https:\/\/www.roundown.net\/nyushi\/kbr201002\/\">\u7d9a\u304d\u3092\u8aad\u3080 <span class=\"meta-nav\">&rarr;<\/span><\/a>","protected":false},"author":1,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"inline_featured_image":false,"footnotes":""},"categories":[40],"tags":[144,14],"class_list":["post-457","post","type-post","status-publish","format-standard","hentry","category-tsukuba_r_2010","tag-tsukuba_r","tag-14"],"_links":{"self":[{"href":"https:\/\/www.roundown.net\/nyushi\/wp-json\/wp\/v2\/posts\/457","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/www.roundown.net\/nyushi\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/www.roundown.net\/nyushi\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/www.roundown.net\/nyushi\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/www.roundown.net\/nyushi\/wp-json\/wp\/v2\/comments?post=457"}],"version-history":[{"count":0,"href":"https:\/\/www.roundown.net\/nyushi\/wp-json\/wp\/v2\/posts\/457\/revisions"}],"wp:attachment":[{"href":"https:\/\/www.roundown.net\/nyushi\/wp-json\/wp\/v2\/media?parent=457"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.roundown.net\/nyushi\/wp-json\/wp\/v2\/categories?post=457"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.roundown.net\/nyushi\/wp-json\/wp\/v2\/tags?post=457"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}