{"id":461,"date":"2012-11-02T12:12:05","date_gmt":"2012-11-02T03:12:05","guid":{"rendered":"http:\/\/www.roundown.net\/nyushi\/?p=461"},"modified":"2021-10-03T15:59:02","modified_gmt":"2021-10-03T06:59:02","slug":"kbr201004","status":"publish","type":"post","link":"https:\/\/www.roundown.net\/nyushi\/kbr201004\/","title":{"rendered":"\u7b51\u6ce2\u5927\u7406\u7cfb2010\uff1a\u7b2c4\u554f"},"content":{"rendered":"
\n

\u70b9 \\(O\\) \u3092\u539f\u70b9\u3068\u3059\u308b\u5ea7\u6a19\u5e73\u9762\u4e0a\u306b, \\(2\\) \u70b9 \\(A \\ (1,0)\\) , \\(B \\ ( \\cos \\theta ,\\sin \\theta ) \\ ( 90^{\\circ} \\lt \\theta \\lt 180^{\\circ} )\\) \u3092\u3068\u308a, \u4ee5\u4e0b\u306e\u6761\u4ef6\u3092\u307f\u305f\u3059 \\(2\\) \u70b9 \\(C , D\\) \u3092\u8003\u3048\u308b.\r\n\\[\r\n\\overrightarrow{OA} \\cdot \\overrightarrow{OC} = 1 , \\ \\overrightarrow{OA} \\cdot \\overrightarrow{OD} = 0 , \\ \\overrightarrow{OB} \\cdot \\overrightarrow{OC} = 0 , \\ \\overrightarrow{OB} \\cdot \\overrightarrow{OD} = 1\r\n\\]\r\n\u307e\u305f, \\(\\triangle OAB\\) \u306e\u9762\u7a4d \\(S _ 1\\) , \\(\\triangle OCD\\) \u306e\u9762\u7a4d \\(S _ 2\\) \u3068\u304a\u304f.<\/p>\r\n

    \r\n

  1. (1)<\/strong>\u3000\u30d9\u30af\u30c8\u30eb \\(\\overrightarrow{OC}\\) , \\(\\overrightarrow{OD}\\) \u306e\u6210\u5206\u3092\u6c42\u3081\u3088.<\/p><\/li>\r\n

  2. (2)<\/strong>\u3000\\(S _ 2 = 2 S _ 1\\) \u304c\u6210\u308a\u7acb\u3064\u3068\u304d, \\(\\theta\\) \u3068 \\(S _ 1\\) \u306e\u5024\u3092\u6c42\u3081\u3088.<\/p><\/li>\r\n

  3. (3)<\/strong>\u3000\\(S = 4 S _ 1 +3 S _ 2\\) \u3092\u6700\u5c0f\u306b\u3059\u308b \\(\\theta\\) \u3068, \u305d\u306e\u3068\u304d\u306e \\(S\\) \u306e\u5024\u3092\u6c42\u3081\u3088.<\/p><\/li>\r\n<\/ol>\r\n

    \r\n\r\n

    \u3010 \u89e3 \u7b54 \u3011<\/h4>\r\n

    (1)<\/strong><\/p>\r\n

    \\(\\overrightarrow{OB} \\cdot \\overrightarrow{OC} =0\\) , \\(\\overrightarrow{OA} \\cdot \\overrightarrow{OD} =0\\) \u3088\u308a, \u5b9f\u6570 \\(s , t\\) \u3092\u7528\u3044\u3066\r\n\\[\r\n\\overrightarrow{OC} = s \\left( \\sin \\theta , -\\cos \\theta \\right) , \\ \\overrightarrow{OD} = t ( 0 , 1 )\r\n\\]\r\n\u3068\u8868\u305b\u308b.
    \r\n\u6761\u4ef6\u3088\u308a\r\n\\[\\begin{align}\r\n\\overrightarrow{OA} \\cdot \\overrightarrow{OC} & = s \\sin \\theta = 1 \\\\\r\n\\text{\u2234} \\quad s & = \\dfrac{1}{\\sin \\theta} \\\\\r\n\\overrightarrow{OB} \\cdot \\overrightarrow{OD} & = t \\sin \\theta = 1 \\\\\r\n\\text{\u2234} \\quad t & = \\dfrac{1}{\\sin \\theta}\r\n\\end{align}\\]\r\n\u3088\u3063\u3066\r\n\\[\r\n\\overrightarrow{OC} = \\underline{\\left( 1 , -\\dfrac{\\cos \\theta}{\\sin \\theta} \\right)} , \\ \\overrightarrow{OD} = \\underline{\\left( 0 , \\dfrac{1}{\\sin \\theta} \\right)}\r\n\\]\r\n

    (2)<\/strong><\/p>\r\n

    \\[\\begin{align}\r\nS _ 1 & = \\dfrac{1}{2} \\cdot 1 \\cdot \\sin \\theta = \\dfrac{\\sin \\theta}{2} , \\\\\r\nS _ 2 & = \\dfrac{1}{2} \\cdot 1 \\cdot \\dfrac{1}{\\sin \\theta} = \\dfrac{1}{2 \\sin \\theta}\r\n\\end{align}\\]\r\n\u306a\u306e\u3067, \\(S _ 2 = 2 S _ 1\\) \u3088\u308a\r\n\\[\\begin{align}\r\n\\dfrac{\\sin \\theta}{2} & = \\dfrac{1}{2 \\sin \\theta} \\\\\r\n\\sin^2 \\theta & = \\dfrac{1}{2} \\\\\r\n\\text{\u2234} \\quad \\sin \\theta & = \\pm \\dfrac{\\sqrt{2}}{2}\r\n\\end{align}\\]\r\n\\(90^{\\circ} \\lt \\theta \\lt 180^{\\circ}\\) \u306a\u306e\u3067\r\n\\[\r\n\\theta = \\underline{135^{\\circ}}\r\n\\]\r\n\u3053\u306e\u3068\u304d\r\n\\[\r\nS _ 1 = \\dfrac{1}{2} \\cdot \\dfrac{\\sqrt{2}}{2} = \\underline{\\dfrac{\\sqrt{2}}{4}}\r\n\\]\r\n

    (3)<\/strong><\/p>\r\n

    \u76f8\u52a0\u76f8\u4e57\u5e73\u5747\u306e\u95a2\u4fc2\u3092\u7528\u3044\u308c\u3070\r\n\\[\\begin{align}\r\nS & = 2 \\sin \\theta +\\dfrac{3}{2 \\sin \\theta} \\\\\r\n& \\geqq 2 \\sqrt{2 \\sin \\theta \\cdot \\dfrac{3}{2 \\sin \\theta}} \\\\\r\n& = 2 \\sqrt{3}\r\n\\end{align}\\]\r\n\u7b49\u53f7\u6210\u7acb\u306f\r\n\\[\\begin{align}\r\n2 \\sin \\theta & = \\dfrac{3}{2 \\sin \\theta} \\\\\r\n\\sin \\theta & = \\pm \\dfrac{\\sqrt{3}}{2}\r\n\\end{align}\\]\r\n\\(90^{\\circ} \\lt \\theta \\lt 180^{\\circ}\\) \u306a\u306e\u3067\r\n\\[\r\n\\theta = 120^{\\circ}\r\n\\]\r\n\u3088\u3063\u3066, \\(\\theta = \\underline{120^{\\circ}}\\) \u306e\u3068\u304d, \u6700\u5c0f\u5024 \\(\\underline{2 \\sqrt{3}}\\) \u3092\u3068\u308b.<\/p>\r\n","protected":false},"excerpt":{"rendered":"\u70b9 \\(O\\) \u3092\u539f\u70b9\u3068\u3059\u308b\u5ea7\u6a19\u5e73\u9762\u4e0a\u306b, \\(2\\) \u70b9 \\(A \\ (1,0)\\) , \\(B \\ ( \\cos \\theta ,\\sin \\theta ) \\ ( 90^{\\circ} \\lt \\theta \\lt … \u7d9a\u304d\u3092\u8aad\u3080 →<\/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-461","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\/461","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=461"}],"version-history":[{"count":0,"href":"https:\/\/www.roundown.net\/nyushi\/wp-json\/wp\/v2\/posts\/461\/revisions"}],"wp:attachment":[{"href":"https:\/\/www.roundown.net\/nyushi\/wp-json\/wp\/v2\/media?parent=461"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.roundown.net\/nyushi\/wp-json\/wp\/v2\/categories?post=461"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.roundown.net\/nyushi\/wp-json\/wp\/v2\/tags?post=461"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}