{"id":286,"date":"2012-01-31T23:38:06","date_gmt":"2012-01-31T14:38:06","guid":{"rendered":"http:\/\/roundown.main.jp\/nyushi\/?p=286"},"modified":"2021-09-10T08:41:01","modified_gmt":"2021-09-09T23:41:01","slug":"osr200802","status":"publish","type":"post","link":"https:\/\/www.roundown.net\/nyushi\/osr200802\/","title":{"rendered":"\u962a\u5927\u7406\u7cfb2008\uff1a\u7b2c2\u554f"},"content":{"rendered":"
\n

\u70b9 O \u3067\u4ea4\u308f\u308b \\(2\\) \u3064\u306e\u534a\u76f4\u7dda OX , OY \u304c\u3042\u3063\u3066 \\(\\angle \\text{XOY} = 60^{\\circ}\\) \u3068\u3059\u308b.\r\n\\(2\\) \u70b9 A , B \u304c OX \u4e0a\u306b, O , A , B \u306e\u9806\u306b, \u307e\u305f, \\(2\\) \u70b9 C , D \u304c OY \u4e0a\u306b O , C , D \u306e\u9806\u306b\u4e26\u3093\u3067\u3044\u308b\u3068\u3057\u3066, \u7dda\u5206 AC \u306e\u4e2d\u70b9\u3092 M , \u7dda\u5206 BD \u306e\u4e2d\u70b9\u3092 N \u3068\u3059\u308b.\r\n\u7dda\u5206 AB \u306e\u9577\u3055\u3092 \\(s\\) , \u7dda\u5206 CD \u306e\u9577\u3055\u3092 \\(t\\) \u3068\u3059\u308b\u3068\u304d, \u4ee5\u4e0b\u306e\u554f\u3044\u306b\u7b54\u3048\u3088.<\/p>\r\n

    \r\n

  1. (1)<\/strong>\u3000\u7dda\u5206 MN \u306e\u9577\u3055\u3092 \\(s\\) \u3068 \\(t\\) \u3092\u7528\u3044\u3066\u8868\u305b.<\/p><\/li>\r\n

  2. (2)<\/strong>\u3000\u70b9 A , B \u3068 C , D \u304c, \\(s^2+t^2=1\\) \u3092\u6e80\u305f\u3057\u306a\u304c\u3089\u52d5\u304f\u3068\u304d, \u7dda\u5206 MN \u306e\u9577\u3055\u306e\u6700\u5927\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{\\text{AB}} =s \\overrightarrow{x}\\) , \\(\\overrightarrow{\\text{CD}} =t \\overrightarrow{y}\\) \u3068\u304a\u304f\u3068, \\(\\overrightarrow{x} , \\overrightarrow{y}\\) \u306f\u305d\u308c\u305e\u308c, \u534a\u76f4\u7dda OX , OY \u306e\u5358\u4f4d\u30d9\u30af\u30c8\u30eb\u3067\r\n\\[\\begin{align}\r\n\\left| \\overrightarrow{x} \\right| & = \\left| \\overrightarrow{y} \\right| = 1 , \\\\\r\n\\overrightarrow{x} \\cdot \\overrightarrow{y} & = 1 \\cdot 1 \\cdot \\cos 60^{\\circ} = \\dfrac{1}{2}\n\\end{align}\\]\r\n\u3053\u306e\u3068\u304d\r\n\\[\\begin{align}\r\n\\overrightarrow{\\text{MN}} & = \\overrightarrow{\\text{ON}} -\\overrightarrow{\\text{OM}} \\\\\r\n& = \\dfrac{\\overrightarrow{\\text{OB}} +\\overrightarrow{\\text{OD}}}{2} -\\dfrac{\\overrightarrow{\\text{OA}} +\\overrightarrow{\\text{OC}}}{2} \\\\\r\n& = \\dfrac{\\overrightarrow{\\text{AB}} +\\overrightarrow{\\text{CD}}}{2} \\\\\r\n& = \\dfrac{s \\overrightarrow{x} +t \\overrightarrow{y}}{2}\n\\end{align}\\]\r\n\u306a\u306e\u3067,\r\n\\[\\begin{align}\r\n\\left| \\overrightarrow{\\text{MN}} \\right|^2 & = \\dfrac{s^2 \\left| \\overrightarrow{x} \\right|^2 +2 st \\overrightarrow{x} \\cdot \\overrightarrow{y} +t^2 \\left| \\overrightarrow{y} \\right|^2}{4} \\\\\r\n& = \\dfrac{s^2 +st +t^2}{4}\n\\end{align}\\]\r\n\u3088\u3063\u3066, MN \u306e\u9577\u3055\u306f\r\n\\[\r\n\\underline{\\dfrac{\\sqrt{s^2 +st +t^2}}{2}}\n\\]\r\n

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

    \\(s =\\sin \\theta , \\ t =\\cos \\theta \\ \\left( 0 \\leqq \\theta \\lt 2\\pi \\right)\\) \u3068\u304a\u304f\u3053\u3068\u304c\u3067\u304d\u308b.
    \r\n\u3053\u306e\u3068\u304d\r\n\\[\\begin{align}\r\n\\text{MN} & = \\dfrac{\\sqrt{1 +\\sin \\theta \\cos \\theta}}{2} = \\dfrac{\\sqrt{4 +2\\sin 2 \\theta}}{4} \\\\\r\n\\text{\u2234} \\quad & \\dfrac{\\sqrt{2}}{4} \\leqq \\text{MN} \\leqq \\dfrac{\\sqrt{6}}{4}\n\\end{align}\\]\r\nMN \u304c\u6700\u5927\u3068\u306a\u308b\u306e\u306f, \\(\\sin 2 \\theta =1\\) \u3059\u306a\u308f\u3061 \\(\\theta =\\dfrac{\\pi}{4}\\) \u306e\u3068\u304d.
    \r\n\u3088\u3063\u3066\r\n\\[\r\n\\underline{s =t = \\dfrac{\\sqrt{2}}{2}} \\text{\u306e\u3068\u304d, \u6700\u5927\u5024} \\quad \\underline{\\dfrac{\\sqrt{6}}{4}}\n\\]\r\n","protected":false},"excerpt":{"rendered":"\u70b9 O \u3067\u4ea4\u308f\u308b \\(2\\) \u3064\u306e\u534a\u76f4\u7dda OX , OY \u304c\u3042\u3063\u3066 \\(\\angle \\text{XOY} = 60^{\\circ}\\) \u3068\u3059\u308b. \\(2\\) \u70b9 A , B \u304c OX \u4e0a\u306b, O , A , B \u306e\u9806\u306b … \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":[51],"tags":[142,16],"class_list":["post-286","post","type-post","status-publish","format-standard","hentry","category-osaka_r_2008","tag-osaka_r","tag-16"],"_links":{"self":[{"href":"https:\/\/www.roundown.net\/nyushi\/wp-json\/wp\/v2\/posts\/286","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=286"}],"version-history":[{"count":0,"href":"https:\/\/www.roundown.net\/nyushi\/wp-json\/wp\/v2\/posts\/286\/revisions"}],"wp:attachment":[{"href":"https:\/\/www.roundown.net\/nyushi\/wp-json\/wp\/v2\/media?parent=286"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.roundown.net\/nyushi\/wp-json\/wp\/v2\/categories?post=286"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.roundown.net\/nyushi\/wp-json\/wp\/v2\/tags?post=286"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}