{"id":281,"date":"2012-01-29T22:34:14","date_gmt":"2012-01-29T13:34:14","guid":{"rendered":"http:\/\/roundown.main.jp\/nyushi\/?p=281"},"modified":"2021-09-10T21:20:01","modified_gmt":"2021-09-10T12:20:01","slug":"tok200804","status":"publish","type":"post","link":"https:\/\/www.roundown.net\/nyushi\/tok200804\/","title":{"rendered":"\u6771\u5de5\u59272008\uff1a\u7b2c4\u554f"},"content":{"rendered":"
\n

\u5e73\u9762\u306e\u539f\u70b9 \\(O\\) \u3092\u7aef\u70b9\u3068\u3057, \\(x\\) \u8ef8\u3068\u306a\u3059\u89d2\u304c\u305d\u308c\u305e\u308c \\(\\alpha , -\\alpha \\ \\left( \\text{\u305f\u3060\u3057} \\ 0 \\lt \\alpha \\lt \\dfrac{\\pi}{3} \\right)\\) \u3067\u3042\u308b\u534a\u76f4\u7dda\u3092 \\(L _ 1 , L _ 2\\) \u3068\u3059\u308b. \\(L _ 1\\) \u4e0a\u306b\u70b9 \\(P\\) , \\(L _ 2\\) \u4e0a\u306b\u70b9 \\(Q\\) \u3092\u7dda\u5206 \\(PQ\\) \u306e\u9577\u3055\u304c \\(1\\) \u3068\u306a\u308b\u3088\u3046\u306b\u3068\u308a, \u70b9 \\(R\\) \u3092\u76f4\u7dda \\(PQ\\) \u306b\u5bfe\u3057\u539f\u70b9 \\(O\\) \u306e\u53cd\u5bfe\u5074\u306b \\(\\triangle PQR\\) \u304c\u6b63\u4e09\u89d2\u5f62\u306b\u306a\u308b\u3088\u3046\u306b\u3068\u308b.<\/p>\r\n

    \r\n

  1. (1)<\/strong>\u3000\u7dda\u5206 \\(PQ\\) \u304c \\(x\\) \u8ef8\u3068\u76f4\u4ea4\u3059\u308b\u3068\u304d, \u70b9 \\(R\\) \u306e\u5ea7\u6a19\u3092\u6c42\u3081\u3088.<\/p><\/li>\r\n

  2. (2)<\/strong>\u3000\\(2\\) \u70b9 \\(P , Q\\) \u304c, \u7dda\u5206 \\(PQ\\) \u306e\u9577\u3055\u3092 \\(1\\) \u306b\u4fdd\u3063\u305f\u307e\u307e \\(L _ 1 , L _ 2\\) \u4e0a\u3092\u52d5\u304f\u3068\u304d, \u70b9 \\(R\\) \u306e\u8ecc\u8de1\u306f\u3042\u308b\u6955\u5186\u306e\u4e00\u90e8\u3067\u3042\u308b\u3053\u3068\u3092\u793a\u305b.<\/p><\/li>\r\n<\/ol>\r\n

    \r\n\r\n

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

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

    \\(PQ\\) \u306e\u4e2d\u70b9\u3092 \\(M\\) \u3068\u304a\u304f\u3068\r\n\\[\\begin{align}\r\nOM \\tan \\alpha & = \\dfrac{1}{2} \\\\\r\n\\text{\u2234} \\quad OM & = \\dfrac{1}{2 \\tan \\alpha}\r\n\\end{align}\\]\r\n\\(MR =\\dfrac{\\sqrt{3}}{2}\\) \u306a\u306e\u3067, \u70b9 \\(R\\) \u306e\u5ea7\u6a19\u306f\r\n\\[\r\n\\underline{\\left( \\dfrac{1}{2 \\tan \\alpha} +\\dfrac{\\sqrt{3}}{2} , 0 \\right)}\r\n\\]\r\n

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

    \\(OP = p , \\ OQ = q\\) \u3068\u304a\u304f\u3068\r\n\\[\\begin{align}\r\nP \\ & ( p \\cos \\alpha , p \\sin \\alpha ) , \\quad Q \\ ( q \\cos \\alpha , -q \\sin \\alpha ) , \\\\\r\nM \\ & \\left( \\dfrac{p+q}{2} \\cos \\alpha , \\dfrac{p-q}{2} \\sin \\alpha \\right)\r\n\\end{align}\\]\r\n\\(PQ = 1\\) \u306a\u306e\u3067, \u4f59\u5f26\u5b9a\u7406\u3088\u308a\r\n\\[\r\np^2 +q^2 -2pq \\cos 2\\alpha = 1 \\quad ... [1]\r\n\\]\r\n\u307e\u305f\r\n\\[\r\n\\overrightarrow{PQ} =\\left( \\begin{array}{c} (q-p) \\cos \\alpha \\\\ -(p+q) \\sin \\alpha \\end{array} \\right)\r\n\\]\r\n\\(\\overrightarrow{PQ} \\perp \\overrightarrow{MR}\\) , \\(MR =\\dfrac{\\sqrt{3}}{2}\\) \u306a\u306e\u3067\r\n\\[\r\n\\overrightarrow{MR} = \\dfrac{\\sqrt{3}}{2} \\left( \\begin{array}{c} (p+q) \\sin \\alpha \\\\ (q-p) \\cos \\alpha \\end{array} \\right)\r\n\\]\r\n\u3057\u305f\u304c\u3063\u3066\r\n\\[\\begin{align}\r\n\\overrightarrow{OR} & = \\overrightarrow{OM} +\\overrightarrow{MR} \\\\\r\n& = \\left( \\begin{array}{c} \\dfrac{p+q}{2} \\cos \\alpha +\\dfrac{\\sqrt{3} (p+q)}{2} \\sin \\alpha \\\\ \\dfrac{p-q}{2} \\sin \\alpha +\\dfrac{\\sqrt{3} (q-p)}{2} \\cos \\alpha \\end{array} \\right) \\\\\r\n& = \\left( \\begin{array}{c} \\dfrac{\\sqrt{3} \\sin \\alpha +\\cos \\alpha}{2} (p+q) \\\\ \\dfrac{\\sin \\alpha -\\sqrt{3} \\cos \\alpha}{2} (p-q) \\end{array} \\right) \\\\\r\n& = \\left( \\begin{array}{c} (p+q) \\sin \\left( \\alpha +\\dfrac{\\pi}{6} \\right) \\\\ (p-q) \\sin \\left( \\alpha -\\dfrac{\\pi}{3} \\right) \\end{array} \\right)\r\n\\end{align}\\]\r\n\\(R \\ (X,Y)\\) \u3068\u8868\u3057, \\(S = \\sin \\left( \\alpha +\\dfrac{\\pi}{6} \\right)\\) , \\(T = \\sin \\left( \\alpha -\\dfrac{\\pi}{3} \\right)\\) \u3068\u304a\u3051\u3070\r\n\\[\\begin{align}\r\nX = (p+q) S & , \\ Y = (p-q) T \\\\\r\n\\text{\u2234} \\quad p = \\dfrac{TX+SY}{2ST} & , \\ q = \\dfrac{TX-SY}{2ST}\r\n\\end{align}\\]\r\n\u3053\u308c\u3092 [1] \u306b\u4ee3\u5165\u3059\u308b\u3068\r\n\\[\\begin{align}\r\n\\left( \\dfrac{TX+SY}{2ST} \\right)^2 +\\left( \\dfrac{TX-SY}{2ST} \\right)^2 \\qquad & \\\\\r\n-2 \\dfrac{TX+SY}{2ST} \\cdot \\dfrac{TX-SY}{2ST} \\cos 2\\alpha & = 1 \\\\\r\n2T^2X^2 +2S^2Y^2 -2 \\left( T^2X^2 -S^2Y^2 \\right) \\cos 2 \\alpha & = 4S^2T^2 \\\\\r\nT^2 ( 1-\\cos 2 \\alpha ) X^2 +3 S^2 ( 1-\\cos 2 \\alpha ) Y^2 & = 2S^2T^2 \\\\\r\n\\dfrac{2 \\sin^2 \\alpha X^2}{2 S^2} +\\dfrac{6 \\sin^2 \\alpha X^2}{2T^2} & = 1 \\\\\r\n\\text{\u2234} \\quad \\dfrac{X^2}{\\left\\{ \\dfrac{\\sin \\left( \\alpha +\\frac{\\pi}{6} \\right)}{\\sin \\alpha} \\right\\}^2} +\\dfrac{Y^2}{\\left\\{ \\dfrac{\\sin \\left( \\alpha -\\frac{\\pi}{3} \\right)}{\\sqrt{3} \\sin \\alpha} \\right\\}^2} & = 1\r\n\\end{align}\\]\r\n\u3088\u3063\u3066, \u70b9 \\(R\\) \u306e\u8ecc\u8de1\u306f\u6955\u5186\u306e\u4e00\u90e8\u3068\u3044\u3048\u308b.<\/p>\r\n","protected":false},"excerpt":{"rendered":"\u5e73\u9762\u306e\u539f\u70b9 \\(O\\) \u3092\u7aef\u70b9\u3068\u3057, \\(x\\) \u8ef8\u3068\u306a\u3059\u89d2\u304c\u305d\u308c\u305e\u308c \\(\\alpha , -\\alpha \\ \\left( \\text{\u305f\u3060\u3057} \\ 0 \\lt \\alpha \\lt \\dfrac{\\pi}{3} \\ … \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":[50],"tags":[141,16],"class_list":["post-281","post","type-post","status-publish","format-standard","hentry","category-toko_2008","tag-toko","tag-16"],"_links":{"self":[{"href":"https:\/\/www.roundown.net\/nyushi\/wp-json\/wp\/v2\/posts\/281","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=281"}],"version-history":[{"count":0,"href":"https:\/\/www.roundown.net\/nyushi\/wp-json\/wp\/v2\/posts\/281\/revisions"}],"wp:attachment":[{"href":"https:\/\/www.roundown.net\/nyushi\/wp-json\/wp\/v2\/media?parent=281"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.roundown.net\/nyushi\/wp-json\/wp\/v2\/categories?post=281"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.roundown.net\/nyushi\/wp-json\/wp\/v2\/tags?post=281"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}