{"id":470,"date":"2012-11-10T22:33:03","date_gmt":"2012-11-10T13:33:03","guid":{"rendered":"http:\/\/www.roundown.net\/nyushi\/?p=470"},"modified":"2021-09-23T10:21:59","modified_gmt":"2021-09-23T01:21:59","slug":"thr201202","status":"publish","type":"post","link":"https:\/\/www.roundown.net\/nyushi\/thr201202\/","title":{"rendered":"\u6771\u5317\u5927\u7406\u7cfb2012\uff1a\u7b2c2\u554f"},"content":{"rendered":"
\n

\\(m\\) \u3092\u5b9f\u6570\u3068\u3059\u308b.\r\n\u5ea7\u6a19\u5e73\u9762\u4e0a\u3067\u76f4\u7dda \\(y = x\\) \u306b\u95a2\u3059\u308b\u5bfe\u79f0\u79fb\u52d5\u3092\u8868\u3059 \\(1\\) \u6b21\u5909\u63db\u3092 \\(f\\) \u3068\u3057, \u76f4\u7dda \\(y = mx\\) \u306b\u95a2\u3059\u308b\u5bfe\u79f0\u79fb\u52d5\u3092\u8868\u3059 \\(1\\) \u6b21\u5909\u63db\u3092 \\(g\\) \u3068\u3059\u308b. \u4ee5\u4e0b\u306e\u554f\u3044\u306b\u7b54\u3048\u3088.<\/p>\r\n

    \r\n

  1. (1)<\/strong>\u3000\\(1\\) \u6b21\u5909\u63db \\(g\\) \u3092\u8868\u3059\u884c\u5217 \\(A\\) \u3092\u6c42\u3081\u3088.<\/p><\/li>\r\n

  2. (2)<\/strong>\u3000\u5408\u6210\u5909\u63db \\(g \\circ f\\) \u3092\u8868\u3059\u884c\u5217 \\(B\\) \u3092\u6c42\u3081\u3088.<\/p><\/li>\r\n

  3. (3)<\/strong>\u3000\\(B^3 = \\left( \\begin{array}{cc} 1 & 0 \\\\ 0 & 1 \\end{array} \\right)\\) \u3068\u306a\u308b \\(m\\) \u3092\u3059\u3079\u3066\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

    \\(g\\) \u306b\u3088\u3063\u3066, \u6b21\u306e \\(2\\) \u70b9\u306f\r\n\\[\r\n(1,m) \\rightarrow (1,m) , \\ (-m,1) \\rightarrow (m,-1)\n\\]\r\n\u3068\u79fb\u52d5\u3059\u308b\u306e\u3067\r\n\\[\r\nA \\left( \\begin{array}{cc} 1 & -m \\\\ m & 1 \\end{array} \\right) = \\left( \\begin{array}{cc} 1 & m \\\\ m & -1 \\end{array} \\right)\n\\]\r\n\u3088\u3063\u3066, \u4e21\u8fba\u53f3\u304b\u3089 \\(\\left( \\begin{array}{cc} 1 & m \\\\ m & 1 \\end{array} \\right)^{-1}\\) \u3092\u639b\u3051\u3066\r\n\\[\\begin{align}\r\nA & =\\dfrac{1}{1+m^2} \\left( \\begin{array}{cc} 1 & m \\\\ m & -1 \\end{array} \\right) \\left( \\begin{array}{cc} 1 & m \\\\ -m & 1 \\end{array} \\right) \\\\\r\n& =\\underline{\\dfrac{1}{1+m^2} \\left( \\begin{array}{cc} 1-m^2 & 2m \\\\ 2m & m^2-1 \\end{array} \\right)}\n\\end{align}\\]\r\n

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

    (1)<\/strong> \u306e\u7d50\u679c\u3088\u308a, \\(f\\) \u3092\u8868\u3059\u884c\u5217 \\(C\\) \u306f\r\n\\[\r\nC = \\dfrac{1}{2} \\left( \\begin{array}{cc} 0 & 2 \\\\ 2 & 0 \\end{array} \\right) =\\left( \\begin{array}{cc} 0 & 1 \\\\ 1 & 0 \\end{array} \\right)\n\\]\r\n\u306a\u306e\u3067\r\n\\[\\begin{align}\r\nB & = AC \\\\\r\n& =\\dfrac{1}{1+m^2} \\left( \\begin{array}{cc} 1-m^2 & 2m \\\\ 2m & m^2-1 \\end{array} \\right) \\left( \\begin{array}{cc} 0 & 1 \\\\ 1 & 0 \\end{array} \\right) \\\\\r\n& =\\underline{\\dfrac{1}{1+m^2} \\left( \\begin{array}{cc} 2m & 1-m^2 \\\\ m^2-1 & 2m \\end{array} \\right)}\n\\end{align}\\]\r\n

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

    \\[\r\n\\left( \\dfrac{2m}{1+m^2} \\right)^2 +\\left( \\dfrac{1-m^2}{1+m^2} \\right)^2 = 1\n\\]\r\n\u306a\u306e\u3067, \\(0 \\leqq \\theta \\lt 2\\pi\\) \u3092\u7528\u3044\u3066\r\n\\[\r\n\\cos \\theta =\\dfrac{2m}{1+m^2} , \\ \\sin \\theta =\\dfrac{1-m^2}{1+m^2} \\quad ... [1]\n\\]\r\n\u3068\u304a\u3044\u3066\r\n\\[\r\nB = \\left( \\begin{array}{cc} \\cos \\theta & -\\sin \\theta \\\\ \\sin \\theta & \\cos \\theta \\end{array} \\right)\n\\]\r\n\u3068\u8868\u305b\u308b.
    \r\n\u3057\u305f\u304c\u3063\u3066\r\n\\[\\begin{align}\r\nB^3 & = \\left( \\begin{array}{cc} \\cos 3 \\theta & -\\sin 3 \\theta \\\\ \\sin 3 \\theta & \\cos 3 \\theta \\end{array} \\right) = E \\\\\r\n\\text{\u2234} \\quad & \\cos 3 \\theta =1 , \\ \\sin 3 \\theta = 0\n\\end{align}\\]\r\n\u3057\u305f\u304c\u3063\u3066, \u6574\u6570 \\(n\\) \u3092\u7528\u3044\u3066\r\n\\[\\begin{align}\r\n3 \\theta & = 2n \\pi \\\\\r\n\\text{\u2234} \\quad \\theta = 0 , & \\dfrac{2 \\pi}{3} , \\dfrac{4 \\pi}{3}\n\\end{align}\\]\r\n

      \r\n

    1. 1*<\/strong>\u3000\\(\\theta = 0\\) \u3059\u306a\u308f\u3061 \\(\\cos \\theta = 1\\) \u306e\u3068\u304d
      \r\n[1] \u3088\u308a\r\n\\[\\begin{align}\r\n\\dfrac{2m}{1+m^2} & = 0 \\\\\r\n\\text{\u2234} \\quad m & = 0\n\\end{align}\\]<\/li>\r\n

    2. 2*<\/strong>\u3000\\(\\theta = \\dfrac{2 \\pi}{3} , \\dfrac{4 \\pi}{3}\\) \u3059\u306a\u308f\u3061 \\(\\cos \\theta = -\\dfrac{1}{2}\\) \u306e\u3068\u304d
      \r\n[1] \u3088\u308a\r\n\\[\\begin{align}\r\n\\dfrac{2m}{1+m^2} & = -\\dfrac{1}{2} \\\\\r\nm^2 +4m +1 & = 0 \\\\\r\n\\text{\u2234} \\quad m & = -2 \\pm \\sqrt{3}\n\\end{align}\\]<\/li>\r\n<\/ol>\r\n

      \u4ee5\u4e0a\u3088\u308a\r\n\\[\r\nm = \\underline{0 , -2 \\pm \\sqrt{3}}\n\\]","protected":false},"excerpt":{"rendered":"\\(m\\) \u3092\u5b9f\u6570\u3068\u3059\u308b. \u5ea7\u6a19\u5e73\u9762\u4e0a\u3067\u76f4\u7dda \\(y = x\\) \u306b\u95a2\u3059\u308b\u5bfe\u79f0\u79fb\u52d5\u3092\u8868\u3059 \\(1\\) \u6b21\u5909\u63db\u3092 \\(f\\) \u3068\u3057, \u76f4\u7dda \\(y = mx\\) \u306b\u95a2\u3059\u308b\u5bfe\u79f0\u79fb\u52d5\u3092\u8868\u3059 \\(1\\) \u6b21\u5909\u63db\u3092 \\(g\\) \u3068 … \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":[72],"tags":[68,148],"class_list":["post-470","post","type-post","status-publish","format-standard","hentry","category-tohoku_r_2012","tag-68","tag-tohoku_r"],"_links":{"self":[{"href":"https:\/\/www.roundown.net\/nyushi\/wp-json\/wp\/v2\/posts\/470","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=470"}],"version-history":[{"count":0,"href":"https:\/\/www.roundown.net\/nyushi\/wp-json\/wp\/v2\/posts\/470\/revisions"}],"wp:attachment":[{"href":"https:\/\/www.roundown.net\/nyushi\/wp-json\/wp\/v2\/media?parent=470"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.roundown.net\/nyushi\/wp-json\/wp\/v2\/categories?post=470"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.roundown.net\/nyushi\/wp-json\/wp\/v2\/tags?post=470"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}