{"id":435,"date":"2012-06-22T22:35:13","date_gmt":"2012-06-22T13:35:13","guid":{"rendered":"http:\/\/roundown.main.jp\/nyushi\/?p=435"},"modified":"2021-09-30T08:43:47","modified_gmt":"2021-09-29T23:43:47","slug":"kbr201205","status":"publish","type":"post","link":"https:\/\/www.roundown.net\/nyushi\/kbr201205\/","title":{"rendered":"\u7b51\u6ce2\u5927\u7406\u7cfb2012\uff1a\u7b2c5\u554f"},"content":{"rendered":"
\n

\u4ee5\u4e0b\u306e\u554f\u3044\u306b\u7b54\u3048\u3088.<\/p>\r\n

    \r\n

  1. (1)<\/strong>\u3000\u5ea7\u6a19\u5e73\u9762\u306b\u304a\u3044\u3066\u539f\u70b9\u306e\u307e\u308f\u308a\u306b\u89d2 \\(\\theta\\) \uff08 \\(0 \\lt \\theta \\lt \\pi\\) \uff09\u3060\u3051\u56de\u8ee2\u3059\u308b\u79fb\u52d5\u3092\u8868\u3059\u884c\u5217\u3092 \\(A\\) \u3068\u3059\u308b.\r\n\\(A\\) \u304c\u7b49\u5f0f \\(A^2 -A +E = O\\) \u3092\u6e80\u305f\u3059\u3068\u304d, \\(\\theta\\) \u3068 \\(A\\) \u3092\u6c42\u3081\u3088.\r\n\u305f\u3060\u3057, \\(E = \\left( \\begin{array}{cc} 1 & 0 \\\\ 0 & 1 \\end{array} \\right)\\) , \\(O = \\left( \\begin{array}{cc} 0 & 0 \\\\ 0 & 0 \\end{array} \\right)\\) \u3067\u3042\u308b.<\/p><\/li>\r\n

  2. (2)<\/strong>\u3000\u76f4\u7dda \\(y = \\sqrt{3} x\\) \u306b\u95a2\u3059\u308b\u5bfe\u79f0\u79fb\u52d5\u3092\u8868\u3059\u884c\u5217 \\(B\\) \u3092\u6c42\u3081\u3088.<\/p><\/li>\r\n

  3. (3)<\/strong>\u3000\u76f4\u7dda \\(y = kx\\) \u306b\u95a2\u3059\u308b\u5bfe\u79f0\u79fb\u52d5\u3092\u8868\u3059\u884c\u5217\u3092 \\(C\\) \u3068\u3059\u308b, (1)<\/strong> , (2)<\/strong> \u306b\u304a\u3044\u3066\u6c42\u3081\u305f \\(A , B\\) \u306b\u5bfe\u3057\u3066 \\(BC = A\\) \u304c\u6210\u308a\u7acb\u3064\u3068\u304d, \\(k\\) \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

    \\(A= \\left( \\begin{array}{cc} \\cos \\theta & -\\sin \\theta \\\\ \\sin \\theta & \\cos \\theta \\end{array} \\right)\\) \u306a\u306e\u3067, \u30b1\u30fc\u30ea\u30fc\u30fb\u30cf\u30df\u30eb\u30c8\u30f3\u306e\u5b9a\u7406\u3088\u308a\r\n\\[\\begin{align}\r\n2 \\cos \\theta & = 1 \\\\\r\n\\text{\u2234} \\quad \\cos \\theta & = \\dfrac{1}{2}\r\n\\end{align}\\]\r\n\\(0 \\lt \\theta \\lt \\pi\\) \u306a\u306e\u3067\r\n\\[\r\n\\theta =\\underline{\\dfrac{\\pi}{3}} , \\ A =\\underline{\\left( \\begin{array}{cc} \\dfrac{1}{2} & -\\dfrac{\\sqrt{3}}{2} \\\\ \\dfrac{\\sqrt{3}}{2} & \\dfrac{1}{2} \\end{array} \\right)}\r\n\\]\r\n

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

    \\(x\\) \u8ef8\u306b\u95a2\u3059\u308b\u5bfe\u79f0\u79fb\u52d5\u3092\u8868\u3059\u884c\u5217 \\(D\\) \u306f\r\n\\[\r\nD = \\left( \\begin{array}{cc} 1 & 0 \\\\ 0 & -1 \\end{array} \\right)\r\n\\]\r\n\u307e\u305f\r\n\\[\r\nA^{-1} = \\left( \\begin{array}{cc} \\dfrac{1}{2} & \\dfrac{\\sqrt{3}}{2} \\\\ -\\dfrac{\\sqrt{3}}{2} & \\dfrac{1}{2} \\end{array} \\right)\r\n\\]\r\n\u3088\u3063\u3066, \u6c42\u3081\u308b\u884c\u5217 \\(B\\) \u306f\r\n\\[\\begin{align}\r\nB & = ADA^{-1} \\\\\r\n& =\\left( \\begin{array}{cc} \\dfrac{1}{2} & -\\dfrac{\\sqrt{3}}{2} \\\\ \\dfrac{\\sqrt{3}}{2} & \\dfrac{1}{2} \\end{array} \\right) \\left( \\begin{array}{cc} 1 & 0 \\\\ 0 & -1 \\end{array} \\right) \\left( \\begin{array}{cc} \\dfrac{1}{2} & \\dfrac{\\sqrt{3}}{2} \\\\ -\\dfrac{\\sqrt{3}}{2} & \\dfrac{1}{2} \\end{array} \\right) \\\\\r\n& =\\underline{\\left( \\begin{array}{cc} -\\dfrac{1}{2} & \\dfrac{\\sqrt{3}}{2} \\\\ \\dfrac{\\sqrt{3}}{2} & \\dfrac{1}{2} \\end{array} \\right)}\r\n\\end{align}\\]\r\n

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

    \\(k =\\tan \\alpha \\ \\left( -\\dfrac{\\pi}{2} \\lt \\alpha \\lt \\dfrac{\\pi}{2} \\right)\\) \u3068\u304a\u304f\u3068, (2)<\/strong> \u3068\u540c\u69d8\u306b\u8003\u3048\u3066\r\n\\[\\begin{align}\r\nC & = \\left( \\begin{array}{cc} \\cos \\alpha & -\\sin \\alpha \\\\ \\sin \\alpha & \\cos \\alpha \\end{array} \\right) \\left( \\begin{array}{cc} 1 & 0 \\\\ 0 & -1 \\end{array} \\right) \\left( \\begin{array}{cc} \\cos \\alpha & \\sin \\alpha \\\\ -\\sin \\alpha & \\cos \\alpha \\end{array} \\right) \\\\\r\n& = \\left( \\begin{array}{cc} \\cos \\alpha & -\\sin \\alpha \\\\ \\sin \\alpha & \\cos \\alpha \\end{array} \\right) \\left( \\begin{array}{cc} \\cos \\alpha & \\sin \\alpha \\\\ \\sin \\alpha & -\\cos \\alpha \\end{array} \\right) \\\\\r\n& = \\left( \\begin{array}{cc} \\cos 2 \\alpha & \\sin 2 \\alpha \\\\ \\sin 2 \\alpha & -\\cos 2 \\alpha \\end{array} \\right) \\quad ... [1]\r\n\\end{align}\\]\r\n\u5bfe\u79f0\u79fb\u52d5\u306e\u6027\u8cea\u3092\u8003\u3048\u308c\u3070, \\(B^{-1} =B\\) \u306a\u306e\u3067, \\(BC=A\\) \u3088\u308a\r\n\\[\\begin{align}\r\nC & = B^{-1}A = BA \\\\\r\n& = \\left( \\begin{array}{cc} -\\dfrac{1}{2} & \\dfrac{\\sqrt{3}}{2} \\\\ \\dfrac{\\sqrt{3}}{2} & \\dfrac{1}{2} \\end{array} \\right) \\left( \\begin{array}{cc} \\dfrac{1}{2} & -\\dfrac{\\sqrt{3}}{2} \\\\ \\dfrac{\\sqrt{3}}{2} & \\dfrac{1}{2} \\end{array} \\right) \\\\\r\n& = \\left( \\begin{array}{cc} \\dfrac{1}{2} & \\dfrac{\\sqrt{3}}{2} \\\\ \\dfrac{\\sqrt{3}}{2} & -\\dfrac{1}{2} \\end{array} \\right) \\quad ... [2]\r\n\\end{align}\\]\r\n[1] \u3068 [2] \u3092\u6bd4\u8f03\u3057\u3066\r\n\\[\\begin{align}\r\n\\cos 2 \\alpha =\\dfrac{1}{2} & , \\ \\sin 2 \\alpha =\\dfrac{\\sqrt{3}}{2} \\\\\r\n\\text{\u2234} \\quad \\alpha & = \\dfrac{\\pi}{6}\r\n\\end{align}\\]\r\n\u3088\u3063\u3066\r\n\\[\r\nk = \\underline{\\dfrac{\\sqrt{3}}{3}}\r\n\\]\r\n","protected":false},"excerpt":{"rendered":"\u4ee5\u4e0b\u306e\u554f\u3044\u306b\u7b54\u3048\u3088. (1)\u3000\u5ea7\u6a19\u5e73\u9762\u306b\u304a\u3044\u3066\u539f\u70b9\u306e\u307e\u308f\u308a\u306b\u89d2 \\(\\theta\\) \uff08 \\(0 \\lt \\theta \\lt \\pi\\) \uff09\u3060\u3051\u56de\u8ee2\u3059\u308b\u79fb\u52d5\u3092\u8868\u3059\u884c\u5217\u3092 \\(A\\) \u3068\u3059\u308b. \\(A\\) \u304c\u7b49\u5f0f \\(A … \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":[65],"tags":[144,68],"class_list":["post-435","post","type-post","status-publish","format-standard","hentry","category-tsukuba_r_2012","tag-tsukuba_r","tag-68"],"_links":{"self":[{"href":"https:\/\/www.roundown.net\/nyushi\/wp-json\/wp\/v2\/posts\/435","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=435"}],"version-history":[{"count":0,"href":"https:\/\/www.roundown.net\/nyushi\/wp-json\/wp\/v2\/posts\/435\/revisions"}],"wp:attachment":[{"href":"https:\/\/www.roundown.net\/nyushi\/wp-json\/wp\/v2\/media?parent=435"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.roundown.net\/nyushi\/wp-json\/wp\/v2\/categories?post=435"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.roundown.net\/nyushi\/wp-json\/wp\/v2\/tags?post=435"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}