{"id":229,"date":"2011-12-03T00:26:13","date_gmt":"2011-12-02T15:26:13","guid":{"rendered":"http:\/\/roundown.main.jp\/nyushi\/?p=229"},"modified":"2021-10-03T20:21:37","modified_gmt":"2021-10-03T11:21:37","slug":"kbr200901","status":"publish","type":"post","link":"https:\/\/www.roundown.net\/nyushi\/kbr200901\/","title":{"rendered":"\u7b51\u6ce2\u5927\u7406\u7cfb2009\uff1a\u7b2c1\u554f"},"content":{"rendered":"
    \r\n

  1. (1)<\/strong>\u3000\u7b49\u5f0f \\(\\cos 3\\theta = 4\\cos^3 \\theta -3 \\cos \\theta\\) \u3092\u793a\u305b.<\/p><\/li>\r\n

  2. (2)<\/strong>\u3000\\(2 \\cos 80^{\\circ}\\) \u306f \\(3\\) \u6b21\u65b9\u7a0b\u5f0f \\(x^3-3x+1 = 0\\) \u306e\u89e3\u3067\u3042\u308b\u3053\u3068\u3092\u793a\u305b.<\/p><\/li>\r\n

  3. (3)<\/strong>\u3000\\(x^3-3x+1 = \\left( x -2\\cos 80^{\\circ} \\right) \\left( x -2\\cos \\alpha \\right) \\left( x -2\\cos \\beta \\right)\\) \u3068\u306a\u308b\u89d2\u5ea6 \\(\\alpha , \\beta\\) \u3092\u6c42\u3081\u3088. \u305f\u3060\u3057, \\(0^{\\circ} \\lt \\alpha \\lt \\beta \\lt 180^{\\circ}\\) \u3068\u3059\u308b.<\/p><\/li>\r\n<\/ol>\r\n

    \r\n\r\n

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

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

    \u52a0\u6cd5\u5b9a\u7406\u3092\u7528\u3044\u308c\u3070\r\n\\[\\begin{align}\r\n\\sin 2 \\theta & = \\sin \\left( \\theta +\\theta \\right) \\\\\r\n& = \\sin \\theta \\cos \\theta +\\cos \\theta \\sin \\theta \\\\\r\n& = 2 \\sin \\theta \\cos \\theta , \\\\\r\n\\cos 2\\theta & = \\cos \\left( \\theta +\\theta \\right) \\\\\r\n& = \\cos \\theta \\cos \\theta -\\sin \\theta \\sin \\theta \\\\\r\n& = 2\\cos^2 \\theta -1\r\n\\end{align}\\]\r\n\u3053\u308c\u3089\u3092\u7528\u3044\u308c\u3070\r\n\\[\\begin{align}\r\n\\cos 3 \\theta & = \\cos \\left( 2\\theta +\\theta \\right) \\\\\r\n& =\\cos 2\\theta \\cos \\theta -\\sin 2\\theta \\sin \\theta \\\\\r\n& =\\left( 2\\cos^2 \\theta -1 \\right) \\cos \\theta -2\\sin^2 \\theta \\cos \\theta \\\\\r\n& = 2\\cos^3 \\theta -\\cos \\theta -2\\cos \\theta +2\\cos^3 \\theta \\\\\r\n& = 4\\cos^3 \\theta -3\\cos \\theta\r\n\\end{align}\\]\r\n

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

    \\(f(x) =x^3 -3x +1\\) \u3068\u304a\u304f.
    \r\n(1)<\/strong> \u306e\u7d50\u679c\u3088\u308a, \\(\\cos^3 \\theta = \\dfrac{\\cos 3\\theta +3\\cos \\theta}{4}\\) \u306a\u306e\u3067\r\n\\[\\begin{align}\r\nf \\left( 2 \\cos 80^{\\circ} \\right) & = 8\\cos^3 80^{\\circ} -6\\cos 80^{\\circ} +1 \\\\\r\n& = 2 \\left( \\cos 240^{\\circ} +3\\cos 80^{\\circ} \\right) -6\\cos 80^{\\circ} +1 \\\\\r\n& = 2 \\left( - \\dfrac{1}{2} \\right) +1 = 0\r\n\\end{align}\\]\r\n\u3088\u3063\u3066, \\(2 \\cos 80^{\\circ}\\) \u306f \\(f(x)=0\\) \u306e\u89e3\u3067\u3042\u308b.<\/p>\r\n

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

    \\(f(x) = 0\\) \u306e\u89e3\u3092\u6c42\u3081\u308c\u3070\u3088\u3044.
    \r\n(2)<\/strong> \u306e\u7d4c\u904e\u3088\u308a, \\(2 \\cos t \\ ( \\ 0^{\\circ} \\lt t \\lt 180^{\\circ} \\ ... [1] \\ )\\) \u304c \\(f(x)\\) \u306e\u89e3\u306b\u306a\u308b\u306e\u306f\r\n\\[\r\n\\cos 3t = -\\dfrac{1}{2}\r\n\\]\r\n\u3068\u306a\u308b\u3068\u304d\u3067\u3042\u308b.
    \r\n[1] \u3088\u308a, \\(0^{\\circ} \\lt 3t \\lt 540^{\\circ}\\) \u306a\u306e\u3067\r\n\\[\\begin{align}\r\n3t & = 120^{\\circ} , 240^{\\circ} , 480^{\\circ} \\\\\r\n\\text{\u2234} \\quad t & = 40^{\\circ} , 80^{\\circ} , 160^{\\circ}\r\n\\end{align}\\]\r\n\u3088\u3063\u3066,\r\n\\[\r\n\\alpha = \\underline{40^{\\circ}} , \\ \\beta =\\underline{160^{\\circ}}\r\n\\]\r\n","protected":false},"excerpt":{"rendered":"(1)\u3000\u7b49\u5f0f \\(\\cos 3\\theta = 4\\cos^3 \\theta -3 \\cos \\theta\\) \u3092\u793a\u305b. (2)\u3000\\(2 \\cos 80^{\\circ}\\) \u306f \\(3\\) \u6b21\u65b9\u7a0b\u5f0f \\(x^3-3x+1 … \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":[39],"tags":[144,15],"class_list":["post-229","post","type-post","status-publish","format-standard","hentry","category-tsukuba_r_2009","tag-tsukuba_r","tag-15"],"_links":{"self":[{"href":"https:\/\/www.roundown.net\/nyushi\/wp-json\/wp\/v2\/posts\/229","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=229"}],"version-history":[{"count":0,"href":"https:\/\/www.roundown.net\/nyushi\/wp-json\/wp\/v2\/posts\/229\/revisions"}],"wp:attachment":[{"href":"https:\/\/www.roundown.net\/nyushi\/wp-json\/wp\/v2\/media?parent=229"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.roundown.net\/nyushi\/wp-json\/wp\/v2\/categories?post=229"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.roundown.net\/nyushi\/wp-json\/wp\/v2\/tags?post=229"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}