{"id":474,"date":"2012-11-18T18:29:45","date_gmt":"2012-11-18T09:29:45","guid":{"rendered":"http:\/\/www.roundown.net\/nyushi\/?p=474"},"modified":"2021-09-23T10:26:09","modified_gmt":"2021-09-23T01:26:09","slug":"thr201205","status":"publish","type":"post","link":"https:\/\/www.roundown.net\/nyushi\/thr201205\/","title":{"rendered":"\u6771\u5317\u5927\u7406\u7cfb2012\uff1a\u7b2c5\u554f"},"content":{"rendered":"
\n

\u9577\u3055 \\(1\\) \u306e\u7dda\u5206 AB \u3092\u76f4\u5f84\u3068\u3059\u308b\u5186\u5468 \\(C\\) \u4e0a\u306b\u70b9 P \u3092\u3068\u308b.\r\n\u305f\u3060\u3057, P \u306f\u70b9 A , B \u3068\u306f\u4e00\u81f4\u3057\u3066\u3044\u306a\u3044\u3068\u3059\u308b.\r\n\u7dda\u5206 AB \u4e0a\u306e\u70b9 Q \u3092 \\(\\angle \\text{BPQ} =\\dfrac{\\pi}{3}\\) \u3068\u306a\u308b\u3088\u3046\u306b\u3068\u308a, \u7dda\u5206 BP \u306e\u9577\u3055\u3092 \\(x\\) \u3068\u3057, \u7dda\u5206 PQ \u306e\u9577\u3055\u3092 \\(y\\) \u3068\u3059\u308b. \u4ee5\u4e0b\u306e\u554f\u3044\u306b\u7b54\u3048\u3088.<\/p>\r\n

    \r\n

  1. (1)<\/strong>\u3000\\(y\\) \u3092 \\(x\\) \u3092\u7528\u3044\u3066\u8868\u305b.<\/p><\/li>\r\n

  2. (2)<\/strong>\u3000\u70b9 P \u304c \\(2\\) \u70b9 A , B \u3092\u9664\u3044\u305f\u5186\u5468 \\(C\\) \u4e0a\u3092\u52d5\u304f\u3068\u304d, \\(y\\) \u304c\u6700\u5927\u3068\u306a\u308b \\(x\\) \u3092\u6c42\u3081\u3088.<\/p><\/li>\r\n<\/ol>\r\n

    \r\n\r\n

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

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

    \u25b3APB \u306e\u9762\u7a4d\u306b\u7740\u76ee\u3059\u308c\u3070\r\n\\[\\begin{align}\r\n\\dfrac{1}{2} x \\sqrt{1-x^2} & = \\dfrac{1}{2} xy \\sin \\dfrac{\\pi}{3} +\\dfrac{1}{2} y\\sqrt{1-x^2} \\sin \\dfrac{\\pi}{6} \\\\\r\n2x \\sqrt{1-x^2} & = \\sqrt{3} xy +y\\sqrt{1-x^2} \\\\\r\n\\text{\u2234} \\quad y & =\\underline{\\dfrac{2x \\sqrt{1-x^2}}{\\sqrt{3} x +\\sqrt{1-x^2}}}\n\\end{align}\\]\r\n

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

    \\(0 \\lt x \\lt 1\\) \u306a\u306e\u3067, \\(x = \\cos \\theta \\ \\left( 0 \\lt \\theta \\lt \\dfrac{\\pi}{2} \\right)\\) \u3068\u304a\u304f\u3068, \\(\\sqrt{1 -x^2} = \\sin \\theta\\) \u3068\u8868\u305b\u3066\r\n\\[\r\ny = \\dfrac{2 \\sin \\theta \\cos \\theta}{\\sqrt{3} \\cos \\theta +\\sin \\theta}\n\\]\r\n\u3053\u308c\u3092 \\(f( \\theta )\\) \u3068\u304a\u3051\u3070\r\n\\[\\begin{align}\r\nf'( \\theta ) & = 2 \\cdot \\dfrac{\\left( \\cos^2 \\theta -\\sin^2 \\theta \\right) \\left( \\sqrt{3} \\cos \\theta +\\sin \\theta \\right) -\\sin \\theta \\cos \\theta \\left( -\\sqrt{3} \\sin \\theta +\\cos \\theta \\right)}{\\left( \\sqrt{3} \\cos \\theta +\\sin \\theta \\right)^2} \\\\\r\n& = 2 \\cdot \\dfrac{\\sqrt{3} \\cos^3 \\theta -\\sin^3 \\theta}{\\left( \\sqrt{3} \\cos \\theta +\\sin \\theta \\right)^2} \\\\\r\n& = 2 \\cdot \\dfrac{\\cos^3 \\theta \\left( \\sqrt{3} -\\tan^3 \\theta \\right)}{\\left( \\sqrt{3} \\cos \\theta +\\sin \\theta \\right)^2}\n\\end{align}\\]\r\n\u3053\u3053\u3067 \\(\\tan^3 \\alpha = \\sqrt{3} \\ \\left( 0 \\lt \\alpha \\lt \\dfrac{\\pi}{2} \\right)\\) \u3092\u307f\u305f\u3059 \\(\\alpha\\) \u3092\u304a\u304f\u3068, \\(f( \\theta )\\) \u306e \\(0 \\lt \\theta \\lt \\dfrac{\\pi}{2}\\) \u306b\u304a\u3051\u308b\u5897\u6e1b\u306f\u4e0b\u8868\u306e\u3088\u3046\u306b\u306a\u308b.\r\n\\[\r\n\\begin{array}{c|ccccc} \\theta & (0) & \\cdots & \\alpha & \\cdots & \\left( \\frac{\\pi}{2} \\right) \\\\ \\hline f'( \\theta ) & & + & 0 & - & \\\\ \\hline f( \\theta ) & & \\nearrow & \\text{\u6700\u5927} & \\searrow & \\end{array}\r\n\\]\r\n\u3088\u3063\u3066, \\(y\\) \u3092\u6700\u5927\u306b\u3059\u308b \\(x\\) \u306f\r\n\\[\\begin{align}\r\nx & = \\sqrt{\\dfrac{1}{1+\\tan^2 \\alpha}} \\\\\r\n& =\\underline{\\dfrac{1}{\\sqrt{1 +\\sqrt[3]{3}}}}\n\\end{align}\\]\r\n","protected":false},"excerpt":{"rendered":"\u9577\u3055 \\(1\\) \u306e\u7dda\u5206 AB \u3092\u76f4\u5f84\u3068\u3059\u308b\u5186\u5468 \\(C\\) \u4e0a\u306b\u70b9 P \u3092\u3068\u308b. \u305f\u3060\u3057, P \u306f\u70b9 A , B \u3068\u306f\u4e00\u81f4\u3057\u3066\u3044\u306a\u3044\u3068\u3059\u308b. \u7dda\u5206 AB \u4e0a\u306e\u70b9 Q \u3092 \\(\\angle \\text{BPQ} =\\df … \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-474","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\/474","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=474"}],"version-history":[{"count":0,"href":"https:\/\/www.roundown.net\/nyushi\/wp-json\/wp\/v2\/posts\/474\/revisions"}],"wp:attachment":[{"href":"https:\/\/www.roundown.net\/nyushi\/wp-json\/wp\/v2\/media?parent=474"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.roundown.net\/nyushi\/wp-json\/wp\/v2\/categories?post=474"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.roundown.net\/nyushi\/wp-json\/wp\/v2\/tags?post=474"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}