{"id":668,"date":"2013-03-07T00:40:08","date_gmt":"2013-03-06T15:40:08","guid":{"rendered":"http:\/\/www.roundown.net\/nyushi\/?p=668"},"modified":"2021-09-29T21:28:41","modified_gmt":"2021-09-29T12:28:41","slug":"thr200702","status":"publish","type":"post","link":"https:\/\/www.roundown.net\/nyushi\/thr200702\/","title":{"rendered":"\u6771\u5317\u5927\u7406\u7cfb2007\uff1a\u7b2c2\u554f"},"content":{"rendered":"
\n

\\(\\angle \\text{C}\\) \u3092\u76f4\u89d2\u3068\u3059\u308b\u76f4\u89d2\u4e09\u89d2\u5f62 ABC \u306b\u5bfe\u3057\u3066, \\(\\angle \\text{A}\\) \u306e\u4e8c\u7b49\u5206\u7dda\u3068\u7dda\u5206 BC \u306e\u4ea4\u70b9\u3092 D \u3068\u3059\u308b.\r\n\u307e\u305f, \u7dda\u5206 AD , DC , CA \u306e\u9577\u3055\u3092\u305d\u308c\u305e\u308c \\(5, 3, 4\\) \u3068\u3059\u308b.\r\n\\(\\angle \\text{A} = \\theta\\) \u3068\u304a\u304f\u3068\u304d, \u6b21\u306e\u554f\u3044\u306b\u7b54\u3048\u3088.<\/p>\r\n

    \r\n

  1. (1)<\/strong>\u3000\\(\\sin \\theta\\) \u3092\u6c42\u3081\u3088.<\/p><\/li>\r\n

  2. (2)<\/strong>\u3000\\(\\theta \\lt \\dfrac{5}{12} \\pi\\) \u3092\u793a\u305b. \u305f\u3060\u3057, \\(\\sqrt{2} = 1.414 \\cdots\\) , \\(\\sqrt{3} = 1.732 \\cdots\\) \u3092\u7528\u3044\u3066\u3082\u3088\u3044.<\/p><\/li>\r\n<\/ol>\r\n

    \r\n\r\n

    \u3010 \u89e3 \u7b54 \u3011<\/h2>\r\n\"tohoku_r_2007_02_01\"\r\n

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

    \\[\r\n\\cos \\dfrac{\\theta}{2} = \\dfrac{4}{5} , \\ \\sin \\dfrac{\\theta}{2} = \\dfrac{3}{5}\r\n\\]\r\n\u306a\u306e\u3067\r\n\\[\\begin{align}\r\n\\sin \\theta & = 2 \\sin \\dfrac{\\theta}{2} \\cos \\dfrac{\\theta}{2} \\\\\r\n& = 2 \\cdot \\dfrac{4}{5} \\cdot \\dfrac{3}{5} = \\underline{\\dfrac{24}{25}}\r\n\\end{align}\\]\r\n

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

    \\[\\begin{align}\r\n\\cos \\theta & = 2 \\cos^2 \\dfrac{\\theta}{2} -1 \\\\\r\n& = 2 \\left( \\dfrac{4}{5} \\right)^2 -1 = \\dfrac{7}{25} \\gt 0\r\n\\end{align}\\]\r\n\u306a\u306e\u3067\r\n\\[\r\n0 \\lt \\theta \\lt \\dfrac{\\pi}{2}\r\n\\]\r\n\\(0 \\lt x \\lt \\dfrac{\\pi}{2}\\) \u306b\u304a\u3044\u3066, \\(\\sin x\\) \u306f\u5358\u8abf\u5897\u52a0\u306a\u306e\u3067\r\n\\[\r\n\\sin \\theta \\lt \\sin \\dfrac{5 \\pi}{12}\r\n\\]\r\n\u3092\u793a\u305b\u3070\u3088\u3044.\r\n\\[\\begin{align}\r\n\\sin \\dfrac{5 \\pi}{12} & = \\sin \\left( \\dfrac{\\pi}{3} +\\dfrac{\\pi}{4} \\right) \\\\\r\n& = \\sin \\dfrac{\\pi}{3} \\cos \\dfrac{\\pi}{4} +\\cos \\dfrac{\\pi}{3} \\sin \\dfrac{\\pi}{4} \\\\\r\n& = \\dfrac{\\sqrt{3}}{2} \\cdot \\dfrac{\\sqrt{2}}{2} +\\dfrac{1}{2} \\cdot \\dfrac{\\sqrt{2}}{2} \\\\\r\n& = \\dfrac{\\sqrt{2} \\left( \\sqrt{3} +1 \\right)}{4} \\\\\r\n& \\gt \\dfrac{1.41 \\cdot 2.73}{4} \\\\\r\n& = 0.962325 \\gt \\dfrac{24}{25} = \\sin \\theta\r\n\\end{align}\\]\r\n\u3088\u3063\u3066\r\n\\[\r\n\\theta \\lt \\dfrac{5 \\pi}{12}\r\n\\]\r\n","protected":false},"excerpt":{"rendered":"\\(\\angle \\text{C}\\) \u3092\u76f4\u89d2\u3068\u3059\u308b\u76f4\u89d2\u4e09\u89d2\u5f62 ABC \u306b\u5bfe\u3057\u3066, \\(\\angle \\text{A}\\) \u306e\u4e8c\u7b49\u5206\u7dda\u3068\u7dda\u5206 BC \u306e\u4ea4\u70b9\u3092 D \u3068\u3059\u308b. \u307e\u305f, \u7dda\u5206 AD , DC , CA \u306e\u9577\u3055\u3092 … \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":[95],"tags":[148,109],"class_list":["post-668","post","type-post","status-publish","format-standard","hentry","category-tohoku_r_2007","tag-tohoku_r","tag-109"],"_links":{"self":[{"href":"https:\/\/www.roundown.net\/nyushi\/wp-json\/wp\/v2\/posts\/668","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=668"}],"version-history":[{"count":0,"href":"https:\/\/www.roundown.net\/nyushi\/wp-json\/wp\/v2\/posts\/668\/revisions"}],"wp:attachment":[{"href":"https:\/\/www.roundown.net\/nyushi\/wp-json\/wp\/v2\/media?parent=668"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.roundown.net\/nyushi\/wp-json\/wp\/v2\/categories?post=668"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.roundown.net\/nyushi\/wp-json\/wp\/v2\/tags?post=668"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}