{"id":548,"date":"2012-12-29T10:07:57","date_gmt":"2012-12-29T01:07:57","guid":{"rendered":"http:\/\/www.roundown.net\/nyushi\/?p=548"},"modified":"2021-10-31T07:24:06","modified_gmt":"2021-10-30T22:24:06","slug":"tkb201001","status":"publish","type":"post","link":"https:\/\/www.roundown.net\/nyushi\/tkb201001\/","title":{"rendered":"\u6771\u5927\u6587\u7cfb2010\uff1a\u7b2c1\u554f"},"content":{"rendered":"
\n

O \u3092\u539f\u70b9\u3068\u3059\u308b\u5ea7\u6a19\u5e73\u9762\u4e0a\u306b\u70b9 A \\(( -3 , 0 )\\) \u3092\u3068\u308a, \\(0^{\\circ} \\lt \\theta \\lt 120^{\\circ}\\) \u306e\u7bc4\u56f2\u306b\u3042\u308b \\(\\theta\\) \u306b\u5bfe\u3057\u3066, \u6b21\u306e\u6761\u4ef6 (i) , (ii) \u3092\u307f\u305f\u3059 \\(2\\) \u70b9 B , C \u3092\u8003\u3048\u308b.<\/p>\r\n

    \r\n

  1. (i)\u3000B \u306f \\(y \\gt 0\\) \u306e\u90e8\u5206\u306b\u3042\u308a, \\(\\text{OB} = 2\\) \u304b\u3064 \\(\\angle \\text{AOB} = 180^{\\circ} -\\theta\\) \u3067\u3042\u308b.<\/p><\/li>\r\n

  2. (ii)\u3000C \u306f \\(y \\lt 0\\) \u306e\u90e8\u5206\u306b\u3042\u308a, \\(\\text{OC} = 1\\) \u304b\u3064 \\(\\angle \\text{BOC} = 120^{\\circ}\\) \u3067\u3042\u308b.<\/p><\/li>\r\n<\/ol>\r\n

    \u4ee5\u4e0b\u306e\u554f (1)<\/strong> , (2)<\/strong> \u306b\u7b54\u3048\u3088.<\/p>\r\n

      \r\n

    1. (1)<\/strong>\u3000\u25b3OAB \u3068 \u25b3OAC \u306e\u9762\u7a4d\u304c\u7b49\u3057\u3044\u3068\u304d, \\(\\theta\\) \u306e\u5024\u3092\u6c42\u3081\u3088.<\/p><\/li>\r\n

    2. (2)<\/strong>\u3000\\(\\theta\\) \u3092 \\(0^{\\circ} \\lt \\theta \\lt 120^{\\circ}\\) \u306e\u7bc4\u56f2\u3067\u52d5\u304b\u3059\u3068\u304d, \u25b3OAB \u3068 \u25b3OAC \u306e\u9762\u7a4d\u306e\u548c\u306e\u6700\u5927\u5024\u3068, \u305d\u306e\u3068\u304d\u306e \\(\\sin \\theta\\) \u306e\u5024\u3092\u6c42\u3081\u3088.<\/p><\/li>\r\n<\/ol>\r\n

      \r\n\r\n

      \u3010 \u89e3 \u7b54 \u3011<\/h2>\r\n\"tokyo_b_2010_01_01\"\r\n

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

      \u6761\u4ef6\u3088\u308a\r\n\\[\r\n\\angle \\text{AOC} = 180^{\\circ} -( 120^{\\circ} -\\theta ) = \\theta +60^{\\circ}\r\n\\]\r\n\u306a\u306e\u3067\r\n\\[\\begin{align}\r\n\\triangle \\text{OAB} & = \\dfrac{1}{2} \\cdot 3 \\cdot 2 \\sin ( 180^{\\circ} -\\theta ) = 3 \\sin \\theta , \\\\\r\n\\triangle \\text{OAC} & = \\dfrac{1}{2} \\cdot 3 \\cdot 1 \\sin ( \\theta +60^{\\circ} ) \\\\\r\n& = \\dfrac{3}{4} \\left( \\sin \\theta +\\sqrt{3} \\cos \\theta \\right)\r\n\\end{align}\\]\r\n\u3057\u305f\u304c\u3063\u3066, \u6761\u4ef6\u3088\u308a\r\n\\[\\begin{align}\r\n3 \\sin \\theta & = \\dfrac{3}{4} \\left( \\sin \\theta +\\sqrt{3} \\cos \\theta \\right) \\\\\r\n3 \\sin \\theta & = \\sqrt{3} \\cos \\theta \\\\\r\n\\text{\u2234} \\quad \\tan \\theta & = \\dfrac{1}{\\sqrt{3}}\r\n\\end{align}\\]\r\n\\(0^{\\circ} \\lt \\theta \\lt 120^{\\circ}\\) \u3088\u308a\r\n\\[\r\n\\theta = \\underline{30^{\\circ}}\r\n\\]\r\n

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

      \u25b3OAB \u3068 \u25b3OAC \u306e\u9762\u7a4d\u306e\u548c\u3092 \\(S\\) \u3068\u304a\u304f\u3068\r\n\\[\\begin{align}\r\nS & = \\dfrac{3}{4} \\left( 5 \\sin \\theta +\\sqrt{3} \\cos \\theta \\right) \\\\\r\n& = \\dfrac{3}{4} \\cdot 2 \\sqrt{7} \\sin ( \\theta +\\alpha ) \\\\\r\n& = \\dfrac{3 \\sqrt{7}}{2} \\sin ( \\theta +\\alpha ) \\\\\r\n\\text{\u2234} \\quad & -\\dfrac{3 \\sqrt{7}}{2} \\leqq S \\leqq \\dfrac{3 \\sqrt{7}}{2}\r\n\\end{align}\\]\r\n\u3053\u3053\u3067\r\n\\[\r\n\\sin \\alpha = \\dfrac{\\sqrt{3}}{2 \\sqrt{7}} , \\ \\cos \\alpha = \\dfrac{5}{2 \\sqrt{7}}\r\n\\]\r\n\u3088\u3063\u3066\r\n\\[\\begin{align}\r\n\\sin \\theta & = \\sin ( 90^{\\circ} -\\alpha ) \\\\\r\n& = \\cos \\alpha = \\underline{\\dfrac{5 \\sqrt{7}}{14}}\r\n\\end{align}\\]\r\n\u306e\u3068\u304d\u306b, \u6700\u5927\u5024 \\(\\underline{\\dfrac{3 \\sqrt{7}}{2}}\\) \u3092\u3068\u308b.<\/p>\r\n","protected":false},"excerpt":{"rendered":"O \u3092\u539f\u70b9\u3068\u3059\u308b\u5ea7\u6a19\u5e73\u9762\u4e0a\u306b\u70b9 A \\(( -3 , 0 )\\) \u3092\u3068\u308a, \\(0^{\\circ} \\lt \\theta \\lt 120^{\\circ}\\) \u306e\u7bc4\u56f2\u306b\u3042\u308b \\(\\theta\\) \u306b\u5bfe\u3057\u3066, \u6b21\u306e\u6761\u4ef6 (i … \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":[80],"tags":[149,14],"class_list":["post-548","post","type-post","status-publish","format-standard","hentry","category-tokyo_b_2010","tag-tokyo_b","tag-14"],"_links":{"self":[{"href":"https:\/\/www.roundown.net\/nyushi\/wp-json\/wp\/v2\/posts\/548","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=548"}],"version-history":[{"count":0,"href":"https:\/\/www.roundown.net\/nyushi\/wp-json\/wp\/v2\/posts\/548\/revisions"}],"wp:attachment":[{"href":"https:\/\/www.roundown.net\/nyushi\/wp-json\/wp\/v2\/media?parent=548"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.roundown.net\/nyushi\/wp-json\/wp\/v2\/categories?post=548"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.roundown.net\/nyushi\/wp-json\/wp\/v2\/tags?post=548"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}