{"id":59,"date":"2011-11-26T18:29:52","date_gmt":"2011-11-26T09:29:52","guid":{"rendered":"http:\/\/roundown.main.jp\/nyushi\/?p=59"},"modified":"2021-10-23T04:13:07","modified_gmt":"2021-10-22T19:13:07","slug":"wsr201102","status":"publish","type":"post","link":"https:\/\/www.roundown.net\/nyushi\/wsr201102\/","title":{"rendered":"\u65e9\u7a32\u7530\u7406\u5de52011\uff1a\u7b2c2\u554f"},"content":{"rendered":"
\n

\\(xy\\) \u5e73\u9762\u4e0a\u306e\u5186 \\(C : \\ x^2+y^2 = 1\\) \u306e\u5185\u5074\u3092\u534a\u5f84 \\(\\dfrac{1}{2}\\) \u306e\u5186 \\(D\\) \u304c \\(C\\) \u306b\u63a5\u3057\u306a\u304c\u3089\u3059\u3079\u3089\u305a\u306b\u8ee2\u304c\u308b.\r\n\u6642\u523b \\(t\\) \u306b\u304a\u3044\u3066 \\(D\\) \u306f\u70b9 \\(( \\cos t , \\sin t )\\) \u3067 \\(C\\) \u306b\u63a5\u3057\u3066\u3044\u308b\u3068\u3059\u308b. \\(D\\) \u306e\u5468\u4e0a\u306e\u70b9 P \u306e\u8ecc\u8de1\u306b\u3064\u3044\u3066\u8003\u3048\u308b. \u3042\u308b\u6642\u523b \\(t _ 0\\) \u306b\u304a\u3044\u3066\u70b9 P \u304c \\(\\left( \\dfrac{1}{4} , \\dfrac{\\sqrt{3}}{4} \\right)\\) \u306b\u3042\u308a, \\(D\\) \u306e\u4e2d\u5fc3\u304c\u7b2c \\(2\\) \u8c61\u9650\u306b\u3042\u308b\u3068\u3059\u308b. \u4ee5\u4e0b\u306e\u554f\u306b\u7b54\u3048\u3088.<\/p>\r\n

    \r\n

  1. (1)<\/strong>\u3000\u6642\u523b \\(t _ 0\\) \u306b\u304a\u3051\u308b \\(D\\) \u306e\u4e2d\u5fc3\u306e\u5ea7\u6a19\u3092\u6c42\u3081\u3088.<\/p><\/li>\r\n

  2. (2)<\/strong>\u3000\u7b2c \\(1\\) \u8c61\u9650\u306b\u304a\u3044\u3066, \u70b9 P \u304c \\(C\\) \u4e0a\u306b\u3042\u308b\u3068\u304d\u306e P \u306e\u5ea7\u6a19\u3092\u6c42\u3081\u3088.<\/p><\/li>\r\n

  3. (3)<\/strong>\u3000\u70b9 P \u306e\u8ecc\u8de1\u3092 \\(xy\\) \u5e73\u9762\u4e0a\u306b\u56f3\u793a\u305b\u3088.<\/p><\/li>\r\n<\/ol>\r\n

    \r\n\r\n

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

    (1)<\/strong><\/p>\r\n\"waseda_2011_02_01\"\r\n

    \u6642\u523b \\(t\\) \u306b\u304a\u3051\u308b\u70b9 P \u3092 \\(\\text{P}{} _ t\\) , \u5186 \\(D\\) \u306e\u4e2d\u5fc3\u3092 \\(\\text{O}{} _ t\\) , \u5186 \\(C\\) \u3068 \\(D\\) \u306e\u63a5\u70b9\u3092 \\(\\text{Q}{} _ t\\) \u3068\u304a\u304f\u3068\r\n\\[\r\n\\text{Q}{} _ t ( \\cos t , \\sin t ) , \\ \\text{O}{} _ t \\left( \\dfrac{1}{2} \\cos t , \\dfrac{1}{2} \\sin t \\right)\r\n\\]\r\n\\(\\text{P}{} _ {t _ 0}\\text{O}{} _ {t _ 0} = \\dfrac{1}{2}\\) \u306a\u306e\u3067\r\n\\[\\begin{align}\r\n\\left( \\dfrac{1}{4} -\\dfrac{1}{2} \\cos t _ 0 \\right)^2 +\\left( \\dfrac{\\sqrt{3}}{4} -\\dfrac{1}{2} \\sin t _ 0 \\right)^2 & = \\dfrac{1}{4} \\\\\r\n( 1 -2 \\cos t _ 0 )^2 +( \\sqrt{3} -2 \\sin t _ 0 )^2 & = 4 \\\\\r\n-4 \\cos t _ 0 -2\\sqrt{3} \\sin t _ 0 +4 & = 0 \\\\\r\n\\dfrac{\\sqrt{3}}{2} \\sin t _ 0 +\\dfrac{1}{2} \\cos t _ 0 & = \\dfrac{1}{2} \\\\\r\n\\text{\u2234} \\quad \\sin \\left( t _ 0 +\\dfrac{\\pi}{6} \\right) & = \\dfrac{1}{2}\r\n\\end{align}\\]\r\n\\(\\text{O}{} _ {t _ 0}\\) \u306f\u7b2c \\(2\\) \u8c61\u9650\u306b\u3042\u308b\u306e\u3067, \\(\\dfrac{\\pi}{2} \\lt t _ 0 \\lt \\pi\\) \u306a\u306e\u3067\r\n\\[\r\nt _ 0 = \\dfrac{2 \\pi}{3}\r\n\\]\r\n\u3086\u3048\u306b\u6c42\u3081\u308b\u5ea7\u6a19\u306f,\r\n\\[\r\n\\underline{\\left( -\\dfrac{1}{4} , \\dfrac{\\sqrt{3}}{4} \\right)}\r\n\\]\r\n

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

    \u7b2c \\(1\\) \u8c61\u9650\u306b\u304a\u3044\u3066, \\(\\text{P}{} _ t = \\text{Q}{} _ t\\) \u3068\u306a\u308b\u6642\u523b\u3092 \\(a\\) \u3068\u304a\u304f.\r\n\\[\r\n\\angle \\text{P}{} _ {t _ 0}\\text{O}{} _ {t _ 0}\\text{Q}{} _ {t _ 0} =\\dfrac{2 \\pi}{3} , \\ \\overset{\\frown}{\\text{P}{} _ {t _ 0}\\text{Q}{} _ {t _ 0}} = \\overset{\\frown}{\\text{P}{} _ {a}\\text{Q}{} _ {t _ 0}}\r\n\\]\r\n\u5186 \\(C , D\\) \u306e\u534a\u5f84\u306f\u305d\u308c\u305e\u308c, \\(1 , \\dfrac{1}{2}\\) \u306a\u306e\u3067\r\n\\[\\begin{align}\r\n\\dfrac{1}{2} \\cdot \\dfrac{2 \\pi}{3} & = 1 \\cdot \\left( \\dfrac{2 \\pi}{3} -a \\right) \\\\\r\n\\text{\u2234} \\quad a & = \\dfrac{\\pi}{3}\r\n\\end{align}\\]\r\n\u3088\u3063\u3066, \u6c42\u3081\u308b\u5ea7\u6a19\u306f\r\n\\[\r\n\\underline{\\left( \\dfrac{1}{4} , \\dfrac{\\sqrt{3}}{4} \\right)}\r\n\\]\r\n

    (3)<\/strong><\/p>\r\n\"waseda_2011_02_02\"\r\n

    \\(\\text{P}{} _ t ( X , Y )\\) \u3068\u304a\u304f.\r\n\\[\r\n\\angle \\text{P}{} _ {\\frac{\\pi}{3}}\\text{O}{} _ {t _ 0}\\text{Q}{} _ {t _ 0} = t-\\dfrac{\\pi}{3} , \\ \\overset{\\frown}{\\text{P}{} _ {t}\\text{Q}{} _ {t}} = \\overset{\\frown}{\\text{P}{} _ {\\frac{\\pi}{3}}\\text{Q}{} _ {t}}\r\n\\]\r\n\u306a\u306e\u3067\r\n\\[\\begin{align}\r\n\\dfrac{1}{2} \\angle \\text{P}{} _ {t}\\text{O}{} _ {t}\\text{Q}{} _ {t} & = 1 \\cdot \\left( t -\\dfrac{\\pi}{3} \\right) \\\\\r\n\\text{\u2234} \\quad \\angle \\text{P}{} _ {t}\\text{O}{} _ {t}\\text{Q}{} _ {t} & = 2t-\\dfrac{2 \\pi}{3}\r\n\\end{align}\\]\r\n\u3057\u305f\u304c\u3063\u3066, \\(\\text{O}{} _ t\\text{P}{} _ t\\) \u304c \\(x\\) \u8ef8\u6b63\u65b9\u5411\u3068\u306a\u3059\u89d2\u306f\r\n\\[\r\nt -\\angle \\text{P}{} _ {t}\\text{O}{} _ {t}\\text{Q}{} _ {t} = \\dfrac{2 \\pi}{3} -t\r\n\\]\r\n\u4ee5\u4e0a\u3088\u308a\r\n\\[\\begin{align}\r\nX & = \\dfrac{1}{2} \\cos t +\\dfrac{1}{2} \\cos \\left( \\dfrac{2 \\pi}{3} -t \\right) \\\\\r\n& = \\cos \\dfrac{\\pi}{3} \\cos \\left( t -\\dfrac{\\pi}{3} \\right) \\\\\r\n& = \\dfrac{1}{2} \\cos \\left( t -\\dfrac{\\pi}{3} \\right) \\quad ... [2] , \\\\\r\nY & = \\dfrac{1}{2} \\sin t +\\dfrac{1}{2} \\sin \\left( \\dfrac{2 \\pi}{3} -t \\right) \\\\\r\n& = \\sin \\dfrac{\\pi}{3} \\cos \\left( t -\\dfrac{\\pi}{3} \\right) \\\\\r\n& = \\dfrac{\\sqrt{3}}{2} \\cos \\left( t -\\dfrac{\\pi}{3} \\right) \\quad ... [3]\r\n\\end{align}\\]\r\n[2] [3] \u3088\u308a\r\n\\[\r\nY = \\sqrt{3}X \\ \\left( -\\dfrac{1}{2} \\leqq X \\leqq \\dfrac{1}{2} \\right)\r\n\\]\r\n\u3086\u3048\u306b, \u70b9 P \u306e\u8ecc\u8de1\u306f\u4e0b\u56f3\u5b9f\u7dda\u90e8\u3068\u306a\u308b.<\/p>\r\n\"waseda_2011_02_03\"\r\n","protected":false},"excerpt":{"rendered":"\\(xy\\) \u5e73\u9762\u4e0a\u306e\u5186 \\(C : \\ x^2+y^2 = 1\\) \u306e\u5185\u5074\u3092\u534a\u5f84 \\(\\dfrac{1}{2}\\) \u306e\u5186 \\(D\\) \u304c \\(C\\) \u306b\u63a5\u3057\u306a\u304c\u3089\u3059\u3079\u3089\u305a\u306b\u8ee2\u304c\u308b. \u6642\u523b \\(t\\) \u306b\u304a\u3044\u3066 \\(D\\ … \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":[38],"tags":[147,13],"class_list":["post-59","post","type-post","status-publish","format-standard","hentry","category-waseda_r_2011","tag-waseda_r","tag-13"],"_links":{"self":[{"href":"https:\/\/www.roundown.net\/nyushi\/wp-json\/wp\/v2\/posts\/59","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=59"}],"version-history":[{"count":0,"href":"https:\/\/www.roundown.net\/nyushi\/wp-json\/wp\/v2\/posts\/59\/revisions"}],"wp:attachment":[{"href":"https:\/\/www.roundown.net\/nyushi\/wp-json\/wp\/v2\/media?parent=59"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.roundown.net\/nyushi\/wp-json\/wp\/v2\/categories?post=59"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.roundown.net\/nyushi\/wp-json\/wp\/v2\/tags?post=59"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}