{"id":508,"date":"2012-12-07T23:40:30","date_gmt":"2012-12-07T14:40:30","guid":{"rendered":"http:\/\/www.roundown.net\/nyushi\/?p=508"},"modified":"2021-09-28T20:47:35","modified_gmt":"2021-09-28T11:47:35","slug":"thr200904","status":"publish","type":"post","link":"https:\/\/www.roundown.net\/nyushi\/thr200904\/","title":{"rendered":"\u6771\u5317\u5927\u7406\u7cfb2009\uff1a\u7b2c4\u554f"},"content":{"rendered":"
\n

\\(a\\) \u3092 \\(0 \\leqq a \\leqq \\dfrac{\\pi}{2}\\) \u3092\u6e80\u305f\u3059\u5b9f\u6570\u3068\u3059\u308b.\r\n\u4ee5\u4e0b\u306e\u554f\u3044\u306b\u7b54\u3048\u3088.<\/p>\r\n

    \r\n

  1. (1)<\/strong>\u3000\u5b9f\u6570 \\(\\theta\\) \u306b\u5bfe\u3057\u3066 \\(\\sin \\theta\\) \u3068 \\(\\sin ( \\theta -2a )\\) \u306e\u3046\u3061\u5c0f\u3055\u304f\u306a\u3044\u307b\u3046\u3092 \\(f( \\theta )\\) \u3068\u304a\u304f. \u3059\u306a\u308f\u3061,\r\n\\[\\begin{align}\r\n\\sin \\theta \\geqq \\sin ( \\theta -2a ) \\text{\u306e\u3068\u304d} , & \\quad f( \\theta ) = \\sin \\theta \\\\\r\n\\sin \\theta \\lt \\sin ( \\theta -2a ) \\text{\u306e\u3068\u304d} , & \\quad f( \\theta ) = \\sin ( \\theta -2a )\r\n\\end{align}\\]\r\n\u3068\u306a\u308b\u95a2\u6570 \\(f( \\theta )\\) \u3092\u8003\u3048\u308b. \u3053\u306e\u3068\u304d\u5b9a\u7a4d\u5206\r\n\\[\r\nI = \\displaystyle\\int _ 0^{\\pi} f( \\theta ) \\, d \\theta\r\n\\]\r\n\u3092\u6c42\u3081\u3088.<\/p><\/li>\r\n

  2. (2)<\/strong>\u3000\\(a\\) \u3092 \\(0 \\leqq a \\leqq \\dfrac{\\pi}{2}\\) \u306e\u7bc4\u56f2\u3067\u52d5\u304b\u3059\u3068\u304d, (1)<\/strong> \u306e \\(I\\) \u306e\u6700\u5927\u5024\u3092\u6c42\u3081\u3088.<\/p><\/li>\r\n<\/ol>\r\n

    \r\n\r\n

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

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

    \u4e0a\u56f3\u304b\u3089\u8003\u3048\u3066\r\n\\[\r\nf( \\theta ) =\\left\\{ \\begin{array}{ll} \\sin \\theta & \\left( \\ 0 \\leqq \\theta \\leqq \\dfrac{\\pi}{2} +a \\text{\u306e\u3068\u304d} \\right) \\\\ \\sin ( \\theta -2a ) & \\left( \\ \\dfrac{\\pi}{2} +a \\lt \\theta \\leqq \\pi \\text{\u306e\u3068\u304d} \\right) \\end{array} \\right.\r\n\\]\r\n\u3088\u3063\u3066\r\n\\[\\begin{align}\r\nI & = \\displaystyle\\int _ 0^{\\frac{\\pi}{2} +a} \\sin \\theta \\, d \\theta +\\displaystyle\\int _ {\\frac{\\pi}{2} +a}^{\\pi} \\sin ( \\theta -2a ) \\, d \\theta \\\\\r\n& = \\left[ -\\cos \\theta \\right] _ 0^{\\frac{\\pi}{2} +a} +\\left[ -\\cos ( \\theta -2a ) \\right] _ {\\frac{\\pi}{2} +a}^{\\pi} \\\\\r\n& = -\\cos \\left( \\dfrac{\\pi}{2} +a \\right) +1 -\\cos \\left( \\pi -2a \\right) +\\cos \\left( \\dfrac{\\pi}{2} -a \\right) \\\\\r\n& = \\sin a +1 +\\cos 2a +\\sin a \\\\\r\n& = \\underline{\\cos 2a +2 \\sin a +1}\r\n\\end{align}\\]\r\n

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

    \\[\\begin{align}\r\nI & = 2 \\left( 1 -\\sin^2 a \\right) +2\\sin a \\\\\r\n& = -2 \\left( \\sin a -\\dfrac{1}{2} \\right)^2 +\\dfrac{5}{2}\r\n\\end{align}\\]\r\n\\(0 \\leqq a \\leqq \\dfrac{\\pi}{2}\\) \u3088\u308a \\(0 \\leqq \\sin a \\leqq 1\\) \u306a\u306e\u3067, \u6c42\u3081\u308b\u6700\u5927\u5024\u306f\r\n\\[\r\n\\underline{\\dfrac{5}{2} \\quad \\left( a = \\dfrac{\\pi}{6} \\text{\u306e\u3068\u304d} \\right)}\r\n\\]\r\n","protected":false},"excerpt":{"rendered":"\\(a\\) \u3092 \\(0 \\leqq a \\leqq \\dfrac{\\pi}{2}\\) \u3092\u6e80\u305f\u3059\u5b9f\u6570\u3068\u3059\u308b. \u4ee5\u4e0b\u306e\u554f\u3044\u306b\u7b54\u3048\u3088. (1)\u3000\u5b9f\u6570 \\(\\theta\\) \u306b\u5bfe\u3057\u3066 \\(\\sin \\theta\\) \u3068 \\(\\s … \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":[75],"tags":[148,15],"class_list":["post-508","post","type-post","status-publish","format-standard","hentry","category-tohoku_r_2009","tag-tohoku_r","tag-15"],"_links":{"self":[{"href":"https:\/\/www.roundown.net\/nyushi\/wp-json\/wp\/v2\/posts\/508","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=508"}],"version-history":[{"count":0,"href":"https:\/\/www.roundown.net\/nyushi\/wp-json\/wp\/v2\/posts\/508\/revisions"}],"wp:attachment":[{"href":"https:\/\/www.roundown.net\/nyushi\/wp-json\/wp\/v2\/media?parent=508"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.roundown.net\/nyushi\/wp-json\/wp\/v2\/categories?post=508"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.roundown.net\/nyushi\/wp-json\/wp\/v2\/tags?post=508"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}