{"id":1316,"date":"2015-10-19T00:54:55","date_gmt":"2015-10-18T15:54:55","guid":{"rendered":"http:\/\/www.roundown.net\/nyushi\/?p=1316"},"modified":"2021-10-20T13:33:02","modified_gmt":"2021-10-20T04:33:02","slug":"ykr201505","status":"publish","type":"post","link":"https:\/\/www.roundown.net\/nyushi\/ykr201505\/","title":{"rendered":"\u6a2a\u56fd\u5927\u7406\u7cfb2015\uff1a\u7b2c5\u554f"},"content":{"rendered":"<hr \/>\n<p>\\(1\\) \u500b\u306e\u3055\u3044\u3053\u308d\u3092 \\(3\\) \u56de\u6295\u3052, \u51fa\u305f\u76ee\u306e\u9806\u306b \\(a , b , c\\) \u3068\u3059\u308b. \u4e0d\u7b49\u5f0f\r\n\\[\r\n\\displaystyle\\int _ 0^{\\pi} ( \\cos ax ) ( \\cos bx ) ( \\cos cx ) \\, dx \\gt 0\r\n\\]\r\n\u3092\u307f\u305f\u3059\u78ba\u7387\u3092\u6c42\u3081\u3088.<\/p>\r\n<hr \/>\r\n<!--more-->\r\n<h4>\u3010 \u89e3 \u7b54 \u3011<\/h4>\r\n<p>\\(I = \\displaystyle\\int _ 0^{\\pi} ( \\cos ax ) ( \\cos bx ) ( \\cos cx ) \\, dx\\) \u3068\u304a\u304f.<br \/>\r\n\u7a4d\u548c\u306e\u516c\u5f0f\u3092\u7528\u3044\u308c\u3070\r\n\\[\\begin{align}\r\n( \\cos ax ) & ( \\cos bx ) ( \\cos cx ) \\\\\r\n& = \\dfrac{1}{2} \\{ \\cos (a+b) x +\\cos (a-b) x \\} ( \\cos cx ) \\\\\r\n& = \\dfrac{1}{4} \\{ \\cos (a+b+c) x +\\cos (a+b-c) x \\\\\r\n& \\qquad +\\cos (a-b+c) x +\\cos (a-b-c) x \\}\r\n\\end{align}\\]\r\n\u3053\u3053\u3067, \u6574\u6570 \\(m \\ (m \\neq 0 )\\) \u306b\u3064\u3044\u3066<\/p>\r\n<ol>\r\n<li><p><strong>1*<\/strong>\u3000\\(m = 0\\) \u306e\u3068\u304d\r\n\\[\r\n\\displaystyle\\int _ 0^{\\pi} \\cos mx \\, dx = \\displaystyle\\int _ 0^{\\pi} 1 \\, dx = \\pi\r\n\\]<\/li>\r\n<li><p><strong>2*<\/strong>\u3000\\(m \\neq 0\\) \u306e\u3068\u304d\r\n\\[\r\n\\displaystyle\\int _ 0^{\\pi} \\cos mx \\, dx = \\dfrac{1}{m} \\left[ \\sin mx \\right] _ 0^{\\pi} = 0\r\n\\]<\/li>\r\n<\/ol>\r\n<p>\u3057\u305f\u304c\u3063\u3066, \\(I \\gt 0\\) \u3068\u306a\u308b\u305f\u3081\u306e\u6761\u4ef6\u306f\r\n\\[\r\na+b-c = 0 \\ \\text{\u307e\u305f\u306f} \\ a-b+c = 0 \\ \\text{\u307e\u305f\u306f} \\ a-b-c = 0\r\n\\]\r\n\u3059\u306a\u308f\u3061\r\n\\[\r\nc = a+b \\ \\text{\u307e\u305f\u306f} \\ b = c+a \\ \\text{\u307e\u305f\u306f} \\ a = b+c\r\n\\]\r\n\u8a00\u3044\u63db\u3048\u308b\u3068, \u300c \\(a , b , c\\) \u306e\u3046\u3061\u306e \\(1\\) \u3064\u304c, \u6b8b\u308a \\(2\\) \u3064\u306e\u548c\u306b\u306a\u308b. \u300d ... [1]\r\n\u3053\u306e\u3088\u3046\u306a \\(3\\) \u3064\u306e\u6570\u306e\u7d44\u5408\u305b\u306f\r\n\\[\\begin{align}\r\n& ( 1 , 1 , 2 ) , ( 1 , 2 , 3 ) , ( 1 , 3 , 4 ) , ( 1 , 4 , 5 ) , \\\\\r\n& \\qquad ( 1 , 5 , 6 ) , ( 2 , 2 , 4 ) , ( 2 , 3 , 5 ) , ( 2 , 4 , 6 ) , ( 3 , 3 , 6 )\r\n\\end{align}\\]\r\n\u3053\u306e\u3046\u3061, \\(2\\) \u3064\u306e\u6570\u304c\u540c\u3058\u7d44\u304c \\(3\\) \u7d44, \\(3\\) \u3064\u306e\u6570\u304c\u3059\u3079\u3066\u7570\u306a\u308b\u7d44\u304c \\(6\\) \u7d44\u3042\u308b\u306e\u3067, [1] \u3092\u307f\u305f\u3059 \\(a , b, c\\) \u306e\u7d44\u306f\r\n\\[\r\n3 \\cdot {} _ 1 \\text{C} {} _ 3 +6 \\cdot 3 ! = 45 \\quad \\text{\u7d44}\r\n\\]\r\n\u3088\u3063\u3066, \u6c42\u3081\u308b\u78ba\u7387\u306f\r\n\\[\r\n\\dfrac{45}{6^3} = \\underline{\\dfrac{5}{24}}\r\n\\]\r\n","protected":false},"excerpt":{"rendered":"\\(1\\) \u500b\u306e\u3055\u3044\u3053\u308d\u3092 \\(3\\) \u56de\u6295\u3052, \u51fa\u305f\u76ee\u306e\u9806\u306b \\(a , b , c\\) \u3068\u3059\u308b. \u4e0d\u7b49\u5f0f \\[ \\displaystyle\\int _ 0^{\\pi} ( \\cos ax ) ( \\cos bx )  &hellip; <a href=\"https:\/\/www.roundown.net\/nyushi\/ykr201505\/\">\u7d9a\u304d\u3092\u8aad\u3080 <span class=\"meta-nav\">&rarr;<\/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":[133],"tags":[137,9],"class_list":["post-1316","post","type-post","status-publish","format-standard","hentry","category-yokokoku_r_2015","tag-137","tag-yokokoku_r"],"_links":{"self":[{"href":"https:\/\/www.roundown.net\/nyushi\/wp-json\/wp\/v2\/posts\/1316","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=1316"}],"version-history":[{"count":0,"href":"https:\/\/www.roundown.net\/nyushi\/wp-json\/wp\/v2\/posts\/1316\/revisions"}],"wp:attachment":[{"href":"https:\/\/www.roundown.net\/nyushi\/wp-json\/wp\/v2\/media?parent=1316"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.roundown.net\/nyushi\/wp-json\/wp\/v2\/categories?post=1316"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.roundown.net\/nyushi\/wp-json\/wp\/v2\/tags?post=1316"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}