{"id":1232,"date":"2015-08-19T10:45:21","date_gmt":"2015-08-19T01:45:21","guid":{"rendered":"http:\/\/www.roundown.net\/nyushi\/?p=1232"},"modified":"2021-03-22T20:05:06","modified_gmt":"2021-03-22T11:05:06","slug":"kyr201501","status":"publish","type":"post","link":"https:\/\/www.roundown.net\/nyushi\/kyr201501\/","title":{"rendered":"\u4eac\u5927\u7406\u7cfb2015\uff1a\u7b2c1\u554f"},"content":{"rendered":"<hr \/>\n<p>\\(2\\) \u3064\u306e\u95a2\u6570 \\(y = \\sin \\left( x +\\dfrac{\\pi}{8} \\right)\\) \u3068 \\(y = \\sin 2x\\) \u306e\u30b0\u30e9\u30d5\u306e \\(0 \\leqq x \\leqq \\dfrac{\\pi}{2}\\) \u306e\u90e8\u5206\u3067\u56f2\u307e\u308c\u308b\u9818\u57df\u3092, \\(x\\) \u8ef8\u306e\u307e\u308f\u308a\u306b \\(1\\) \u56de\u8ee2\u3055\u305b\u3066\u3067\u304d\u308b\u7acb\u4f53\u306e\u4f53\u7a4d\u3092\u6c42\u3081\u3088.<\/p>\r\n<hr>\r\n<!--more-->\r\n<h4>\u3010 \u89e3 \u7b54 \u3011<\/h4>\r\n<img decoding=\"async\" src=\"\/\/www.roundown.net\/nyushi\/wp-content\/uploads\/kyr20150101.svg\" alt=\"kyr20150101\" class=\"aligncenter size-full\" \/>\r\n<p>\\(0 \\leqq x \\leq\\dfrac{\\pi}{2}\\) \u306b\u304a\u3044\u3066, \\(2\\) \u3064\u306e\u30b0\u30e9\u30d5\u304c\u56f2\u3080\u90e8\u5206\u306f\u4e0a\u56f3\u306e\u3088\u3046\u306b\u306a\u308b.<br \/>\r\n\u30b0\u30e9\u30d5\u306e\u5f0f\u304b\u3089 \\(y\\) \u3092\u6d88\u53bb\u3059\u308b\u3068\r\n\\[\\begin{align}\r\n\\sin \\left( x +\\dfrac{\\pi}{8} \\right) = \\sin 2x & \\\\\r\n2 \\cos \\dfrac{2x +x +\\frac{\\pi}{8}}{2} \\sin \\dfrac{2x -x -\\frac{\\pi}{8}}{2} & = 0 \\\\\r\n\\cos \\left( \\dfrac{3x}{2} +\\dfrac{\\pi}{16} \\right) \\sin \\left( \\dfrac{x}{2} -\\dfrac{\\pi}{16} \\right) & = 0\r\n\\end{align}\\]\r\n\u3053\u308c\u3092, \\(0 \\leqq x \\leqq \\dfrac{\\pi}{2}\\) \u306e\u7bc4\u56f2\u3067\u3068\u304f\u3068\r\n\\[\\begin{align}\r\n\\dfrac{3x}{2} +\\dfrac{\\pi}{16} = \\dfrac{\\pi}{2} & , \\ \\dfrac{x}{2} -\\dfrac{\\pi}{16} = 0 \\\\\r\n\\text{\u2234} \\quad x = \\dfrac{7 \\pi}{24} & , \\ \\dfrac{\\pi}{8}\r\n\\end{align}\\]\r\n\u3088\u3063\u3066, \u6c42\u3081\u308b\u4f53\u7a4d \\(V\\) \u306f\r\n\\[\\begin{align}\r\nV & = \\pi \\displaystyle\\int _ {\\frac{\\pi}{8}}^{\\frac{7 \\pi}{24}} \\left\\{ \\sin^2 2x -\\sin^2 \\left( x +\\dfrac{\\pi}{8} \\right) \\right\\} \\, dx \\\\\r\n& = \\dfrac{\\pi}{2} \\displaystyle\\int _ {\\frac{\\pi}{8}}^{\\frac{7 \\pi}{24}} \\left\\{ 1 -\\cos 4x -1 +\\cos \\left( 2x +\\dfrac{\\pi}{4} \\right) \\right\\} \\, dx \\\\\r\n& = \\dfrac{\\pi}{2} \\left[ \\dfrac{1}{2} \\sin \\left( 2x +\\dfrac{\\pi}{4} \\right) -\\dfrac{1}{4} \\sin 4x \\right] _ {\\frac{\\pi}{8}}^{\\frac{7 \\pi}{24}} \\\\\r\n& = \\dfrac{\\pi}{8} \\left( 2 \\sin \\dfrac{5 \\pi}{6} -\\sin \\dfrac{7 \\pi}{6} \\right) -\\dfrac{\\pi}{8} \\left( 2 \\sin \\dfrac{\\pi}{2} -\\sin \\dfrac{\\pi}{2} \\right) \\\\\r\n& = \\dfrac{3 \\pi}{16} -\\dfrac{\\pi}{8} \\\\\r\n& = \\underline{\\dfrac{\\pi}{16}}\r\n\\end{align}\\]\r\n","protected":false},"excerpt":{"rendered":"\\(2\\) \u3064\u306e\u95a2\u6570 \\(y = \\sin \\left( x +\\dfrac{\\pi}{8} \\right)\\) \u3068 \\(y = \\sin 2x\\) \u306e\u30b0\u30e9\u30d5\u306e \\(0 \\leqq x \\leqq \\dfrac{\\pi} &hellip; <a href=\"https:\/\/www.roundown.net\/nyushi\/kyr201501\/\">\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":[126],"tags":[140,137],"class_list":["post-1232","post","type-post","status-publish","format-standard","hentry","category-kyoto_r_2015","tag-kyoto_r","tag-137"],"_links":{"self":[{"href":"https:\/\/www.roundown.net\/nyushi\/wp-json\/wp\/v2\/posts\/1232","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=1232"}],"version-history":[{"count":0,"href":"https:\/\/www.roundown.net\/nyushi\/wp-json\/wp\/v2\/posts\/1232\/revisions"}],"wp:attachment":[{"href":"https:\/\/www.roundown.net\/nyushi\/wp-json\/wp\/v2\/media?parent=1232"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.roundown.net\/nyushi\/wp-json\/wp\/v2\/categories?post=1232"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.roundown.net\/nyushi\/wp-json\/wp\/v2\/tags?post=1232"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}