{"id":84,"date":"2011-11-26T23:07:21","date_gmt":"2011-11-26T14:07:21","guid":{"rendered":"http:\/\/roundown.main.jp\/nyushi\/?p=84"},"modified":"2021-10-20T15:19:29","modified_gmt":"2021-10-20T06:19:29","slug":"ykr201102","status":"publish","type":"post","link":"https:\/\/www.roundown.net\/nyushi\/ykr201102\/","title":{"rendered":"\u6a2a\u56fd\u5927\u7406\u7cfb2011\uff1a\u7b2c2\u554f"},"content":{"rendered":"
\n

\u6b21\u306e\u554f\u3044\u306b\u7b54\u3048\u3088.<\/p>\r\n

    \r\n

  1. (1)<\/strong>\u3000\\(0 \\leqq x \\leqq \\pi\\) \u306b\u304a\u3044\u3066, \\(\\big| \\cos x \\big| = \\sin x\\) \u3092\u6e80\u305f\u3059 \\(x\\) \u3092\u6c42\u3081, \\(0 \\leqq x \\leqq \\pi\\) \u306b\u304a\u3044\u3066, \\(\\cos ( \\cos x )\\) , \\(\\cos ( \\sin x )\\) \u306e\u5927\u5c0f\u3092\u6bd4\u8f03\u305b\u3088.<\/p><\/li>\r\n

  2. (2)<\/strong>\u3000\\(\\alpha \\geqq 0\\) , \\(\\beta \\geqq 0\\) , \\(\\alpha +\\beta \\lt \\dfrac{\\pi}{2}\\) \u306e\u3068\u304d, \\(\\cos \\alpha \\gt \\sin \\beta\\) \u3068\u306a\u308b\u3053\u3068\u3092\u793a\u3057, \\(0 \\leqq x \\leqq \\pi\\) \u306b\u304a\u3044\u3066, \\(\\cos ( \\cos x ) \\gt \\sin ( \\sin x )\\) \u3092\u793a\u305b.<\/p><\/li>\r\n<\/ol>\r\n

    \r\n\r\n

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

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

    \\(\\big| \\cos x \\big| = \\sin x\\) \u3088\u308a\r\n\\[\\begin{gather}\r\n\\cos x = \\pm \\sin x \\\\\r\n\\sqrt{2} \\left( \\dfrac{1}{\\sqrt{2}} \\cos x \\mp \\dfrac{1}{\\sqrt{2}} \\sin x \\right) = 0 \\\\\r\n\\text{\u2234} \\quad \\cos \\left( x \\pm \\dfrac{\\pi}{4} \\right) = 0\r\n\\end{gather}\\]\r\n\\(0 \\leqq x \\leqq \\pi\\) \u306b\u304a\u3044\u3066, \u3053\u308c\u3092\u89e3\u3051\u3070\r\n\\[\r\nx = \\underline{\\dfrac{\\pi}{4} , \\dfrac{3 \\pi}{4}}\r\n\\]\r\n\u7d9a\u3044\u3066, \\(\\cos ( \\cos x )\\) , \\(\\cos ( \\sin x )\\) \u306e\u5927\u5c0f\u3092\u6bd4\u8f03\u3059\u308b.
    \r\n\\(\\cos (-x) = \\cos x\\) \u3067\u3042\u308a, \\(0 \\leqq x \\leqq 1\\) \u306b\u304a\u3044\u3066, \\(\\cos x\\) \u306f\u5358\u8abf\u6e1b\u5c11\u3059\u308b\u306e\u3067, \\(\\big| \\cos x \\big|\\) , \\(\\sin x\\) \u306e\u5927\u5c0f\u3092\u6bd4\u8f03\u3059\u308c\u3070\u3088\u3044.
    \r\n\u3057\u305f\u304c\u3063\u3066,\r\n\\[\r\n\\underline{\\left\\{ \\begin{array}{ll} \\cos ( \\cos x ) \\lt \\cos ( \\sin x ) & \\ \\left( 0 \\leqq x \\lt \\dfrac{\\pi}{4} , \\dfrac{3 \\pi}{4} \\lt x \\leqq \\pi \\text{\u306e\u3068\u304d} \\right) \\\\ \\cos ( \\cos x ) = \\cos ( \\sin x ) & \\ \\left( 0 \\leqq x = \\dfrac{\\pi}{4} , \\dfrac{3 \\pi}{4} \\text{\u306e\u3068\u304d} \\right) \\\\ \\cos ( \\cos x ) \\gt \\cos ( \\sin x ) & \\ \\left( \\dfrac{\\pi}{4} \\lt x \\lt \\dfrac{3 \\pi}{4} \\text{\u306e\u3068\u304d} \\right) \\end{array} \\right. }\r\n\\]\r\n

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

    \u6761\u4ef6\u3088\u308a\r\n\\[\r\n\\alpha \\lt \\dfrac{\\pi}{2} -\\beta\r\n\\]\r\n\\(0 \\leqq \\alpha \\lt \\dfrac{\\pi}{2}\\) , \\(0 \\leqq \\beta \\lt \\dfrac{\\pi}{2}\\) \u306a\u306e\u3067\r\n\\[\r\n\\cos \\alpha \\gt \\cos \\left( \\dfrac{\\pi}{2} -\\beta \\right) = \\sin \\beta \\quad ... [1]\r\n\\]\r\n\u307e\u305f\r\n\\[\r\n\\cos x +\\sin x = \\sqrt{2} \\sin \\left( x+\\dfrac{\\pi}{4} \\right) \\lt \\sqrt{2} \\lt \\dfrac{\\pi}{2}\r\n\\]\r\n\u306a\u306e\u3067, [1] \u3092\u7528\u3044\u308c\u3070,\r\n\\[\r\n\\cos ( \\cos x ) \\gt \\sin ( \\sin x )\r\n\\]\r\n","protected":false},"excerpt":{"rendered":"\u6b21\u306e\u554f\u3044\u306b\u7b54\u3048\u3088. (1)\u3000\\(0 \\leqq x \\leqq \\pi\\) \u306b\u304a\u3044\u3066, \\(\\big| \\cos x \\big| = \\sin x\\) \u3092\u6e80\u305f\u3059 \\(x\\) \u3092\u6c42\u3081, \\(0 \\leqq x \\leqq … \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":[44],"tags":[13,9],"class_list":["post-84","post","type-post","status-publish","format-standard","hentry","category-yokokoku_r_2011","tag-13","tag-yokokoku_r"],"_links":{"self":[{"href":"https:\/\/www.roundown.net\/nyushi\/wp-json\/wp\/v2\/posts\/84","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=84"}],"version-history":[{"count":0,"href":"https:\/\/www.roundown.net\/nyushi\/wp-json\/wp\/v2\/posts\/84\/revisions"}],"wp:attachment":[{"href":"https:\/\/www.roundown.net\/nyushi\/wp-json\/wp\/v2\/media?parent=84"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.roundown.net\/nyushi\/wp-json\/wp\/v2\/categories?post=84"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.roundown.net\/nyushi\/wp-json\/wp\/v2\/tags?post=84"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}