{"id":2023,"date":"2021-12-11T10:00:32","date_gmt":"2021-12-11T01:00:32","guid":{"rendered":"https:\/\/www.roundown.net\/nyushi\/?p=2023"},"modified":"2021-12-11T10:00:32","modified_gmt":"2021-12-11T01:00:32","slug":"tbr202102","status":"publish","type":"post","link":"https:\/\/www.roundown.net\/nyushi\/tbr202102\/","title":{"rendered":"\u7b51\u6ce2\u5927\u7406\u7cfb2021\uff1a\u7b2c2\u554f"},"content":{"rendered":"
\n

\\(t = \\sin \\theta +\\cos \\theta\\) \u3068\u3057,\r\n\\(\\theta\\) \u306f \\(-\\dfrac{\\pi}{2} \\lt \\theta \\lt \\dfrac{\\pi}{2}\\) \u306e\u7bc4\u56f2\u3092\u52d5\u304f\u3082\u306e\u3068\u3059\u308b.<\/p>\r\n

    \r\n

  1. (1)<\/strong>\u3000\\(t\\) \u306e\u3068\u308a\u3046\u308b\u5024\u306e\u7bc4\u56f2\u3092\u6c42\u3081\u3088.<\/p><\/li>\r\n

  2. (2)<\/strong>\u3000\\(\\sin^3 \\theta +\\cos^3 \\theta\\) \u3068 \\(\\cos 4 \\theta\\) \u3092, \u305d\u308c\u305e\u308c \\(t\\) \u3092\u7528\u3044\u3066\u8868\u305b.<\/p><\/li>\r\n

  3. (3)<\/strong>\u3000\\(\\sin^3 \\theta +\\cos^3 \\theta = \\cos 4 \\theta\\) \u3067\u3042\u308b\u3068\u304d, \\(t\\) \u306e\u5024\u3092\u3059\u3079\u3066\u6c42\u3081\u3088.<\/p><\/li>\r\n<\/ol>\r\n

    \r\n\r\n

    \u3010 \u89e3 \u7b54 \u3011<\/h4>\r\n

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

    \\[\r\nt = \\sqrt{2} \\sin \\left( \\theta +\\dfrac{\\pi}{4} \\right)\r\n\\]\r\n\\(-\\dfrac{\\pi}{2} \\lt \\theta \\lt \\dfrac{\\pi}{2}\\) \u306a\u306e\u3067, \\(-\\dfrac{\\pi}{4} \\lt \\theta +\\dfrac{\\pi}{4} \\lt \\dfrac{3 \\pi}{4}\\) .
    \r\n\u3088\u3063\u3066\r\n\\[\r\n\\underline{-1 \\lt t \\leqq \\sqrt{2}} \\quad ... [1]\r\n\\]\r\n

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

    \\[\\begin{align}\r\nt^2 & = 1 +2 \\sin \\theta \\cos \\theta \\\\\r\n\\text{\u2234} \\quad \\sin \\theta \\cos \\theta & = \\dfrac{t^2 -1}{2}\r\n\\end{align}\\]\r\n\u3057\u305f\u304c\u3063\u3066\r\n\\[\\begin{align}\r\n\\sin^3 \\theta +\\cos^3 \\theta & = \\left( \\sin \\theta +\\cos \\theta \\right) \\left( \\sin^2 \\theta -\\sin \\theta \\cos \\theta +\\cos^2 \\theta \\right) \\\\\r\n& = t \\left( 1 -\\dfrac{t^2 -1}{2} \\right) \\\\\r\n& = \\underline{\\dfrac{1}{2} t ( 3 -t^2 )} \\ , \\\\\r\n\\cos 4 \\theta & = 1 -2 \\sin^2 2 \\theta \\\\\r\n& = 1 -8 \\left( \\sin \\theta \\cos \\theta \\right)^2 \\\\\r\n& = 1 -2( t^2 -1 )^2 \\\\\r\n& = \\underline{-2x^4 +4t^2 -1}\r\n\\end{align}\\]\r\n

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

    (2)<\/strong> \u306e\u7d50\u679c\u3068\u6761\u4ef6\u3088\u308a\r\n\\[\\begin{align}\r\n\\dfrac{1}{2} t ( 3 -t^2 ) & = -2x^4 +4t^2 -1 \\\\\r\n4t^4 -t^3 -8t^2 +3t +2 & = 0 \\\\\r\n( t-1 )^2 ( 4t^2 +7t +2 ) & = 0 \\\\\r\n\\text{\u2234} \\quad t = 1 , \\dfrac{-7 \\pm \\sqrt{17}}{8}\r\n\\end{align}\\]\r\n\\(4 \\lt \\sqrt{17} \\lt 5\\) \u306b\u6ce8\u610f\u3059\u308c\u3070, [1] \u3092\u307f\u305f\u3059\u89e3\u306f\r\n\\[\r\nt = \\underline{1 , \\dfrac{-7 +\\sqrt{17}}{8}}\r\n\\]\r\n","protected":false},"excerpt":{"rendered":"\\(t = \\sin \\theta +\\cos \\theta\\) \u3068\u3057, \\(\\theta\\) \u306f \\(-\\dfrac{\\pi}{2} \\lt \\theta \\lt \\dfrac{\\pi}{2}\\) \u306e\u7bc4\u56f2\u3092\u52d5\u304f\u3082\u306e\u3068\u3059 … \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":[178],"tags":[144,165],"class_list":["post-2023","post","type-post","status-publish","format-standard","hentry","category-tsukuba_r_2021","tag-tsukuba_r","tag-165"],"_links":{"self":[{"href":"https:\/\/www.roundown.net\/nyushi\/wp-json\/wp\/v2\/posts\/2023","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=2023"}],"version-history":[{"count":0,"href":"https:\/\/www.roundown.net\/nyushi\/wp-json\/wp\/v2\/posts\/2023\/revisions"}],"wp:attachment":[{"href":"https:\/\/www.roundown.net\/nyushi\/wp-json\/wp\/v2\/media?parent=2023"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.roundown.net\/nyushi\/wp-json\/wp\/v2\/categories?post=2023"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.roundown.net\/nyushi\/wp-json\/wp\/v2\/tags?post=2023"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}