{"id":64,"date":"2011-11-26T20:43:42","date_gmt":"2011-11-26T11:43:42","guid":{"rendered":"http:\/\/roundown.main.jp\/nyushi\/?p=64"},"modified":"2021-10-23T04:17:25","modified_gmt":"2021-10-22T19:17:25","slug":"wsr201104","status":"publish","type":"post","link":"https:\/\/www.roundown.net\/nyushi\/wsr201104\/","title":{"rendered":"\u65e9\u7a32\u7530\u7406\u5de52011\uff1a\u7b2c4\u554f"},"content":{"rendered":"
\n

\\(xy\\) \u5e73\u9762\u4e0a\u306e\u539f\u70b9\u3092 O \u3068\u3057, \u6955\u5186 \\(\\dfrac{x^2}{a^2} +\\dfrac{y^2}{b^2} = 1 \\ ( a \\gt b \\gt 0 )\\) \u3092 \\(E\\) \u3068\u3059\u308b.\r\n\\(E\\) \u4e0a\u306e\u70b9 P \\(( s , t )\\) \u306b\u304a\u3051\u308b \\(E\\) \u306e\u6cd5\u7dda\u3068 \\(x\\) \u8ef8\u3068\u306e\u4ea4\u70b9\u3092 Q \u3068\u3059\u308b. \u70b9 P \u304c \\(s \\gt 0 , \\ t \\gt 0\\) \u306e\u7bc4\u56f2\u3092\u52d5\u304f\u3068\u304d, \\(\\angle \\text{OPQ}\\) \u304c\u6700\u5927\u306b\u306a\u308b\u70b9 P \u3092\u6c42\u3081\u3088.<\/p>\r\n

\r\n\r\n

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

\\(s =a \\cos \\theta\\) , \\(t =b \\sin \\theta \\ \\left( 0 \\lt \\theta \\lt \\dfrac{\\pi}{2} \\right) \\quad ... [1]\\) \u3068\u304a\u304f.<\/p>\r\n\"waseda_2011_04_01\"\r\n

\u70b9 P \u306b\u304a\u3051\u308b \\(E\\) \u306e\u6cd5\u7dda, \u76f4\u7dda OP \u304c \\(x\\) \u8ef8\u6b63\u65b9\u5411\u3068\u306a\u3059\u89d2\u3092, \u305d\u308c\u305e\u308c \\(\\alpha\\) , \\(\\beta\\) \u3068\u304a\u304f\u3068\r\n\\[\r\n\\angle \\text{OPQ} = \\alpha -\\beta\r\n\\]\r\n\\(0 \\lt \\alpha \\lt \\beta \\lt \\dfrac{\\pi}{2}\\) \u3088\u308a, \\(0 \\lt \\angle \\text{OPQ} \\lt \\dfrac{\\pi}{2}\\) \u306a\u306e\u3067, \\(\\tan (\\alpha -\\beta)\\) \u304c\u6700\u5927\u306b\u306a\u308b\u3068\u304d\u3092\u8003\u3048\u308c\u3070\u3088\u3044.
\r\n\u70b9 P \u306b\u304a\u3051\u308b\u63a5\u7dda\u306e\u65b9\u7a0b\u5f0f\u306f\r\n\\[\r\n\\dfrac{x \\cos \\theta}{a} +\\dfrac{y \\sin \\theta}{b} = 1\r\n\\]\r\n\u63a5\u7dda\u306e\u50be\u304d\u306f, \\(-\\dfrac{b \\cos \\theta}{a \\sin \\theta}\\) \u3060\u304b\u3089, \u6cd5\u7dda\u306e\u50be\u304d\u306f, \\(\\dfrac{a \\sin \\theta}{b \\cos \\theta}\\) \u306a\u306e\u3067\r\n\\[\r\n\\tan \\alpha = \\dfrac{a \\sin \\theta}{b \\cos \\theta}\r\n\\]\r\n\u307e\u305f, \u76f4\u7dda OP \u306e\u50be\u304d\u306f \\(\\dfrac{b \\sin \\theta}{a \\cos \\theta}\\) \u306a\u306e\u3067\r\n\\[\r\n\\tan \\beta = \\dfrac{b \\sin \\theta}{a \\cos \\theta}\r\n\\]\r\n\u4ee5\u4e0a\u3088\u308a\r\n\\[\\begin{align}\r\n\\tan (\\alpha -\\beta) & = \\dfrac{\\tan \\alpha -\\tan \\beta}{1+\\tan \\alpha \\tan \\beta} \\\\\r\n& = \\dfrac{\\dfrac{a \\sin \\theta}{b \\cos \\theta}-\\dfrac{b \\sin \\theta}{a \\cos \\theta}}{1+\\dfrac{a \\sin \\theta}{b \\cos \\theta} \\cdot \\dfrac{b \\sin \\theta}{a \\cos \\theta}} \\\\\r\n& = \\dfrac{\\left( a^2-b^2 \\right) \\cos \\theta \\sin \\theta}{ab \\left( \\cos^2 \\theta +\\sin^2 \\theta \\right)} \\\\\r\n& = \\dfrac{a^2-b^2}{2ab} \\sin 2\\theta\r\n\\end{align}\\]\r\n\\(a \\gt b \\gt 0\\) \u306a\u306e\u3067, \\(\\theta\\) \u304c[1] \u306e\u7bc4\u56f2\u3092\u52d5\u304f\u3068\u304d, \\(\\tan (\\alpha -\\beta)\\) \u306f \\(\\theta = \\dfrac{\\pi}{4}\\) \u306e\u3068\u304d\u306b, \u6700\u5927\u3068\u306a\u308b.
\r\n\u3088\u3063\u3066, \u6c42\u3081\u308b\u70b9 P \u306f\r\n\\[\r\n\\underline{\\left( \\dfrac{\\sqrt{2} a}{2} , \\dfrac{\\sqrt{2} b}{2} \\right)}\r\n\\]\r\n","protected":false},"excerpt":{"rendered":"\\(xy\\) \u5e73\u9762\u4e0a\u306e\u539f\u70b9\u3092 O \u3068\u3057, \u6955\u5186 \\(\\dfrac{x^2}{a^2} +\\dfrac{y^2}{b^2} = 1 \\ ( a \\gt b \\gt 0 )\\) \u3092 \\(E\\) \u3068\u3059\u308b. \\(E\\) \u4e0a\u306e\u70b9 … \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":[38],"tags":[147,13],"class_list":["post-64","post","type-post","status-publish","format-standard","hentry","category-waseda_r_2011","tag-waseda_r","tag-13"],"_links":{"self":[{"href":"https:\/\/www.roundown.net\/nyushi\/wp-json\/wp\/v2\/posts\/64","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=64"}],"version-history":[{"count":0,"href":"https:\/\/www.roundown.net\/nyushi\/wp-json\/wp\/v2\/posts\/64\/revisions"}],"wp:attachment":[{"href":"https:\/\/www.roundown.net\/nyushi\/wp-json\/wp\/v2\/media?parent=64"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.roundown.net\/nyushi\/wp-json\/wp\/v2\/categories?post=64"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.roundown.net\/nyushi\/wp-json\/wp\/v2\/tags?post=64"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}