{"id":12579,"date":"2023-02-05T00:20:26","date_gmt":"2023-02-04T15:20:26","guid":{"rendered":"https:\/\/hatsudy.com\/jp\/?p=12579"},"modified":"2023-02-08T09:24:03","modified_gmt":"2023-02-08T00:24:03","slug":"polar-coordinates","status":"publish","type":"post","link":"https:\/\/hatsudy.com\/jp\/polar-coordinates.html","title":{"rendered":"\u6975\u5ea7\u6a19\u30fb\u6975\u65b9\u7a0b\u5f0f\uff1a\u76f4\u7dda\u3001\u5186\u3001\u4e8c\u6b21\u66f2\u7dda\u3067\u306e\u8ddd\u96e2\u3084\u9762\u7a4d\u306e\u516c\u5f0f"},"content":{"rendered":"\n<p>\u5ea7\u6a19\u3092\u8868\u3059\u3068\u304d\u3001\u901a\u5e38\u306f\\(x\\)\u8ef8\u3068\\(y\\)\u8ef8\u3092\u5229\u7528\u3057\u307e\u3059\u3002\u305f\u3060\u70b9\u306e\u5ea7\u6a19\u3092\u793a\u3059\u3068\u304d\u3001\u539f\u70b9\u3068\u306e\u8ddd\u96e2\\(r\\)\u3068\\(x\\)\u8ef8\u3068\u306e\u89d2\u5ea6\\(\u03b8\\)\u3092\u7528\u3044\u3066\u8868\u3059\u3053\u3068\u3082\u53ef\u80fd\u3067\u3059\u3002<\/p>\n<p>\\(r\\)\u3068\\(\u03b8\\)\u3092\u7528\u3044\u3066\u8868\u3055\u308c\u308b\u5ea7\u6a19\u3092\u6975\u5ea7\u6a19\u3068\u3044\u3044\u307e\u3059\u3002\u307e\u305f\u3001\u6975\u5ea7\u6a19\u3092\u7528\u3044\u3066\u8868\u3059\u65b9\u7a0b\u5f0f\u3092\u6975\u65b9\u7a0b\u5f0f\u3068\u3044\u3044\u307e\u3059\u3002<\/p>\n<p>\u6975\u65b9\u7a0b\u5f0f\u3092\u7528\u3044\u3066\u76f4\u7dda\u3084\u5186\u3092\u8868\u3059\u3068\u304d\u3001\u8907\u6570\u306e\u65b9\u6cd5\u304c\u3042\u308a\u307e\u3059\u3002\u6975\u65b9\u7a0b\u5f0f\u3092\u899a\u3048\u3066\u3082\u610f\u5473\u304c\u306a\u3044\u306e\u3067\u3001\u3069\u306e\u3088\u3046\u306b\u6975\u65b9\u7a0b\u5f0f\u3092\u4f5c\u308c\u3070\u3044\u3044\u306e\u304b\u7406\u89e3\u3057\u307e\u3057\u3087\u3046\u3002\u307e\u305f\u6975\u65b9\u7a0b\u5f0f\u306e\u4f5c\u308a\u65b9\u3092\u77e5\u308c\u3070\u3001\u4e8c\u6b21\u66f2\u7dda\uff08\u653e\u7269\u7dda\u3001\u6955\u5186\u3001\u53cc\u66f2\u7dda\uff09\u306e\u6975\u65b9\u7a0b\u5f0f\u3092\u5f97\u308b\u3053\u3068\u3082\u3067\u304d\u307e\u3059\u3002<\/p>\n<p>\u305d\u308c\u3067\u306f\u3001\u6975\u5ea7\u6a19\u3084\u6975\u65b9\u7a0b\u5f0f\u3092\u5229\u7528\u3057\u3066\u3069\u306e\u3088\u3046\u306b\u8ddd\u96e2\u3084\u9762\u7a4d\u3092\u8a08\u7b97\u3059\u308c\u3070\u3044\u3044\u306e\u3067\u3057\u3087\u3046\u304b\u3002\u516c\u5f0f\u306e\u5229\u7528\u6cd5\u3084\u6975\u65b9\u7a0b\u5f0f\u306e\u5c0e\u51fa\u6cd5\u3092\u89e3\u8aac\u3057\u3066\u3044\u304d\u307e\u3059\u3002<\/p>\n<h2>\u8ddd\u96e2\u3068\u89d2\u5ea6\u3092\u7528\u3044\u3066\u8868\u3059\u6975\u5ea7\u6a19<\/h2>\n<p>\u5ea7\u6a19\u3092\u7528\u3044\u308b\u3053\u3068\u306b\u3088\u308a\u3001\u5e73\u9762\u4e0a\u306e\u4e00\u3064\u306e\u70b9\u3092\u8868\u3059\u3053\u3068\u304c\u3067\u304d\u307e\u3059\u3002\u4e00\u65b9\u3001\u539f\u70b9\u304b\u3089\u306e\u8ddd\u96e2\u3068\u89d2\u5ea6\u3092\u7528\u3044\u3066\u4e00\u3064\u306e\u70b9\u3092\u8868\u3059\u3053\u3068\u3082\u3067\u304d\u307e\u3059\u3002<\/p>\n<p>\u4f8b\u3048\u3070\u70b9P\u304c\\((4,4)\\)\u306e\u5834\u5408\u3001\u539f\u70b9\u304b\u3089\u306e\u9577\u3055\u306f\\(4\\sqrt{2}\\)\u3067\u3042\u308a\u3001\u89d2\u5ea6\u306f\\(\\displaystyle\\frac{\u03c0}{4}\\)\u3067\u3059\u3002\u305d\u306e\u305f\u3081\u3001<span style=\"color: #0000ff;\">\u9577\u3055\u3068\u89d2\u5ea6\u3092\u7528\u3044\u3066\u70b9P\u3092\u8868\u3059\u3053\u3068\u304c\u3067\u304d\u307e\u3059\u3002<\/span>\u6975\u5ea7\u6a19\u306f\\((r,\u03b8)\\)\u3067\u8868\u3059\u305f\u3081\u3001\\((4,4)\\)\u306f\\(\\left(4\\sqrt{2},\\displaystyle\\frac{\u03c0}{4}\\right)\\)\u3068\u8868\u305b\u307e\u3059\u3002<\/p>\n<p><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/hatsudy.com\/jp\/wp-content\/uploads\/2023\/02\/jdh1.jpg\" alt=\"\" width=\"483\" height=\"202\" class=\"aligncenter size-full wp-image-12580\" \/><\/p>\n<p>\u3053\u306e\u3068\u304d\u3001\\((x,y)\\)\u306f\u4ee5\u4e0b\u306e\u3088\u3046\u306b\u8868\u3059\u3053\u3068\u304c\u3067\u304d\u307e\u3059\u3002<\/p>\n<ul>\n<li>\\(x=rcos\u03b8\\)<\/li>\n<li>\\(y=rsin\u03b8\\)<\/li>\n<\/ul>\n<p>\u307e\u305f\u3001\\((x,y)\\)\u3092\u7528\u3044\u3066\u4ee5\u4e0b\u306e\u3088\u3046\u306b\\(r\\)\u3068\\(\u03b8\\)\u3092\u8a08\u7b97\u3067\u304d\u307e\u3059\u3002<\/p>\n<ul>\n<li>\\(r=\\sqrt{x^2+y^2}\\)<\/li>\n<li>\\(cos\u03b8=\\displaystyle\\frac{x}{r}\\)\u3001\\(sin\u03b8=\\displaystyle\\frac{y}{r}\\)<\/li>\n<\/ul>\n<p>\u3053\u308c\u3089\u306e\u95a2\u4fc2\u306b\u3064\u3044\u3066\u306f\u3001\u8aac\u660e\u3057\u306a\u304f\u3066\u3082\u7406\u89e3\u3067\u304d\u308b\u3068\u601d\u3044\u307e\u3059\u3002<\/p>\n<h3>2\u70b9\u9593\u306e\u8ddd\u96e2\u306e\u9577\u3055\u3068\u9762\u7a4d\u306e\u8a08\u7b97<\/h3>\n<p>\u305d\u308c\u3067\u306f\u3001\u6975\u5ea7\u6a19\u3092\u7528\u3044\u30662\u70b9\u9593\u306e\u8ddd\u96e2\u3092\u8a08\u7b97\u3067\u304d\u308b\u3088\u3046\u306b\u306a\u308a\u307e\u3057\u3087\u3046\u3002\u65b9\u6cd5\u306f\u7c21\u5358\u3067\u3042\u308a\u3001\u4f59\u5f26\u5b9a\u7406\u3092\u5229\u7528\u3057\u307e\u3059\u3002<\/p>\n<p>\u70b9O\u3092\u6975\uff08\u539f\u70b9\uff09\u3068\u3059\u308b\u3068\u3001\u70b9A\\((r_1,\u03b8_1)\\)\u3068\u70b9B\\((r_2,\u03b8_2)\\)\u306e\u8ddd\u96e2AB\u3092\u4ee5\u4e0b\u306e\u3088\u3046\u306b\u8868\u3059\u3053\u3068\u304c\u3067\u304d\u307e\u3059\u3002<\/p>\n<ul>\n<li>\\(AB=\\sqrt{r_1^2+r_2^2-2r_1r_2cos(\u03b8_2-\u03b8_1)}\\)<\/li>\n<\/ul>\n<p><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/hatsudy.com\/jp\/wp-content\/uploads\/2023\/02\/jdh3.jpg\" alt=\"\" width=\"324\" height=\"245\" class=\"aligncenter size-full wp-image-12582\" \/><\/p>\n<p>\u4f59\u5f26\u5b9a\u7406\u3092\u5229\u7528\u3057\u3066\u5f0f\u3092\u8868\u3057\u3066\u3044\u308b\u3060\u3051\u306a\u306e\u3067\u3001\u7279\u306b\u554f\u984c\u306a\u304f\u7406\u89e3\u3067\u304d\u308b\u3068\u601d\u3044\u307e\u3059\u3002\u4f59\u5f26\u5b9a\u7406\u3092\u5229\u7528\u3057\u3066\u8a08\u7b97\u3059\u308c\u3070\u3044\u3044\u3068\u5b66\u3079\u3070\u3001\u65b0\u305f\u306b\u516c\u5f0f\u3092\u899a\u3048\u306a\u304f\u3066\u3082\u3044\u3044\u3068\u308f\u304b\u308a\u307e\u3059\u3002<\/p>\n<p>\u307e\u305f\u3001\u6975\u65b9\u7a0b\u5f0f\u3092\u5229\u7528\u3057\u3066\u9762\u7a4d\u3092\u8a08\u7b97\u3059\u308b\u3053\u3068\u3082\u3067\u304d\u307e\u3059\u3002\u9762\u7a4d\\(S\\)\u3092\u5f97\u308b\u516c\u5f0f\u3092\u899a\u3048\u308b\u5fc5\u8981\u3082\u306a\u304f\u3001\\(S=\\displaystyle\\frac{1}{2}absin\u03b8\\)\u3092\u5229\u7528\u3057\u3066\u8a08\u7b97\u3057\u307e\u3057\u3087\u3046\u3002<\/p>\n<p><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/hatsudy.com\/jp\/wp-content\/uploads\/2022\/03\/ijhg2.jpg\" alt=\"\" width=\"600\" height=\"168\" class=\"aligncenter size-full wp-image-4829\" \/><\/p>\n<p>\u5148\u307b\u3069\u3068\u540c\u3058\u304f\u3001\u70b9A\\((r_1,\u03b8_1)\\)\u3068\u70b9B\\((r_2,\u03b8_2)\\)\u3092\u5229\u7528\u3059\u308b\u3068\u3001\u9762\u7a4d\u306e\u516c\u5f0f\u306f\u4ee5\u4e0b\u306e\u3088\u3046\u306b\u306a\u308a\u307e\u3059\u3002<\/p>\n<ul>\n<li>\\(S=\\displaystyle\\frac{1}{2}r_1r_2|sin(\u03b8_2-\u03b8_1)|\\)<\/li>\n<\/ul>\n<p><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/hatsudy.com\/jp\/wp-content\/uploads\/2023\/02\/jdh4.jpg\" alt=\"\" width=\"324\" height=\"245\" class=\"aligncenter size-full wp-image-12583\" \/><\/p>\n<p>\u4e09\u89d2\u5f62\u306e\u9762\u7a4d\u3092\u8a08\u7b97\u3059\u308b\u3068\u304d\u306b\u3064\u3044\u3066\u3082\u3001\u516c\u5f0f\u3092\u899a\u3048\u308b\u3053\u3068\u306a\u304f\u3001\u6975\u5ea7\u6a19\u3092\u5229\u7528\u3057\u3066\u9762\u7a4d\u3092\u5f97\u307e\u3057\u3087\u3046\u3002<\/p>\n<h2>\u6975\u65b9\u7a0b\u5f0f\u3092\u5229\u7528\u3057\u3066\u76f4\u7dda\u3068\u5186\u3092\u8868\u73fe\u3059\u308b<\/h2>\n<p>\u305d\u308c\u3067\u306f\u3001\u6975\u5ea7\u6a19\u3092\u7528\u3044\u3066\u76f4\u7dda\u3084\u5186\u3092\u8868\u73fe\u3057\u307e\u3057\u3087\u3046\u3002\u6975\u5ea7\u6a19\u3092\u7528\u3044\u3066\u8868\u3059\u76f4\u7dda\u3084\u5186\u306e\u5f0f\u3092\u6975\u65b9\u7a0b\u5f0f\u3068\u3044\u3044\u307e\u3059\u3002<\/p>\n<p>\u6975\u65b9\u7a0b\u5f0f\u306b\u3064\u3044\u3066\u3082\u3001\u6975\u5ea7\u6a19\u3068\u540c\u69d8\u306b\u6697\u8a18\u3057\u3066\u306f\u3044\u3051\u307e\u305b\u3093\u3002\u6559\u79d1\u66f8\u306b\u8a18\u8f09\u3055\u308c\u3066\u3044\u308b\u6975\u65b9\u7a0b\u5f0f\u3092\u899a\u3048\u3066\u3082\u610f\u5473\u304c\u306a\u3044\u305f\u3081\u3001\u76f4\u7dda\u306e\u6975\u65b9\u7a0b\u5f0f\u3084\u5186\u306e\u6975\u65b9\u7a0b\u5f0f\u3092\u5f97\u308b\u65b9\u6cd5\u3092\u5b66\u3076\u5fc5\u8981\u304c\u3042\u308a\u307e\u3059\u3002<\/p>\n<p>\u306a\u304a\u3001\u6975\u65b9\u7a0b\u5f0f\u306e\u516c\u5f0f\u3092\u898b\u3066\u3082\u7406\u89e3\u3067\u304d\u307e\u305b\u3093\u3002\u305d\u3053\u3067\u3001\u56f3\u3092\u5229\u7528\u3057\u307e\u3057\u3087\u3046\u3002\u56f3\u3092\u63cf\u3051\u3070\u3001\u306a\u305c\u305d\u306e\u3088\u3046\u306a\u6975\u65b9\u7a0b\u5f0f\u306b\u306a\u308b\u306e\u304b\u5bb9\u6613\u306b\u308f\u304b\u308a\u307e\u3059\u3002<\/p>\n<h3>\u56f3\u3092\u7528\u3044\u3066\u76f4\u7dda\u306e\u6975\u65b9\u7a0b\u5f0f\u3092\u8868\u3059<\/h3>\n<p>\u6975\u5ea7\u6a19\u3092\u7528\u3044\u3066\u76f4\u7dda\u3092\u8868\u3059\u3068\u304d\u30012\u3064\u306e\u65b9\u6cd5\u304c\u3042\u308a\u307e\u3059\u3002\u4ee5\u4e0b\u304c\u76f4\u7dda\u306e\u6975\u65b9\u7a0b\u5f0f\u3067\u3059\u3002<\/p>\n<ul>\n<li>\u6975O\u3092\u901a\u308a\u3001\u59cb\u7dda\u3068\u306e\u306a\u3059\u89d2\u304c\\(\u03b1\\)\u306e\u5834\u5408\uff1a\\(\u03b8=\u03b1\\)<\/li>\n<li>\u70b9A\\((a,\u03b1)\\)\u3092\u901a\u308a\u3001OA\u306b\u5782\u76f4\u306a\u76f4\u7dda\uff1a\\(rcos(\u03b8-\u03b1)=a\\)<\/li>\n<\/ul>\n<p>\u6050\u3089\u304f\u610f\u5473\u3092\u7406\u89e3\u3067\u304d\u306a\u3044\u3068\u601d\u3046\u306e\u3067\u3001\u3053\u306e\u6975\u65b9\u7a0b\u5f0f\u304c\u4f55\u3092\u610f\u5473\u3057\u3066\u3044\u308b\u306e\u304b\u5b66\u3073\u307e\u3057\u3087\u3046\u3002<\/p>\n<p><strong>\u30fb\u6975O\u3092\u901a\u308a\u3001\u59cb\u7dda\u3068\u306e\u306a\u3059\u89d2\u304c\\(\u03b1\\)\u306e\u5834\u5408\uff1a\\(\u03b8=\u03b1\\)<\/strong><\/p>\n<p>\u4f8b\u3068\u3057\u3066\u3001\u59cb\u7dda\u3068\u306e\u306a\u3059\u89d2\u304c\\(\\displaystyle\\frac{\u03c0}{4}\\)\u306e\u30b1\u30fc\u30b9\u3092\u8003\u3048\u307e\u3057\u3087\u3046\u3002\u89d2\u5ea6\u306f\\(\\displaystyle\\frac{\u03c0}{4}\\)\u3067\u3042\u308b\u3082\u306e\u306e\u3001\u9577\u3055\\(r\\)\u304c\u6c7a\u307e\u3063\u3066\u3044\u306a\u3044\u5834\u5408\u3001\u89d2\u5ea6\u304c\\(\\displaystyle\\frac{\u03c0}{4}\\)\u3067\u6975O\u3092\u901a\u308b\u76f4\u7dda\u3068\u306a\u308a\u307e\u3059\u3002<\/p>\n<p><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/hatsudy.com\/jp\/wp-content\/uploads\/2023\/02\/jdh5.jpg\" alt=\"\" width=\"248\" height=\"271\" class=\"aligncenter size-full wp-image-12584\" \/><\/p>\n<p>\u305d\u306e\u305f\u3081\u3001\u76f4\u7dda\u306e\u6975\u65b9\u7a0b\u5f0f\u306f\\(\u03b8=\u03b1\\)\u3068\u306a\u308b\u306e\u3067\u3059\u3002<\/p>\n<p><strong>\u30fb\u70b9A\\((a,\u03b1)\\)\u3092\u901a\u308a\u3001OA\u306b\u5782\u76f4\u306a\u76f4\u7dda\uff1a\\(rcos(\u03b8-\u03b1)=a\\)<\/strong><\/p>\n<p>\u70b9A\\((a,\u03b1)\\)\u3092\u901a\u308b\u5834\u5408\u3001\u89d2\u5ea6\\(\u03b8\\)\u306b\u3088\u3063\u3066\u70b9P\u306e\u5834\u6240\u304c\u5909\u5316\u3057\u307e\u3059\u3002\u4e00\u65b9\u3001\u6975O\u3068\u70b9A\u306e\u8ddd\u96e2\u306f\u5909\u5316\u3057\u307e\u305b\u3093\u3002\u305d\u3053\u3067\u3001OA\u306e\u9577\u3055\u3092\u5f0f\u3067\u8868\u3057\u307e\u3057\u3087\u3046\u3002\u56f3\u3092\u4f5c\u308b\u3068\u3001\u4ee5\u4e0b\u306e\u95a2\u4fc2\u304c\u6210\u308a\u7acb\u3064\u3068\u308f\u304b\u308a\u307e\u3059\u3002<\/p>\n<ul>\n<li>\\(OA=OPcos\u2220POA\\)<\/li>\n<\/ul>\n<p><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/hatsudy.com\/jp\/wp-content\/uploads\/2023\/02\/jdh7.jpg\" alt=\"\" width=\"406\" height=\"248\" class=\"aligncenter size-full wp-image-12587\" \/><\/p>\n<p>\\(OA=a\\)\u3001\\(OP=r\\)\u3001\\(\u2220POA=\u03b8-\u03b1\\)\u3067\u3059\u3002\u305d\u306e\u305f\u3081\u3001\u4ee5\u4e0b\u306e\u65b9\u7a0b\u5f0f\u304c\u6210\u308a\u7acb\u3064\u3068\u308f\u304b\u308a\u307e\u3059\u3002<\/p>\n<ul>\n<li>\\(rcos(\u03b8-\u03b1)=a\\)<\/li>\n<\/ul>\n<p>\u6559\u79d1\u66f8\u306b\u8a18\u8f09\u3055\u308c\u3066\u3044\u308b\u6975\u65b9\u7a0b\u5f0f\u3092\u898b\u3066\u3082\u7406\u89e3\u3067\u304d\u306a\u3044\u3082\u306e\u306e\u3001\u56f3\u3092\u5229\u7528\u3059\u308c\u3070\u5bb9\u6613\u306b\u6975\u65b9\u7a0b\u5f0f\u3092\u4f5c\u308c\u308b\u3088\u3046\u306b\u306a\u308a\u307e\u3059\u3002<\/p>\n<h3>\u5186\u306e\u6975\u65b9\u7a0b\u5f0f\uff1a\u4e2d\u5fc3\u3068\u534a\u5f84\u306e\u95a2\u4fc2<\/h3>\n<p>\u6b21\u306b\u3001\u5186\u306e\u6975\u65b9\u7a0b\u5f0f\u3092\u78ba\u8a8d\u3057\u307e\u3057\u3087\u3046\u3002\u4ee5\u4e0b\u304c\u5186\u306e\u6975\u65b9\u7a0b\u5f0f\u3067\u3059\u3002<\/p>\n<ul>\n<li>\u4e2d\u5fc3\u304c\u6975O\u3001\u534a\u5f84\\(a\\)\u306e\u5186\uff1a\\(r=a\\)<\/li>\n<li>\u4e2d\u5fc3\\((a,0)\\)\u3001\u534a\u5f84\\(a\\)\u306e\u5186\uff1a\\(r=2acos\u03b8\\)<\/li>\n<li>\u4e2d\u5fc3\\((r_0,\u03b8_0)\\)\u3001\u534a\u5f84\\(a\\)\u306e\u5186\uff1a\\(r^2-2rr_0cos(\u03b8-\u03b8_0)\\)\\(+r_0^2\\)\\(=a^2\\)<\/li>\n<\/ul>\n<p>\u305d\u308c\u305e\u308c\u306e\u6975\u65b9\u7a0b\u5f0f\u304c\u4f55\u3092\u8868\u3059\u306e\u304b\u78ba\u8a8d\u3057\u307e\u3057\u3087\u3046\u3002<\/p>\n<p><strong>\u30fb\u4e2d\u5fc3\u304c\u6975O\u3001\u534a\u5f84\\(a\\)\u306e\u5186\uff1a\\(r=a\\)<\/strong><\/p>\n<p>\u4e2d\u5fc3\u304c\u6975O\u306e\u5834\u5408\u3001\u534a\u5f84\\(a\\)\u306fOP\u306e\u9577\u3055\\(r\\)\u3068\u306a\u308a\u307e\u3059\u3002\u305d\u306e\u305f\u3081\u3001\\(r=a\\)\u304c\u6210\u308a\u7acb\u3061\u307e\u3059\u3002<\/p>\n<p><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/hatsudy.com\/jp\/wp-content\/uploads\/2023\/02\/jdh8.jpg\" alt=\"\" width=\"316\" height=\"297\" class=\"aligncenter size-full wp-image-12588\" \/><\/p>\n<p><strong>\u30fb\u4e2d\u5fc3\\((a,0)\\)\u3001\u534a\u5f84\\(a\\)\u306e\u5186\uff1a\\(r=2acos\u03b8\\)<\/strong><\/p>\n<p>\u4e2d\u5fc3\\((a,0)\\)\u3001\u534a\u5f84\\(a\\)\u306e\u5186\u306f\u3069\u306e\u3088\u3046\u306b\u8868\u305b\u3070\u3044\u3044\u3067\u3057\u3087\u3046\u304b\u3002\u4ee5\u4e0b\u306e\u56f3\u3092\u4f5c\u308a\u307e\u3057\u3087\u3046\u3002<\/p>\n<p><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/hatsudy.com\/jp\/wp-content\/uploads\/2023\/02\/jdh11.jpg\" alt=\"\" width=\"338\" height=\"297\" class=\"aligncenter size-full wp-image-12591\" \/><\/p>\n<p>\u3053\u306e\u56f3\u3092\u4f5c\u308b\u3068\u3001\u4ee5\u4e0b\u306e\u5f0f\u3092\u4f5c\u308c\u307e\u3059\u3002<\/p>\n<p>\\(OP=OCcos\u2220BOP\\)<\/p>\n<p>\\(r=2acos\u03b8\\)<\/p>\n<p>\u3053\u308c\u304c\u3001\u5186\u306e\u6975\u65b9\u7a0b\u5f0f\u3067\u3059\u3002\u8fba\u306e\u9577\u3055\u3068\u89d2\u5ea6\u3092\u5229\u7528\u3059\u308b\u3053\u3068\u306b\u3088\u308a\u3001\u6975\u65b9\u7a0b\u5f0f\u3067\u8868\u3059\u3053\u3068\u304c\u3067\u304d\u307e\u3059\u3002<\/p>\n<p><strong>\u30fb\u4e2d\u5fc3\\((r_0,\u03b8_0)\\)\u3001\u534a\u5f84\\(a\\)\u306e\u5186\uff1a\\(r^2-2rr_0cos(\u03b8-\u03b8_0)\\)\\(+r_0^2\\)\\(=a^2\\)<\/strong><\/p>\n<p>\u305f\u3060\u3001\u5186\u306e\u4e2d\u5fc3\u304c\u6975O\u3084\u59cb\u7dda\u4e0a\u306b\u5b58\u5728\u3057\u306a\u3044\u30b1\u30fc\u30b9\u304c\u591a\u3044\u3067\u3059\u3002\u305d\u3053\u3067\u4e2d\u5fc3\\((r_0,\u03b8_0)\\)\u3001\u534a\u5f84\\(a\\)\u306e\u5186\u3092\u6975\u65b9\u7a0b\u5f0f\u3067\u8868\u305b\u308b\u3088\u3046\u306b\u306a\u308a\u307e\u3057\u3087\u3046\u3002<\/p>\n<p>\u5148\u307b\u3069\u30012\u70b9\u9593\u306e\u8ddd\u96e2\u3092\u6975\u5ea7\u6a19\u3067\u8868\u3059\u3068\u304d\u306b\u4f59\u5f26\u5b9a\u7406\u3092\u5229\u7528\u3057\u307e\u3057\u305f\u3002<span style=\"color: #0000ff;\">\u5186\u3092\u6975\u65b9\u7a0b\u5f0f\u3067\u8868\u3059\u3068\u304d\u306b\u3064\u3044\u3066\u3082\u3001\u4f59\u5f26\u5b9a\u7406\u3092\u5229\u7528\u3057\u3066\u8a08\u7b97\u3057\u307e\u3057\u3087\u3046\u3002<\/span>\u307e\u305a\u3001\u4ee5\u4e0b\u306e\u56f3\u3092\u4f5c\u308a\u307e\u3059\u3002<\/p>\n<p><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/hatsudy.com\/jp\/wp-content\/uploads\/2023\/02\/jdh12.jpg\" alt=\"\" width=\"359\" height=\"254\" class=\"aligncenter size-full wp-image-12592\" \/><\/p>\n<p>\u4f59\u5f26\u5b9a\u7406\u3092\u5229\u7528\u3059\u308b\u3068\u3001\u4ee5\u4e0b\u306e\u5f0f\u3092\u4f5c\u308c\u307e\u3059\u3002<\/p>\n<ul>\n<li>\\(a^2=r^2+r_0^2-2rr_0cos(\u03b8-\u03b8_0)\\)<\/li>\n<\/ul>\n<p>\u3053\u3046\u3057\u3066\u3001\u5148\u307b\u3069\u8a18\u3057\u305f\u5f0f\u3092\u4f5c\u308b\u3053\u3068\u304c\u3067\u304d\u307e\u3057\u305f\u3002\u4f59\u5f26\u5b9a\u7406\u3092\u5229\u7528\u3059\u308c\u3070\u3044\u3044\u3068\u5b66\u3079\u3070\u3001\u5186\u306e\u6975\u65b9\u7a0b\u5f0f\u3092\u899a\u3048\u308b\u5fc5\u8981\u304c\u306a\u3044\u3068\u308f\u304b\u308a\u307e\u3059\u3002<\/p>\n<h4>\u6975\u65b9\u7a0b\u5f0f\u3092\u76f4\u4ea4\u5ea7\u6a19\u306e\u65b9\u7a0b\u5f0f\u3067\u8868\u3059<\/h4>\n<p>\u6975\u5ea7\u6a19\u306b\u5bfe\u3057\u3066\u3001\\(x\\)\u5ea7\u6a19\u3068\\(y\\)\u5ea7\u6a19\u3092\u7528\u3044\u3066\u8868\u3059\u65b9\u6cd5\u3092\u76f4\u4ea4\u5ea7\u6a19\u3068\u3044\u3044\u307e\u3059\u3002\u79c1\u305f\u3061\u304c\u3053\u308c\u307e\u3067\u5b66\u3093\u3067\u304d\u305f\u56f3\u5f62\u306f\u76f4\u4ea4\u5ea7\u6a19\u3092\u7528\u3044\u3066\u3044\u305f\u306e\u3067\u3059\u3002\u305d\u308c\u3067\u306f\u6975\u65b9\u7a0b\u5f0f\u306b\u3064\u3044\u3066\u3001\u76f4\u4ea4\u5ea7\u6a19\u3067\u306e\u65b9\u7a0b\u5f0f\u3067\u8868\u305b\u308b\u3088\u3046\u306b\u3057\u307e\u3057\u3087\u3046\u3002<\/p>\n<p>\u5fa9\u7fd2\u3059\u308b\u3068\u3001\u4ee5\u4e0b\u306e\u95a2\u4fc2\u304c\u6210\u308a\u7acb\u3061\u307e\u3059\u3002<\/p>\n<ul>\n<li>\\(r^2=x^2+y^2\\)<\/li>\n<li>\\(cos\u03b8=\\displaystyle\\frac{x}{r}\\)\u3001\\(sin\u03b8=\\displaystyle\\frac{y}{r}\\)<\/li>\n<\/ul>\n<p>\u305d\u3053\u3067\u3001\u3053\u306e\u95a2\u4fc2\u3092\u5229\u7528\u3059\u308b\u3053\u3068\u306b\u3088\u3063\u3066\u5f0f\u3092\u5909\u5f62\u3057\u307e\u3057\u3087\u3046\u3002\u4ee5\u4e0b\u306e\u6975\u65b9\u7a0b\u5f0f\u306b\u3064\u3044\u3066\u3001\u76f4\u4ea4\u5ea7\u6a19\u306e\u65b9\u7a0b\u5f0f\u3067\u8868\u3059\u3068\u3069\u306e\u3088\u3046\u306b\u306a\u308b\u3067\u3057\u3087\u3046\u304b\u3002<\/p>\n<ul>\n<li>\\(r=\\sqrt{3}cos\u03b8+sin\u03b8\\)<\/li>\n<\/ul>\n<p>\u4e21\u8fba\u306b\\(r\\)\u3092\u304b\u3051\u305f\u5f8c\u3001\\(r^2=x^2+y^2\\)\u3092\u4ee3\u5165\u3057\u307e\u3057\u3087\u3046\u3002<\/p>\n<p>\\(r=\\sqrt{3}cos\u03b8+sin\u03b8\\)<\/p>\n<p>\\(r^2=\\sqrt{3}rcos\u03b8+rsin\u03b8\\)<\/p>\n<p>\\(x^2+y^2=\\sqrt{3}rcos\u03b8+rsin\u03b8\\)<\/p>\n<p>\u307e\u305f\\(cos\u03b8=\\displaystyle\\frac{x}{r}\\)\u3001\\(sin\u03b8=\\displaystyle\\frac{y}{r}\\)\u3088\u308a\u3001\\(x=rcos\u03b8\\)\u3001\\(y=rsin\u03b8\\)\u3068\u306a\u308a\u307e\u3059\u3002\u305d\u3053\u3067\u3001\u3053\u306e\u5f0f\u3092\u4ee3\u5165\u3057\u307e\u3057\u3087\u3046\u3002<\/p>\n<p>\\(x^2+y^2=\\sqrt{3}rcos\u03b8+rsin\u03b8\\)<\/p>\n<p>\\(x^2+y^2=\\sqrt{3}x+y\\)<\/p>\n<p>\\(x^2-\\sqrt{3}x+y^2-y=0\\)<\/p>\n<p>\\(\\left(x-\\displaystyle\\frac{\\sqrt{3}}{2}\\right)^2+\\left(y-\\displaystyle\\frac{1}{2}\\right)^2=1\\)<\/p>\n<p>\u3053\u3046\u3057\u3066\u3001\u5186\u306e\u65b9\u7a0b\u5f0f\u3092\u5f97\u308b\u3053\u3068\u304c\u3067\u304d\u307e\u3057\u305f\u3002<\/p>\n<p>\u3061\u306a\u307f\u306b\u3001\u76f4\u4ea4\u5ea7\u6a19\u306e\u65b9\u7a0b\u5f0f\u3092\u6975\u65b9\u7a0b\u5f0f\u3078\u5909\u63db\u3059\u308b\u3068\u304d\u3001\\(x=rcos\u03b8\\)\u3068\\(y=rsin\u03b8\\)\u3092\u5229\u7528\u3057\u3066\u4ee3\u5165\u3057\u307e\u3057\u3087\u3046\u3002<\/p>\n<h3>\u96e2\u5fc3\u7387\u3092\u5229\u7528\u3057\u3001\u4e8c\u6b21\u66f2\u7dda\u306e\u6975\u65b9\u7a0b\u5f0f\u3092\u8868\u3059<\/h3>\n<p>\u305d\u308c\u3067\u306f\u3001\u4e8c\u6b21\u66f2\u7dda\uff08\u653e\u7269\u7dda\u3001\u6955\u5186\u3001\u53cc\u66f2\u7dda\uff09\u3092\u6975\u65b9\u7a0b\u5f0f\u3067\u8868\u3059\u3068\u3069\u306e\u3088\u3046\u306b\u306a\u308b\u306e\u3067\u3057\u3087\u3046\u304b\u3002\u539f\u70b9O\u304c\u7126\u70b9\u306e\u4e00\u3064\u3067\u3042\u308a\u3001\u6e96\u7dda\u304c\\(x=-a\\)\u306e\u3068\u304d\u3001\u70b9P\\((r,\u03b8)\\)\u3092\u3069\u306e\u3088\u3046\u306b\u8868\u305b\u3070\u3044\u3044\u3067\u3057\u3087\u3046\u304b\u3002\u70b9P\u304b\u3089\u6e96\u7dda\u3078\u5782\u76f4\u306b\u7dda\u3092\u5f15\u304f\u3068\u304d\u306e\u4ea4\u70b9\u3092H\u3001\u96e2\u5fc3\u7387\u3092\\(e\\)\u3068\u3059\u308b\u3068\u4ee5\u4e0b\u306e\u56f3\u3092\u63cf\u3051\u307e\u3059\u3002<\/p>\n<p><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/hatsudy.com\/jp\/wp-content\/uploads\/2023\/02\/jdh13.jpg\" alt=\"\" width=\"274\" height=\"210\" class=\"aligncenter size-full wp-image-12593\" \/><\/p>\n<p>\\(OP=r\\)\u3067\u3042\u308a\u3001\\(HP=a+rcos\u03b8\\)\u3067\u3059\u3002\u307e\u305f\u3001\u96e2\u5fc3\u7387\u3092\u7528\u3044\u3066\u4ee5\u4e0b\u306e\u5f0f\u3092\u4f5c\u308a\u307e\u3057\u3087\u3046\u3002<\/p>\n<p>\\(1:e=HP:OP\\)<\/p>\n<p>\\(eHP=OP\\)<\/p>\n<p>\\(e(a+rcos\u03b8)=r\\)<\/p>\n<p>\\(ea+ercos\u03b8=r\\)<\/p>\n<p>\\(r(1-ecos\u03b8)=ea\\)<\/p>\n<p>\\(r=\\displaystyle\\frac{ea}{1-ecos\u03b8}\\)<\/p>\n<p>\u3053\u3046\u3057\u3066\u3001\u4e8c\u6b21\u66f2\u7dda\u306e\u6975\u65b9\u7a0b\u5f0f\u3092\u8868\u3059\u3053\u3068\u304c\u3067\u304d\u307e\u3057\u305f\u3002<\/p>\n<p>\u306a\u304a\u5148\u307b\u3069\u3001\u6e96\u7dda\u304c\u7126\u70b9\uff08\u6975\uff09\u306e\u5de6\u5074\u306b\u5b58\u5728\u3059\u308b\u5834\u5408\u3092\u60f3\u5b9a\u3057\u3066\u6975\u65b9\u7a0b\u5f0f\u3092\u4f5c\u308a\u307e\u3057\u305f\u3002\u4e00\u65b9\u3067\u6e96\u7dda\u304c\u7126\u70b9\uff08\u6975\uff09\u306e\u53f3\u5074\u306b\u5b58\u5728\u3059\u308b\u5834\u5408\u3001\u6975\u65b9\u7a0b\u5f0f\u306f\\(r=\\displaystyle\\frac{ea}{1+ecos\u03b8}\\)\u3068\u306a\u308a\u307e\u3059\u3002<\/p>\n<p>\u96e2\u5fc3\u7387\\(e\\)\u306b\u3088\u3063\u3066\u3001\u4e8c\u6b21\u66f2\u7dda\u306f\u4ee5\u4e0b\u306e\u3088\u3046\u306b\u5909\u5316\u3057\u307e\u3059\u3002<\/p>\n<ul>\n<li>\\(0&lt;e&lt;1\\)\uff1a\u6955\u5186<\/li>\n<li>\\(e=1\\)\uff1a\u653e\u7269\u7dda<\/li>\n<li>\\(e&gt;1\\)\uff1a\u53cc\u66f2\u7dda<\/li>\n<\/ul>\n<p>\u6975\u65b9\u7a0b\u5f0f\u3067\u306f\u3001\u3059\u3079\u3066\u306e\u4e8c\u6b21\u66f2\u7dda\u3092\u4e00\u3064\u306e\u5f0f\u3067\u8868\u3059\u3053\u3068\u304c\u3067\u304d\u307e\u3059\u3002\u3053\u306e\u70b9\u306b\u3064\u3044\u3066\u3001\u6975\u65b9\u7a0b\u5f0f\u306f\u4fbf\u5229\u3067\u3059\u3002<\/p>\n<h2>\u6975\u5ea7\u6a19\u30fb\u6975\u65b9\u7a0b\u5f0f\u3092\u7528\u3044\u3066\u70b9\u3092\u8868\u3059<\/h2>\n<p>\u79c1\u305f\u3061\u304c\u65e5\u5e38\u7684\u306b\u5229\u7528\u3059\u308b\u5e73\u9762\u56f3\u5f62\u306e\u6982\u5ff5\u304c\u76f4\u4ea4\u5ea7\u6a19\u3067\u3059\u3002\u4e00\u65b9\u3067\u6975\u5ea7\u6a19\u3067\u306f\u3001\u6975\uff08\u539f\u70b9\uff09\u304b\u3089\u70b9\u307e\u3067\u306e\u9577\u3055\\(r\\)\u3068\u89d2\u5ea6\\(\u03b8\\)\u3092\u5229\u7528\u3057\u3066\u8868\u3057\u307e\u3059\u3002\u306a\u304a\u6975\u5ea7\u6a19\u3092\u7528\u3044\u30662\u70b9\u9593\u306e\u8ddd\u96e2\u3084\u9762\u7a4d\u3092\u8a08\u7b97\u3059\u308b\u3068\u304d\u3001\u516c\u5f0f\u3092\u899a\u3048\u308b\u306e\u3067\u306f\u306a\u304f\u3001\u8a08\u7b97\u65b9\u6cd5\u3092\u7406\u89e3\u3057\u307e\u3057\u3087\u3046\u3002<\/p>\n<p>\u6975\u5ea7\u6a19\u3092\u7528\u3044\u3066\u76f4\u7dda\u3084\u5186\u3092\u8868\u3059\u5834\u5408\u3001\u6975\u65b9\u7a0b\u5f0f\u3068\u547c\u3070\u308c\u307e\u3059\u3002\u6975\u65b9\u7a0b\u5f0f\u3092\u899a\u3048\u3066\u3082\u610f\u5473\u304c\u306a\u3044\u305f\u3081\u3001\u56f3\u3092\u5229\u7528\u3057\u3066\u6975\u65b9\u7a0b\u5f0f\u3092\u4f5c\u308c\u308b\u3088\u3046\u306b\u306a\u308a\u307e\u3057\u3087\u3046\u3002\u305d\u3046\u3059\u308c\u3070\u899a\u3048\u308b\u5fc5\u8981\u304c\u306a\u3044\u3067\u3059\u3057\u3001\u3059\u3079\u3066\u306e\u5fdc\u7528\u554f\u984c\u306b\u5bfe\u51e6\u3067\u304d\u307e\u3059\u3002<\/p>\n<p>\u306a\u304a\u6975\u65b9\u7a0b\u5f0f\u3092\u5229\u7528\u3059\u308b\u3053\u3068\u306b\u3088\u308a\u3001\u4e8c\u6b21\u66f2\u7dda\uff08\u653e\u7269\u7dda\u3001\u6955\u5186\u3001\u53cc\u66f2\u7dda\uff09\u3092\u8868\u3059\u3053\u3068\u3082\u3067\u304d\u307e\u3059\u3002\u6e96\u7dda\u306e\u4f4d\u7f6e\u306b\u3088\u3063\u3066\u6975\u65b9\u7a0b\u5f0f\u306f\u7570\u306a\u308b\u3082\u306e\u306e\u3001\u4e00\u3064\u306e\u5f0f\u306b\u3088\u3063\u3066\u3059\u3079\u3066\u306e\u4e8c\u6b21\u66f2\u7dda\u3092\u8868\u3059\u3053\u3068\u304c\u3067\u304d\u307e\u3059\u3002<\/p>\n<p>\u76f4\u4ea4\u5ea7\u6a19\u3060\u3051\u3067\u306a\u304f\u3001\u6975\u5ea7\u6a19\u3092\u7528\u3044\u3066\u70b9\u3092\u8868\u305b\u308b\u3088\u3046\u306b\u306a\u308a\u307e\u3057\u3087\u3046\u3002\u307e\u305f\u56f3\u3092\u63cf\u304f\u3053\u3068\u306b\u3088\u308a\u3001\u6975\u65b9\u7a0b\u5f0f\u3092\u5c0e\u51fa\u3067\u304d\u308b\u3088\u3046\u306b\u306a\u308a\u307e\u3057\u3087\u3046\u3002<\/p>\n","protected":false},"excerpt":{"rendered":"<p>\u5ea7\u6a19\u3092\u8868\u3059\u3068\u304d\u3001\u901a\u5e38\u306f\\(x\\)\u8ef8\u3068\\(y\\)\u8ef8\u3092\u5229\u7528\u3057\u307e\u3059\u3002\u305f\u3060\u70b9\u306e\u5ea7\u6a19\u3092\u793a\u3059\u3068\u304d\u3001\u539f\u70b9\u3068\u306e\u8ddd\u96e2\\(r\\)\u3068\\(x\\)\u8ef8\u3068\u306e\u89d2\u5ea6\\(\u03b8\\)\u3092\u7528\u3044\u3066\u8868\u3059\u3053\u3068\u3082\u53ef\u80fd\u3067\u3059\u3002 \\(r\\)\u3068\\(\u03b8\\)\u3092\u7528\u3044\u3066\u8868\u3055\u308c\u308b\u5ea7\u6a19\u3092\u6975\u5ea7\u6a19 [&hellip;]<\/p>\n","protected":false},"author":1,"featured_media":12595,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[13],"tags":[],"class_list":{"0":"post-12579","1":"post","2":"type-post","3":"status-publish","4":"format-standard","5":"has-post-thumbnail","7":"category-h-math"},"_links":{"self":[{"href":"https:\/\/hatsudy.com\/jp\/wp-json\/wp\/v2\/posts\/12579","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/hatsudy.com\/jp\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/hatsudy.com\/jp\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/hatsudy.com\/jp\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/hatsudy.com\/jp\/wp-json\/wp\/v2\/comments?post=12579"}],"version-history":[{"count":7,"href":"https:\/\/hatsudy.com\/jp\/wp-json\/wp\/v2\/posts\/12579\/revisions"}],"predecessor-version":[{"id":12643,"href":"https:\/\/hatsudy.com\/jp\/wp-json\/wp\/v2\/posts\/12579\/revisions\/12643"}],"wp:featuredmedia":[{"embeddable":true,"href":"https:\/\/hatsudy.com\/jp\/wp-json\/wp\/v2\/media\/12595"}],"wp:attachment":[{"href":"https:\/\/hatsudy.com\/jp\/wp-json\/wp\/v2\/media?parent=12579"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/hatsudy.com\/jp\/wp-json\/wp\/v2\/categories?post=12579"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/hatsudy.com\/jp\/wp-json\/wp\/v2\/tags?post=12579"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}