{"id":11354,"date":"2022-11-30T01:36:34","date_gmt":"2022-11-29T16:36:34","guid":{"rendered":"https:\/\/hatsudy.com\/jp\/?p=11354"},"modified":"2022-12-06T12:30:34","modified_gmt":"2022-12-06T03:30:34","slug":"trigonometric-equations5","status":"publish","type":"post","link":"https:\/\/hatsudy.com\/jp\/trigonometric-equations5.html","title":{"rendered":"\u4e09\u89d2\u65b9\u7a0b\u5f0f\u306e\u89e3\u304d\u65b9\uff1a\u4e0d\u7b49\u5f0f\u3084\u7f6e\u304d\u63db\u3048\u3001\u516c\u5f0f\u306e\u5229\u7528\u6cd5"},"content":{"rendered":"\n<p>\u4e09\u89d2\u95a2\u6570\u3092\u542b\u3080\u65b9\u7a0b\u5f0f\u3092\u4e09\u89d2\u65b9\u7a0b\u5f0f\u3068\u3044\u3044\u307e\u3059\u3002\u5f0f\u306bsin\u03b8\u3084cos\u03b8\u3001tan\u03b8\u3092\u542b\u3080\u3068\u304d\u3001\u5f27\u5ea6\u6cd5\u3092\u5229\u7528\u3057\u3066\u5024\u3084\u89d2\u5ea6\u3092\u8a08\u7b97\u3067\u304d\u308b\u3088\u3046\u306b\u306a\u308a\u307e\u3057\u3087\u3046\u3002\u3053\u306e\u3068\u304d\u3001\u4e0d\u7b49\u5f0f\u3092\u542b\u3080\u554f\u984c\u304c\u51fa\u3055\u308c\u308b\u3053\u3068\u3082\u3042\u308a\u307e\u3059\u3002<\/p>\n<p>\u4e09\u89d2\u65b9\u7a0b\u5f0f\u3067\u306f\u8907\u6570\u306e\u89e3\u304c\u5b58\u5728\u3059\u308b\u30b1\u30fc\u30b9\u304c\u3072\u3093\u3071\u3093\u306b\u3042\u308a\u307e\u3059\u3002\u307e\u305f\u4e0d\u7b49\u5f0f\u3092\u542b\u3080\u65b9\u7a0b\u5f0f\u3067\u306f\u3001\u56f3\u3092\u63cf\u304b\u306a\u3044\u3068\u4e0d\u6b63\u89e3\u306b\u306a\u308a\u3084\u3059\u3044\u3067\u3059\u3002<\/p>\n<p>\u307e\u305f\u7f6e\u304d\u63db\u3048\u3084\u516c\u5f0f\u3092\u5229\u7528\u3059\u308b\u3053\u3068\u306b\u3088\u3063\u3066\u4e09\u89d2\u65b9\u7a0b\u5f0f\u3092\u89e3\u304b\u306a\u3051\u308c\u3070\u3044\u3051\u306a\u3044\u3053\u3068\u3082\u591a\u3044\u3067\u3059\u3002\u3053\u306e\u5834\u5408\u3001\u4e09\u89d2\u65b9\u7a0b\u5f0f\u3092\u542b\u3080\u554f\u984c\u3067\u3042\u3063\u3066\u3082\u3001\u4e8c\u6b21\u65b9\u7a0b\u5f0f\u3084\u5224\u5225\u5f0f\u306a\u3069\u3001\u305d\u306e\u4ed6\u306e\u5206\u91ce\u3067\u5b66\u3076\u6570\u5b66\u306e\u77e5\u8b58\u3092\u5229\u7528\u3059\u308b\u3053\u3068\u306b\u306a\u308a\u307e\u3059\u3002<\/p>\n<p>\u305d\u308c\u3067\u306f\u3001\u3069\u306e\u3088\u3046\u306b\u8003\u3048\u3066\u4e09\u89d2\u65b9\u7a0b\u5f0f\u3092\u89e3\u3051\u3070\u3044\u3044\u306e\u3067\u3057\u3087\u3046\u304b\u3002\u4e09\u89d2\u65b9\u7a0b\u5f0f\u306e\u8a08\u7b97\u65b9\u6cd5\u3092\u89e3\u8aac\u3057\u3066\u3044\u304d\u307e\u3059\u3002<\/p>\n<h2>\u4e09\u89d2\u65b9\u7a0b\u5f0f\u306e\u89e3\uff1asin\u03b8\u3001cos\u03b8\u3001tan\u03b8<\/h2>\n<p>\u5ea6\u6570\u6cd5\u3092\u5229\u7528\u3057\u3066\u4e09\u89d2\u6bd4\u306e\u554f\u984c\u3092\u89e3\u304f\u3053\u3068\u304c\u3067\u304d\u308b\u5834\u5408\u3001\u5f27\u5ea6\u6cd5\u3092\u5229\u7528\u3059\u308b\u4e09\u89d2\u65b9\u7a0b\u5f0f\u306b\u3064\u3044\u3066\u3082\u554f\u984c\u3092\u89e3\u304f\u3053\u3068\u304c\u3067\u304d\u307e\u3059\u3002<\/p>\n<p><span style=\"color: #0000ff;\">\u4e09\u89d2\u65b9\u7a0b\u5f0f\u3092\u89e3\u304f\u3068\u304d\u3001\u5fc5\u305a\u56f3\u5f62\u3092\u5229\u7528\u3057\u307e\u3057\u3087\u3046\u3002<\/span>\u56f3\u3092\u5229\u7528\u3057\u306a\u3044\u5834\u5408\u3001\u9ad8\u78ba\u7387\u3067\u8a08\u7b97\u30df\u30b9\u3092\u3057\u307e\u3059\u3002\u305d\u308c\u3067\u306f\\(0\u2266\u03b8&lt;2\u03c0\\)\u306e\u3068\u304d\u3001\u4ee5\u4e0b\u306e\u65b9\u7a0b\u5f0f\u306e\u7b54\u3048\u306f\u4f55\u3067\u3057\u3087\u3046\u304b\u3002<\/p>\n<ul>\n<li>\\(cos\u03b8=-\\displaystyle\\frac{1}{\\sqrt{2}}\\)<\/li>\n<\/ul>\n<p>\u56f3\u3092\u4f5c\u308b\u3068\u3001\u4ee5\u4e0b\u306e\u3088\u3046\u306b\\(\\displaystyle\\frac{3\u03c0}{4}\\)\uff08135\u00b0\uff09\u3068\\(\\displaystyle\\frac{5\u03c0}{4}\\)\uff08225\u00b0\uff09\u3067\\(cos\u03b8=-\\displaystyle\\frac{1}{\\sqrt{2}}\\)\u306b\u306a\u308b\u3068\u308f\u304b\u308a\u307e\u3059\u3002<\/p>\n<p><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/hatsudy.com\/jp\/wp-content\/uploads\/2022\/11\/fhe3.jpg\" alt=\"\" width=\"400\" height=\"369\" class=\"aligncenter size-full wp-image-11370\" \/><\/p>\n<p>\u305d\u308c\u3067\u306f\\(0\u2266\u03b8&lt;2\u03c0\\)\u306e\u3068\u304d\u3001\u4ee5\u4e0b\u306e\u554f\u984c\u306e\u7b54\u3048\u306f\u4f55\u3067\u3057\u3087\u3046\u304b\u3002<\/p>\n<ul>\n<li>\\(sin\u03b8=\\displaystyle\\frac{\\sqrt{3}}{2}\\)<\/li>\n<\/ul>\n<p>\u5148\u307b\u3069\u3068\u540c\u69d8\u306b\u56f3\u3092\u4f5c\u308b\u3068\u3001\\(\\displaystyle\\frac{\u03c0}{3}\\)\uff0860\u00b0\uff09\u3068\\(\\displaystyle\\frac{2\u03c0}{3}\\)\uff08120\u00b0\uff09\u3067\\(sin\u03b8=\\displaystyle\\frac{\\sqrt{3}}{2}\\)\u306b\u306a\u308b\u3068\u308f\u304b\u308a\u307e\u3059\u3002<\/p>\n<p><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/hatsudy.com\/jp\/wp-content\/uploads\/2022\/11\/fhe4.jpg\" alt=\"\" width=\"400\" height=\"377\" class=\"aligncenter size-full wp-image-11371\" \/><\/p>\n<p>\u56f3\u3092\u5229\u7528\u3059\u308b\u3053\u3068\u306b\u3088\u308a\u3001\u6700\u3082\u57fa\u672c\u7684\u306a\u4e09\u89d2\u65b9\u7a0b\u5f0f\u3092\u89e3\u3051\u308b\u3088\u3046\u306b\u306a\u308a\u307e\u3059\u3002<\/p>\n<h3>\u4e09\u89d2\u4e0d\u7b49\u5f0f\u3068\u4e0d\u7b49\u5f0f\u3067\u306e\u7bc4\u56f2<\/h3>\n<p>\u6b21\u306b\u3001\u4e09\u89d2\u95a2\u6570\u306b\u4e0d\u7b49\u5f0f\u304c\u5229\u7528\u3055\u308c\u3066\u3044\u308b\u5834\u5408\u306e\u554f\u984c\u3092\u89e3\u304d\u307e\u3057\u3087\u3046\u3002\u4e09\u89d2\u4e0d\u7b49\u5f0f\u3092\u89e3\u304f\u3068\u304d\u306b\u306f\u3001\u307e\u305a\u4e09\u89d2\u65b9\u7a0b\u5f0f\u3092\u89e3\u304d\u307e\u3057\u3087\u3046\u3002\u305d\u306e\u5f8c\u3001\u56f3\u3092\u5229\u7528\u3059\u308b\u3053\u3068\u306b\u3088\u3063\u3066\u4e0d\u7b49\u5f0f\u3092\u6e80\u305f\u3059\u03b8\u306e\u7bc4\u56f2\u3092\u78ba\u8a8d\u3059\u308b\u306e\u3067\u3059\u3002<\/p>\n<p>\u305d\u308c\u3067\u306f\\(0\u2266\u03b8&lt;2\u03c0\\)\u306e\u3068\u304d\u3001\u4ee5\u4e0b\u306e\u554f\u984c\u306e\u7b54\u3048\u306f\u4f55\u3067\u3057\u3087\u3046\u304b\u3002<\/p>\n<ul>\n<li>\\(sin\u03b8&lt;-\\displaystyle\\frac{1}{2}\\)<\/li>\n<\/ul>\n<p>\u307e\u305a\u3001\\(sin\u03b8=-\\displaystyle\\frac{1}{2}\\)\u3092\u89e3\u304f\u3068\\(\u03b8=\\displaystyle\\frac{7}{6}\u03c0,\\displaystyle\\frac{11}{6}\u03c0\\)\u3068\u306a\u308a\u307e\u3059\u3002\u305d\u3053\u3067\\(-\\displaystyle\\frac{1}{2}\\)\u3088\u308a\u3082\u5024\u304c\u5c0f\u3055\u304f\u306a\u308b\\(sin\u03b8\\)\u306e\u89d2\u5ea6\u3092\u78ba\u8a8d\u3057\u307e\u3057\u3087\u3046\u3002<\/p>\n<p><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/hatsudy.com\/jp\/wp-content\/uploads\/2022\/11\/fhe6.jpg\" alt=\"\" width=\"400\" height=\"374\" class=\"aligncenter size-full wp-image-11373\" \/><\/p>\n<p>\u305d\u3046\u3059\u308b\u3068\u3001\\(\\displaystyle\\frac{7}{6}\u03c0&lt;\u03b8&lt;\\displaystyle\\frac{11}{6}\u03c0\\)\u304c\u7b54\u3048\u3068\u308f\u304b\u308a\u307e\u3059\u3002\u6b21\u306b\u3001\\(0\u2266\u03b8&lt;2\u03c0\\)\u306e\u3068\u304d\u3001\u4ee5\u4e0b\u306e\u554f\u984c\u3092\u89e3\u3044\u3066\u307f\u307e\u3057\u3087\u3046\u3002<\/p>\n<ul>\n<li>\\(tan\u03b8\u2267\\displaystyle\\frac{1}{\\sqrt{3}}\\)<\/li>\n<\/ul>\n<p>\\(tan\u03b8=\\displaystyle\\frac{1}{\\sqrt{3}}\\)\u3092\u6e80\u305f\u3059\u03b8\u306e\u5024\u306f\\(\u03b8=\\displaystyle\\frac{\u03c0}{6},\\displaystyle\\frac{7\u03c0}{6}\\)\u3067\u3059\u3002\u305d\u3053\u3067\u56f3\u3092\u4f5c\u308a\u3001\u7b54\u3048\u3092\u78ba\u8a8d\u3057\u307e\u3057\u3087\u3046\u3002<\/p>\n<p><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/hatsudy.com\/jp\/wp-content\/uploads\/2022\/11\/fhe7.jpg\" alt=\"\" width=\"400\" height=\"371\" class=\"aligncenter size-full wp-image-11374\" \/><\/p>\n<p>\u3053\u3046\u3057\u3066\u3001\\(\\displaystyle\\frac{\u03c0}{6}\u2266\u03b8&lt;\\displaystyle\\frac{\u03c0}{2}\\)\u3001\\(\\displaystyle\\frac{7\u03c0}{6}\u2266\u03b8&lt;\\displaystyle\\frac{3\u03c0}{2}\\)\u304c\u7b54\u3048\u3067\u3042\u308b\u3068\u308f\u304b\u308a\u307e\u3057\u305f\u3002\u306a\u304atan\u03b8\u3067\u306f\u3001\\(\u03b8\u2260\\displaystyle\\frac{\u03c0}{2},\\displaystyle\\frac{3\u03c0}{2}\\)\u3067\u3042\u308b\u3053\u3068\u306b\u6ce8\u610f\u3057\u307e\u3057\u3087\u3046\u3002<\/p>\n<h2>\u7f6e\u304d\u63db\u3048\u3092\u7528\u3044\u3066\u4e09\u89d2\u65b9\u7a0b\u5f0f\u3001\u4e0d\u7b49\u5f0f\u3092\u89e3\u304f<\/h2>\n<p>\u305d\u308c\u3067\u306f\u3001\u5c11\u3057\u8907\u96d1\u306a\u4e09\u89d2\u65b9\u7a0b\u5f0f\u3092\u89e3\u3044\u3066\u307f\u307e\u3057\u3087\u3046\u3002\u4e09\u89d2\u65b9\u7a0b\u5f0f\u3092\u89e3\u304f\u3068\u304d\u3001\u6700\u3082\u4e00\u822c\u7684\u306a\u65b9\u6cd5\u3068\u3057\u3066\u7f6e\u304d\u63db\u3048\u304c\u3042\u308a\u307e\u3059\u3002<span style=\"color: #0000ff;\">\u7279\u5b9a\u306e\u5909\u6570\u3092\\(t\\)\u306a\u3069\u306e\u6587\u5b57\u306b\u7f6e\u304d\u63db\u3048\u308b\u3053\u3068\u306b\u3088\u308a\u3001\u7b54\u3048\u3092\u5f97\u308b\u306e\u3067\u3059\u3002<\/span>\u305d\u308c\u3067\u306f\\(0\u2266\u03b8&lt;2\u03c0\\)\u306e\u3068\u304d\u3001\u4ee5\u4e0b\u306e\u7b54\u3048\u306f\u4f55\u3067\u3057\u3087\u3046\u304b\u3002<\/p>\n<ul>\n<li>\\(\\sqrt{2}cos\\left(\u03b8+\\displaystyle\\frac{\u03c0}{3}\\right)=1\\)<\/li>\n<\/ul>\n<p>\\(\\sqrt{2}cos\\left(\u03b8+\\displaystyle\\frac{\u03c0}{3}\\right)=1\\)\u306f\\(cos\\left(\u03b8+\\displaystyle\\frac{\u03c0}{3}\\right)=\\displaystyle\\frac{1}{\\sqrt{2}}\\)\u3067\u3059\u3002\u305d\u308c\u3067\u306f\u3001\u03b8\u304c\u3069\u306e\u3088\u3046\u306a\u5024\u306e\u3068\u304d\u306b\\(\\displaystyle\\frac{1}{\\sqrt{2}}\\)\u306b\u306a\u308b\u306e\u3067\u3057\u3087\u3046\u304b\u3002<\/p>\n<p>\\(\u03b8+\\displaystyle\\frac{\u03c0}{3}=t\\)\u3068\u3057\u307e\u3057\u3087\u3046\u3002\u305d\u3046\u3059\u308b\u3068\u3001\u5f0f\u306f\\(cost=\\displaystyle\\frac{1}{\\sqrt{2}}\\)\u306b\u306a\u308a\u307e\u3059\u3002\u3053\u306e\u5f0f\u3092\u89e3\u304f\u3068\u3001\\(t=\\displaystyle\\frac{\u03c0}{4},\\displaystyle\\frac{7\u03c0}{4}\\)\u3067\u3059\u3002<\/p>\n<p><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/hatsudy.com\/jp\/wp-content\/uploads\/2022\/11\/fhe8.jpg\" alt=\"\" width=\"400\" height=\"374\" class=\"aligncenter size-full wp-image-11375\" \/><\/p>\n<p>\u306a\u304a\\(\u03b8+\\displaystyle\\frac{\u03c0}{3}=t\\)\u3067\u3042\u308b\u305f\u3081\u3001\\(t=\\displaystyle\\frac{\u03c0}{4},\\displaystyle\\frac{7\u03c0}{4}\\)\u306b\u4ee3\u5165\u3057\u307e\u3057\u3087\u3046\u3002\u3064\u307e\u308a\u3001\u4ee5\u4e0b\u306e\u5f0f\u3092\u89e3\u304d\u307e\u3059\u3002<\/p>\n<ul>\n<li>\\(\u03b8+\\displaystyle\\frac{\u03c0}{3}=\\displaystyle\\frac{\u03c0}{4}\\)<\/li>\n<li>\\(\u03b8+\\displaystyle\\frac{\u03c0}{3}=\\displaystyle\\frac{7\u03c0}{4}\\)<\/li>\n<\/ul>\n<p>\u3053\u308c\u3089\u306e\u5f0f\u3092\u89e3\u304f\u3068\u3001\\(\u03b8=-\\displaystyle\\frac{\u03c0}{12},\\displaystyle\\frac{17\u03c0}{12}\\)\u3068\u306a\u308a\u307e\u3059\u3002\u306a\u304a\\(0\u2266\u03b8&lt;2\u03c0\\)\u3067\u3042\u308b\u305f\u3081\u3001\\(-\\displaystyle\\frac{\u03c0}{12}\\)\u306e\u4ee3\u308f\u308a\u306b\\(\\displaystyle\\frac{23\u03c0}{12}\\)\u3092\u5229\u7528\u3057\u307e\u3057\u3087\u3046\u3002\u305d\u306e\u305f\u3081\u3001\u7b54\u3048\u306f\\(\u03b8=\\displaystyle\\frac{17\u03c0}{12},\\displaystyle\\frac{23\u03c0}{12}\\)\u3067\u3059\u3002<\/p>\n<h3>\u516c\u5f0f\u3092\u7528\u3044\u3066\u4e09\u89d2\u65b9\u7a0b\u5f0f\u3092\u5909\u5f62\u3059\u308b<\/h3>\n<p>\u6b21\u306b\u3001\u516c\u5f0f\u3092\u5229\u7528\u3059\u308b\u3053\u3068\u3067\u89e3\u304f\u3053\u3068\u306e\u3067\u304d\u308b\u554f\u984c\u3092\u78ba\u8a8d\u3057\u307e\u3057\u3087\u3046\u3002sin\u03b8\u3084cos\u03b8\u3001tan\u03b8\u3092\u542b\u3080\u554f\u984c\u3067\u306f\u3001\u4ee5\u4e0b\u306e\u516c\u5f0f\u3092\u5229\u7528\u3059\u308b\u3053\u3068\u3067\u4e00\u7a2e\u985e\u306e\u4e09\u89d2\u95a2\u6570\u3067\u8868\u3059\u3088\u3046\u306b\u3057\u307e\u3057\u3087\u3046\u3002<\/p>\n<ul>\n<li>\\(sin^2\u03b8+cos^2\u03b8=1\\)<\/li>\n<li>\\(tan\u03b8=\\displaystyle\\frac{sin\u03b8}{cos\u03b8}\\)<\/li>\n<li>\\(1+tan^2\u03b8=\\displaystyle\\frac{1}{cos^2\u03b8}\\)<\/li>\n<\/ul>\n<p>\u305d\u308c\u306b\u52a0\u3048\u3066\u3001\u7f6e\u304d\u63db\u3048\u3092\u5229\u7528\u3059\u308b\u3053\u3068\u306b\u3088\u3063\u3066\u4e8c\u6b21\u65b9\u7a0b\u5f0f\u3084\u4e09\u6b21\u65b9\u7a0b\u5f0f\u306e\u554f\u984c\u306b\u5909\u5f62\u3067\u304d\u307e\u3059\u3002\u305d\u308c\u3067\u306f\\(0\u2266\u03b8&lt;2\u03c0\\)\u306e\u3068\u304d\u3001\u4ee5\u4e0b\u306e\u554f\u984c\u306e\u7b54\u3048\u306f\u4f55\u3067\u3057\u3087\u3046\u304b\u3002<\/p>\n<ul>\n<li>\\(2cos^2\u03b8+sin\u03b8-1=0\\)<\/li>\n<\/ul>\n<p>\\(sin^2\u03b8+cos^2\u03b8=1\\)\u3067\u3042\u308b\u305f\u3081\u3001\u4ee5\u4e0b\u306e\u3088\u3046\u306b\u5f0f\u3092\u5909\u5f62\u3057\u307e\u3057\u3087\u3046\u3002<\/p>\n<p>\\(2cos^2\u03b8+sin\u03b8-1=0\\)<\/p>\n<p>\\(2(1-sin^2\u03b8)+sin\u03b8-1=0\\)<\/p>\n<p>\\(2sin^2\u03b8-sin\u03b8-1=0\\)<\/p>\n<p>\\(sin\u03b8=t\\)\u3068\u3057\u307e\u3057\u3087\u3046\u3002\u305d\u3046\u3059\u308b\u3068\u3001\\(2t^2-t-1=0\\)\u3068\u306a\u308a\u307e\u3059\u3002\u305d\u3053\u3067\u3001\u3053\u306e\u5f0f\u3092\u89e3\u304d\u307e\u3059\u3002<\/p>\n<p>\\(2t^2-t-1=0\\)<\/p>\n<p>\\((2t+1)(t-1)=0\\)<\/p>\n<p>\\(t=-\\displaystyle\\frac{1}{2},1\\)<\/p>\n<p>sin\u03b8\u304c\\(-\\displaystyle\\frac{1}{2},1\\)\u3068\u306a\u308b\u3068\u304d\u3001\\(\u03b8=\\displaystyle\\frac{\u03c0}{2},\\displaystyle\\frac{7\u03c0}{6},\\displaystyle\\frac{11\u03c0}{6}\\)\u3067\u3059\u3002\u3053\u3046\u3057\u3066\u3001\u7b54\u3048\u3092\u5f97\u308b\u3053\u3068\u304c\u3067\u304d\u307e\u3057\u305f\u3002<\/p>\n<h3>\u4e09\u89d2\u95a2\u6570\u306e\u6700\u5927\u5024\u3068\u6700\u5c0f\u5024<\/h3>\n<p>\u4e09\u89d2\u95a2\u6570\u304c\u95a2\u308f\u308b\u8a08\u7b97\u3067\u306f\u3001\u6700\u5927\u5024\u3068\u6700\u5c0f\u5024\u3092\u6c42\u3081\u306a\u3051\u308c\u3070\u3044\u3051\u306a\u3044\u3053\u3068\u3082\u3042\u308a\u307e\u3059\u3002\u3053\u306e\u3068\u304d\u3001\u4e09\u89d2\u95a2\u6570\u304c\u542b\u307e\u308c\u3066\u3044\u308b\u3082\u306e\u306e\u3001\u4e8c\u6b21\u65b9\u7a0b\u5f0f\u3084\u4e09\u6b21\u65b9\u7a0b\u5f0f\u306e\u554f\u984c\u3092\u89e3\u304f\u3068\u304d\u3068\u8003\u3048\u65b9\u306f\u540c\u3058\u3067\u3059\u3002\u305d\u308c\u3067\u306f\\(0\u2266\u03b8&lt;2\u03c0\\)\u306e\u3068\u304d\u3001\u4ee5\u4e0b\u306e\u554f\u984c\u306e\u7b54\u3048\u306f\u4f55\u3067\u3057\u3087\u3046\u304b\u3002<\/p>\n<ul>\n<li>\\(y=2cos^2\u03b8+sin\u03b8-1\\)\u306e\u6700\u5927\u5024\u3068\u6700\u5c0f\u5024\u3092\u6c42\u3081\u307e\u3057\u3087\u3046\u3002<\/li>\n<\/ul>\n<p>\u5148\u307b\u3069\u89e3\u8aac\u3057\u305f\u901a\u308a\u3001\\(sin^2\u03b8+cos^2\u03b8=1\\)\u3092\u5229\u7528\u3057\u3001\\(sin\u03b8=t\\)\u3068\u3059\u308b\u3068\u5f0f\u306f\\(y=2t^2-t-1\\)\u3068\u306a\u308a\u307e\u3059\u3002\u305d\u3053\u3067\u3001\u3053\u306e\u5f0f\u3092\u4ee5\u4e0b\u306e\u3088\u3046\u306b\u5909\u5f62\u3057\u307e\u3057\u3087\u3046\u3002<\/p>\n<p>\\(y=2t^2-t-1\\)<\/p>\n<p>\\(y=2\\left(t^2-\\displaystyle\\frac{t}{2}\\right)-1\\)<\/p>\n<p>\\(y=2\\left(t-\\displaystyle\\frac{1}{4}\\right)^2-\\displaystyle\\frac{9}{8}\\)<\/p>\n<p>\u3053\u3046\u3057\u3066\u3001\u8ef8\u304c\\(t=\\displaystyle\\frac{1}{4}\\)\u3068\u306a\u308b\u4e8c\u6b21\u95a2\u6570\u3067\u3042\u308b\u3068\u308f\u304b\u308a\u307e\u3059\u3002\u306a\u304a\u3001\\(-1\u2266sin\u03b8\u22661\\)\u3067\u3059\u3002\u305d\u306e\u305f\u3081\u3001\\(-1\u2266t\u22661\\)\u306e\u7bc4\u56f2\u3067\u6700\u5927\u5024\u3068\u6700\u5c0f\u5024\u3092\u78ba\u8a8d\u3057\u307e\u3057\u3087\u3046\u3002<\/p>\n<p><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/hatsudy.com\/jp\/wp-content\/uploads\/2022\/11\/oej5.jpg\" alt=\"\" width=\"344\" height=\"279\" class=\"aligncenter size-full wp-image-11425\" \/><\/p>\n<p>\u56f3\u3088\u308a\u3001\u6700\u5c0f\u5024\u306f\u9802\u70b9\u3068\u306a\u308b\u305f\u3081\u3001\\(t=sin\u03b8=\\displaystyle\\frac{1}{4}\\)\u306e\u3068\u304d\u3001\\(y=-\\displaystyle\\frac{9}{8}\\)\u304c\u6700\u5c0f\u5024\u3067\u3059\u3002\u307e\u305f\\(t=sin\u03b8=-1\\)\u306e\u3068\u304d\u3001\\(y=2\\)\u304c\u6700\u5927\u5024\u306b\u306a\u308a\u307e\u3059\u3002\u3053\u3046\u3057\u3066\u3001\u6700\u5927\u5024\u3068\u6700\u5c0f\u5024\u3092\u8a08\u7b97\u3059\u308b\u3053\u3068\u304c\u3067\u304d\u307e\u3057\u305f\u3002<\/p>\n<h3>\u4e09\u89d2\u65b9\u7a0b\u5f0f\u306e\u89e3\u306e\u5b58\u5728\u7bc4\u56f2\u3092\u8a08\u7b97\u3059\u308b<\/h3>\n<p>\u4e09\u89d2\u95a2\u6570\u306e\u6027\u8cea\u3092\u5229\u7528\u3059\u308b\u3082\u306e\u306e\u3001\u5148\u307b\u3069\u306e\u554f\u984c\u306e\u3088\u3046\u306b\u3001\u4e09\u89d2\u65b9\u7a0b\u5f0f\u306e\u554f\u984c\u306f\u4e00\u822c\u7684\u306a\u6570\u5b66\u306e\u8a08\u7b97\u3068\u540c\u3058\u3067\u3059\u3002\u305d\u308c\u3067\u306f\u3001\u6b21\u306f\u4ee5\u4e0b\u306e\u554f\u984c\u3092\u89e3\u3044\u3066\u307f\u307e\u3057\u3087\u3046\u3002<\/p>\n<ul>\n<li>\\(cos^2\u03b8+2\u03b1sin\u03b8-\u03b1-1=0\\)\u3092\u6e80\u305f\u3059\u03b8\u304c\u5b58\u5728\u3059\u308b\u3068\u304d\u3001\u5b9a\u6570\\(\u03b1\\)\u306e\u5024\u306e\u7bc4\u56f2\u3092\u6c42\u3081\u307e\u3057\u3087\u3046\u3002<\/li>\n<\/ul>\n<p>\u516c\u5f0f\u3092\u5229\u7528\u3057\u3001\u4ee5\u4e0b\u306e\u3088\u3046\u306b\u5f0f\u3092\u5909\u5f62\u3057\u307e\u3057\u3087\u3046\u3002<\/p>\n<p>\\(cos^2\u03b8+2\u03b1sin\u03b8-\u03b1-1=0\\)<\/p>\n<p>\\((1-sin^2\u03b8)+2\u03b1sin\u03b8-\u03b1-1=0\\)<\/p>\n<p>\\(sin^2\u03b8-2\u03b1sin\u03b8+\u03b1=0\\)<\/p>\n<p>\\(sin\u03b8=t\\)\u3068\u3059\u308b\u3068\u3001\\(t^2-2\u03b1t+\u03b1=0\\)\u3068\u306a\u308a\u307e\u3059\u3002\\(-1\u2266sin\u03b8\u22661\\)\u3067\u3042\u308b\u305f\u3081\u3001\\(-1\u2266t\u22661\\)\u3067\u3059\u3002\u3064\u307e\u308a\u3001\\(-1\u2266t\u22661\\)\u306e\u7bc4\u56f2\u306b\u5c11\u306a\u304f\u3068\u3082\u4e00\u3064\u306e\u89e3\u3092\u3082\u3064\u3053\u3068\u304c\u3067\u304d\u308c\u3070\u3044\u3044\u3067\u3059\u3002\u305d\u3053\u3067\u3001\u4ee5\u4e0b\u306e\u3088\u3046\u306b\u5834\u5408\u5206\u3051\u3092\u3057\u307e\u3057\u3087\u3046\u3002<\/p>\n<p><strong>\u2460 \\(-1\u2266t\u22661\\)\u306b2\u3064\u306e\u5b9f\u6570\u89e3\u3092\u3082\u3064\uff08\u91cd\u89e3\u3092\u542b\u3080\uff09<\/strong><\/p>\n<p>2\u3064\u306e\u5b9f\u6570\u89e3\uff08\u307e\u305f\u306f\u91cd\u89e3\uff09\u3092\u3082\u3064\u5834\u5408\u3001\u4ee5\u4e0b\u306e\u6761\u4ef6\u3092\u3059\u3079\u3066\u6e80\u305f\u305b\u3070\u3044\u3044\u3067\u3059\u3002<\/p>\n<ul>\n<li>\u5224\u5225\u5f0f\uff1a\\(D\u22670\\)<\/li>\n<li>\\(f(1)\u22670\\)<\/li>\n<li>\\(f(-1)\u22670\\)<\/li>\n<\/ul>\n<p><strong>\u30fb\u5224\u5225\u5f0f\uff1a\\(D\u22670\\)\u306e\u8a08\u7b97<\/strong><\/p>\n<p>\\(4\u03b1^2-4\u03b1\u22670\\)<\/p>\n<p>\\(\u03b1(\u03b1-1)\u22670\\)<\/p>\n<p>\\(\u03b1\u22660,1\u2266\u03b1\\)<\/p>\n<p><strong>\u30fb\\(f(1)\u22670\\)\u306e\u8a08\u7b97<\/strong><\/p>\n<p>\\(1-2\u03b1+\u03b1\u22670\\)<\/p>\n<p>\\(\u03b1\u22661\\)<\/p>\n<p><strong>\u30fb\\(f(-1)\u22670\\)\u306e\u8a08\u7b97<\/strong><\/p>\n<p>\\(1+2\u03b1+\u03b1\u22670\\)<\/p>\n<p>\\(\u03b1\u2267-\\displaystyle\\frac{1}{3}\\)<\/p>\n<p>3\u3064\u306e\u6761\u4ef6\u3092\u6e80\u305f\u3059\u7bc4\u56f2\u306f\\(-\\displaystyle\\frac{1}{3}\u2266\u03b1\u22660\\)\u3001\\(\u03b1=1\\)\u3067\u3059\u3002<\/p>\n<p><strong>\u2461 \\(-1\u2266t\u22661\\)\u306b\u4e00\u3064\u306e\u5b9f\u6570\u89e3\u304c\u3042\u308a\u3001\u305d\u306e\u4ed6\u306e\u5834\u6240\u306b\u4e00\u3064\u306e\u5b9f\u6570\u89e3\u304c\u3042\u308b<\/strong><\/p>\n<p>\\(-1\u2266t\u22661\\)\u306e\u7bc4\u56f2\u306b\u4e8c\u3064\u306e\u5b9f\u6570\u89e3\u304c\u3042\u308b\u306e\u3067\u306f\u306a\u304f\u3001\u300c\\(-1\u2266t\u22661\\)\u306e\u7bc4\u56f2\u306b\u4e00\u3064\u306e\u5b9f\u6570\u89e3\u304c\u3042\u308a\u3001\u305d\u306e\u4ed6\u306e\u5834\u6240\u306b\u3082\u3046\u4e00\u3064\u306e\u5b9f\u6570\u89e3\u3092\u3082\u3064\u30b1\u30fc\u30b9\u300d\u3092\u8003\u3048\u307e\u3057\u3087\u3046\u3002\\(-1\u2266t\u22661\\)\u306e\u7bc4\u56f2\u306b\u4e00\u3064\u306e\u5b9f\u6570\u89e3\u304c\u3042\u308c\u3070\u3001\\(cos^2\u03b8+2\u03b1sin\u03b8-\u03b1-1=0\\)\u3092\u6e80\u305f\u3059\u03b8\u304c\u5b58\u5728\u3059\u308b\u3053\u3068\u306b\u306a\u308a\u307e\u3059\u3002<\/p>\n<p>\u3053\u306e\u6761\u4ef6\u3092\u6e80\u305f\u3059\u5f0f\u306f\u4ee5\u4e0b\u306b\u306a\u308a\u307e\u3059\u3002<\/p>\n<ul>\n<li>\\(f(1)\u00d7f(-1)\u22660\\)<\/li>\n<\/ul>\n<p><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/hatsudy.com\/jp\/wp-content\/uploads\/2022\/11\/oej4.jpg\" alt=\"\" width=\"546\" height=\"188\" class=\"aligncenter size-full wp-image-11424\" 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