{"id":2119,"date":"2025-12-24T17:19:15","date_gmt":"2025-12-24T08:19:15","guid":{"rendered":"https:\/\/math-travel.com\/?p=2119"},"modified":"2026-02-11T16:30:00","modified_gmt":"2026-02-11T07:30:00","slug":"kangenkousiki","status":"publish","type":"post","link":"https:\/\/math-travel.jp\/math-2\/kangenkousiki\/","title":{"rendered":"\u4e09\u89d2\u95a2\u6570\u306e\u516c\u5f0f\uff08\u03b8\uff0b\u03c0\/2, \u03b8+\u03c0\uff09\u306e\u5c0e\u304d\u65b9\uff01\u5358\u4f4d\u5186\u3092\u4f7f\u3048\u3070\u4e38\u6697\u8a18\u306f\u4e0d\u8981"},"content":{"rendered":"\n

\u4e09\u89d2\u95a2\u6570\u306e\u516c\u5f0f\u3092\u7406\u89e3\u3057\u3066\u3001\u3084\u3063\u3068\u6163\u308c\u3066\u304d\u305f\u9803\u306b<\/p>\n\n\n\n

\\(\\sin (\\theta+\\pi)\\)<\/p>\n\n\n\n

\u3053\u3093\u306a\u306e\u3068\u304b<\/p>\n\n\n\n

\\(\\displaystyle \\cos (\\theta+\\frac{\\pi}{2})\\)<\/p>\n\n\n\n

\u3053\u3093\u306a\u306e\u304c\u51fa\u3066\u304f\u308b\u3093\u3067\u3059\u3088\u306d…<\/p>\n\n\n\n

\u3072\u3068\u3064\u3072\u3068\u3064\u306e\u516c\u5f0f\u3092\u899a\u3048\u3066\u3044\u3063\u3066\u3082\u826f\u3044\u306e\u3067\u3059\u304c\u7d50\u69cb\u5927\u5909\u3067\u3059(^^;)<\/p>\n\n\n\n

\u4eca\u56de\u306f\u4e09\u89d2\u95a2\u6570\u306e\u4e2d\u3067\u3082\u3001\\(\\displaystyle \\theta + \\frac{\\pi}{2}\\)\u3084\\(\\theta + \\pi\\)\u306e\u5f62\u3092\u3057\u305f\u4e09\u89d2\u95a2\u6570\u306e\u516c\u5f0f\u3068\u305d\u306e\u5c0e\u304d\u65b9\u3092\u4f1d\u3048\u3066\u3044\u304d\u307e\u3059\u3002<\/p>\n\n\n

\"\"\u30b7\u30fc\u30bf<\/span><\/div>
\n

\u6c17\u306b\u306a\u308b\u898b\u51fa\u3057\u3092\u30af\u30ea\u30c3\u30af\u3057\u3066\u3001
\u305c\u3072\u6700\u5f8c\u307e\u3067\u3054\u89a7\u304f\u3060\u3055\u3044\u3002<\/p>\n<\/span><\/span><\/span><\/div><\/div><\/div><\/div>\n\n\n

\u03b8\uff0b\u03c0\/2\uff0c\u03b8+\u03c0\u4e09\u89d2\u95a2\u6570\u306e\u516c\u5f0f\u307e\u3068\u3081<\/h2>\n\n\n
\n
\"\u03b8\uff0b\u03c0\/2\uff0c\u03b8+\u03c0\u4e09\u89d2\u95a2\u6570\u306e\u516c\u5f0f\u307e\u3068\u3081\"<\/figure>\n<\/div>\n\n\n


\u307e\u305a\u306f\u3058\u3081\u306b\u516c\u5f0f\u3092\u5168\u90e8\u898b\u305b\u3061\u3083\u3044\u307e\u3059\u3002<\/p>\n\n\n\n

\u516c\u5f0f\u304c\u77e5\u308a\u305f\u304b\u3063\u305f\u3060\u3051\u306e\u65b9\u306f\u3001\u3053\u3053\u307e\u3067\u3067OK\u3067\u3059\uff01<\/span><\/p>\n\n\n\n

\uff5e\\(-\\theta\\)\u306e\u516c\u5f0f\uff5e
\\(\\sin (-\\theta)=-\\sin \\theta\\)
\\(\\cos (-\\theta)=\\cos \\theta\\)
\\(\\tan (-\\theta)=-\\tan \\theta\\)<\/p>\n\n\n\n

\uff5e\\(\\displaystyle \\theta+\\frac{\\pi}{2}\\)\u306e\u516c\u5f0f\uff5e
\\(\\displaystyle \\sin (\\theta+\\frac{\\pi}{2})=\\cos \\theta\\)
\\(\\displaystyle \\cos (\\theta+\\frac{\\pi}{2})=-\\sin \\theta \\)
\\(\\displaystyle \\tan (\\theta+\\frac{\\pi}{2})=-\\frac{1}{\\tan \\theta}\\)<\/p>\n\n\n\n

\uff5e\\( \\theta+\\pi \\)\u306e\u516c\u5f0f \uff5e
\\(\\sin (\\theta+\\pi)=-\\sin \\theta \\)
\\(\\cos (\\theta+\\pi)=-\\cos \\theta \\)
\\(\\tan (\\theta+\\pi)=\\tan \\theta\\)<\/p>\n\n\n\n

-\u03b8\u306e\u4e09\u89d2\u95a2\u6570<\/h2>\n\n\n\n
\uff5e\\(-\\theta\\)\u306e\u516c\u5f0f\uff5e<\/span>\\(\\sin (-\\theta)=-\\sin \\theta\\)
\\(\\cos (-\\theta)=\\cos \\theta\\)
\\(\\tan (-\\theta)=-\\tan \\theta\\)<\/div>\n\n\n
\n
\"-\u03b8\u306e\u4e09\u89d2\u95a2\u6570\"<\/figure>\n<\/div>\n\n\n

\u56f3\u3092\u898b\u3066\u307f\u308b\u3068\u516c\u5f0f\u3082\u7d0d\u5f97\u3067\u304d\u308b\u3068\u601d\u3044\u307e\u3059\u3002<\/p>\n\n\n\n

\u4eca\u56de\u306f\u03b8\u3092\u92ed\u89d2\u306b\u3057\u3066\u307f\u307e\u3057\u305f\u3002<\/p>\n\n\n\n

-\u03b8\u3068\u3044\u3046\u306e\u306f\u3001\u5358\u4f4d\u5186\u3092\u9006\u56de\u308a\u306b\u03b8\u3060\u3051\u56de\u305b\u3070\u3088\u3044\u306e\u3067\u3001<\/p>\n\n\n\n

x\u5ea7\u6a19\u306f\u5909\u308f\u3089\u305acos\\(\\theta\\)\u3001y\u5ea7\u6a19\u306e\u6b63\u8ca0\u304c\u9006\u306b\u306a\u308a-sin\\(\\theta\\)\u306b\u306a\u308a\u307e\u3059\u3002<\/span><\/p>\n\n\n\n

\\(\\displaystyle tan \\theta=\\frac{sin \\theta}{cos \\theta}\\)\u306a\u306e\u3067\u3001<\/p>\n\n\n\n

\\(\\displaystyle tan (-\\theta)=\\frac{sin (-\\theta)}{cos (-\\theta)}\\)<\/p>\n\n\n\n

\\(\\displaystyle tan (-\\theta)=\\frac{-sin \\theta}{cos \\theta}\\)<\/p>\n\n\n\n

\\(tan (-\\theta)=-tan (\\theta)\\)<\/p>\n\n\n\n

\u03b8\uff0b\u03c0\/2\u306e\u4e09\u89d2\u95a2\u6570<\/h2>\n\n\n\n
\uff5e\u03b8\uff0b\u03c0\/2\u306e\u516c\u5f0f\uff5e<\/span>\\(\\displaystyle\\sin (\\theta+\\frac{\\pi}{2})=\\cos \\theta\\)
\\(\\displaystyle\\cos (\\theta+\\frac{\\pi}{2})=-\\sin \\theta \\)
\\(\\displaystyle\\tan (\\theta+\\frac{\\pi}{2})=-\\frac{1}{\\tan \\theta}\\)<\/div>\n\n\n
\n
\"\u03b8\uff0b\u03c0\/2\u306e\u4e09\u89d2\u95a2\u6570\"<\/figure>\n<\/div>\n\n\n

\u56f3\u306e\u3088\u3046\u306b\\(\\theta\\)\u306b\u5bfe\u3057\u3066\u3001\\(\\displaystyle \\frac{\\pi}{2}\\)\u56de\u3057\u305f\u5148\u3067\u5408\u540c\u306a\u56f3\u5f62\u3092\u63cf\u304f\u3053\u3068\u304c\u3067\u304d\u307e\u3059\u3002<\/p>\n\n\n\n

\u3088\u3063\u3066x\u5ea7\u6a19\u306e\\(\\displaystyle \\cos (\\theta+\\frac{\\pi}{2})\\)\u306f\\(-\\sin \\theta \\)<\/p>\n\n\n\n

y\u5ea7\u6a19\u306e\\(\\displaystyle \\sin (\\theta+\\frac{\\pi}{2})\\)\u306f\\(\\cos \\theta\\)\u306b\u306a\u308a\u307e\u3059\u3002<\/p>\n\n\n\n

\u305d\u308c\u306b\u5bfe\u3057\u3066\u3001\\(\\displaystyle \\tan \\theta=\\frac{sin \\theta}{cos \\theta}\\)\u306a\u306e\u3067\u3001<\/p>\n\n\n\n

\\(\\displaystyle \\tan (\\theta+\\frac{\\pi}{2})=\\frac{sin (\\theta+\\frac{\\pi}{2})}{cos (\\theta+\\frac{\\pi}{2})}\\)<\/p>\n\n\n\n

\\(\\displaystyle \\tan (\\theta+\\frac{\\pi}{2})=\\frac{\\cos \\theta}{-\\sin \\theta }\\)<\/p>\n\n\n\n

\\(\\displaystyle\\tan (\\theta+\\frac{\\pi}{2})=-\\frac{1}{\\tan \\theta}\\)<\/p>\n\n\n\n

\u03b8+\u03c0\u306e\u4e09\u89d2\u95a2\u6570<\/h2>\n\n\n
\n
\"\u03b8+\u03c0\u306e\u4e09\u89d2\u95a2\u6570\"<\/figure>\n<\/div>\n\n\n
\uff5e \\(\\theta+\\pi\\)\u306e\u516c\u5f0f \uff5e<\/span>\\(\\sin (\\theta+\\pi)=-\\sin \\theta \\)
\\(\\cos (\\theta+\\pi)=-\\cos \\theta \\)
\\(\\tan (\\theta+\\pi)=\\tan \\theta\\)<\/div>\n\n\n
\n
\"\u03b8+\u03c0\u306e\u4e09\u89d2\u95a2\u6570\"<\/figure>\n<\/div>\n\n\n

\u56f3\u306e\u3088\u3046\u306b\\(\\theta\\)\u306b\u5bfe\u3057\u3066\u3001\u539f\u70b9\u3092\u4e2d\u5fc3\u306b\u70b9\u5bfe\u79f0\u306a\u56f3\u5f62\u3092\u63cf\u304f\u3053\u3068\u304c\u3067\u304d\u308b\u3002<\/p>\n\n\n\n

x\u5ea7\u6a19\u3082y\u5ea7\u6a19\u3082\u6b63\u8ca0\u306e\u7b26\u53f7\u3092\u5165\u308c\u66ff\u3048\u308b\u3053\u3068\u306b\u306a\u308a\u3001<\/span><\/p>\n\n\n\n

x\u5ea7\u6a19\u306f-cos\\(\\theta\\)\u3001y\u5ea7\u6a19\u304c-sin\\(\\theta\\)\u306b\u306a\u308a\u307e\u3059\u3002<\/span><\/p>\n\n\n\n

\u305d\u308c\u306b\u5bfe\u3057\u3066\u3001\\(\\displaystyle \\tan \\theta=\\frac{sin \\theta}{cos \\theta}\\)\u306a\u306e\u3067\u3001<\/p>\n\n\n\n

\\(\\displaystyle \\tan (\\theta+\\pi)=\\frac{sin (\\theta+ \\pi)}{cos (\\theta+ \\pi)}\\)<\/p>\n\n\n\n

\\(\\displaystyle \\tan (\\theta+\\pi)=\\frac{-sin \\theta}{-cos \\theta}\\)<\/p>\n\n\n\n

\\(\\tan (\\theta+\\pi)=\\tan \\theta\\)<\/p>\n\n\n\n

\u03b8\uff0b\u03c0\/2\uff0c\u03b8+\u03c0\u306e\u5c0e\u304d\u65b9<\/h2>\n\n\n
\n
\"\u03b8\uff0b\u03c0\/2\uff0c\u03b8+\u03c0\u306e\u5c0e\u304d\u65b9\"<\/figure>\n<\/div>\n\n\n


\u3053\u3053\u307e\u3067\u516c\u5f0f\u3092\u89e3\u8aac\u3057\u3066\u304d\u307e\u3057\u305f\u304c\u3001\u6b63\u76f4\u8a00\u3046\u3068\u899a\u3048\u306a\u304f\u3066\u3082\u826f\u3044\u3067\u3059\u3002<\/p>\n\n\n\n

\u305d\u306e\u4ee3\u308f\u308a\u3001\u516c\u5f0f\u306e\u5c0e\u304d\u65b9\u3092\u899a\u3048\u3066\u304a\u3044\u3066\u304f\u3060\u3055\u3044\u3002<\/span><\/p>\n\n\n\n

\u5c0e\u304d\u65b9\u306b\u306f\uff12\u3064\u3042\u308a\u307e\u3059\u3002<\/p>\n\n\n\n

\u03b8\uff0b\u03c0\/2\uff0c\u03b8+\u03c0\u306e\u516c\u5f0f\u5c0e\u304d\u65b9\u2460<\/h3>\n\n\n\n

\u52a0\u6cd5\u5b9a\u7406\u3092\u7528\u3044\u3066\u8a08\u7b97\u3067\u5c0e\u304f\u65b9\u6cd5\u3067\u3059\u3002<\/span><\/p>\n\n\n\n

\u52a0\u6cd5\u5b9a\u7406<\/span>
\\(\\sin (a\u00b1b)=\\sin a \\cos b \u00b1 \\cos a \\sin b\\)
\\(\\cos (a\u00b1b)=\\cos a \\cos b \u2213 \\sin a \\sin b\\)<\/div>\n\n\n\n

\\(\\sin (\\theta + \\pi)=\\sin \\theta \\cos \\pi + \\cos \\theta \\sin \\pi\\)<\/p>\n\n\n\n

\\(\\sin (\\theta + \\pi)=\\sin \\theta \\times (-1) + \\cos \\theta \\times 0\\)<\/p>\n\n\n\n

\\(\\sin (\\theta + \\pi)=-\\sin \\theta\\)<\/p>\n\n\n\n

\u3053\u306e\u3088\u3046\u306b\u3001\u52a0\u6cd5\u5b9a\u7406\u306b\u6570\u5b57\u3092\u4ee3\u5165\u3059\u308b\u3053\u3068\u3067\u6c42\u3081\u308b\u3053\u3068\u304c\u3067\u304d\u307e\u3059\u3002<\/p>\n\n\n\n

\u03b8\uff0b\u03c0\/2\uff0c\u03b8+\u03c0\u306e\u516c\u5f0f\u5c0e\u304d\u65b9\u2461<\/h3>\n\n\n\n

\u6b21\u306f\u8a08\u7b97\u3092\u3057\u306a\u3044\u899a\u3048\u65b9\u3092\u7d39\u4ecb\u3067\u3059\u3002<\/span><\/p>\n\n\n\n

1\u3064\u76ee\u306b\u95a2\u6570\u306e\u5f62\u3067\u3059\u3002<\/span><\/p>\n\n\n\n

\u307e\u305a\\(\\pi\\)\u306e\u6574\u6570\u500d\u304c\u7d61\u3080\u3082\u306e\u306f\u95a2\u6570\u306e\u90e8\u5206\u304c\u5909\u5316\u3057\u307e\u305b\u3093\u3002
\\(\\displaystyle \\frac{\\pi}{2}\\)\u306e\u5947\u6570\u500d\u304c\u7d61\u3080\u3082\u306e\u306f sin\u27facos\uff0c\\(tan\u27fa\\displaystyle \\frac{1}{\\tan}\\)\u3068\u5909\u5316\u3057\u307e\u3059\u3002<\/p>\n\n\n\n

\uff12\u3064\u76ee\u306b\u7b26\u53f7\u306e\u90e8\u5206\u3067\u3059\u3002<\/span><\/p>\n\n\n\n

\u03b8\u304c\u92ed\u89d2\u306a\u5358\u4f4d\u5186\u3092\u30a4\u30e1\u30fc\u30b8\u3057\u3066\u3001\u4e0a\u306e\u7ae0\u3067\u898b\u305b\u305f\u3088\u3046\u306b\u7b26\u53f7\u3092\u78ba\u8a8d\u3057\u307e\u3059\u3002<\/p>\n\n\n\n

\u3053\u308c\u3067\u95a2\u6570\u306e\u90e8\u5206\u3068\u7b26\u53f7\u304c\u5206\u304b\u3063\u305f\u306e\u3067\u5909\u63db\u304c\u3067\u304d\u307e\u3057\u305f\u3002<\/p>\n\n\n\n

\u03b8\uff0b\u03c0\/2\uff0c\u03b8+\u03c0\uff1c\u7df4\u7fd2\u554f\u984c\uff1e<\/h2>\n\n\n
\n
\"\u03b8\uff0b\u03c0\/2\uff0c\u03b8+\u03c0\uff1c\u7df4\u7fd2\u554f\u984c\uff1e\"<\/figure>\n<\/div>\n\n\n


\u4eca\u56de\u5b66\u3093\u3060\u3053\u3068\u3092\u6d3b\u304b\u3057\u3066\u3001\u7df4\u7fd2\u554f\u984c\u306b\u6311\u6226\u3057\u3066\u307f\u307e\u3057\u3087\u3046\u3002<\/p>\n\n\n\n

\u7df4\u7fd2\u554f\u984c<\/span>\u6b21\u306e\u4e09\u89d2\u6bd4\u3092\u7b2c\u4e00\u8c61\u9650\\(\\displaystyle (0<\\theta<\\frac{\\pi}{2})\\)\u306e\u4e09\u89d2\u6bd4\u3067\u8868\u305b\u3002
\uff11\uff0ecos\\(\\displaystyle \\frac{4}{5}\\pi\\)
\uff12\uff0esin\\(\\displaystyle \\frac{11}{9}\\pi\\)
\uff13\uff0etan\\(\\displaystyle \\frac{13}{18}\\pi\\)<\/div>\n\n\n\n

\u89e3\u7b54<\/span><\/p>\n\n\n\n

\uff11\uff0e\\(\\displaystyle \\cos \\frac{4}{5}\\pi\\)<\/p>\n\n\n\n

\\(\\displaystyle =\\cos (\\frac{3}{10}\\pi+\\frac{\\pi}{2})\\)<\/p>\n\n\n\n

\\(\\displaystyle=-\\sin \\frac{3}{10}\\pi\\)<\/p>\n\n\n\n

\uff12\uff0e\\(\\displaystyle \\sin \\frac{11}{9}\\pi\\)<\/p>\n\n\n\n

\\(\\displaystyle =\\sin (\\frac{2}{9}\\pi+\\pi)\\)<\/p>\n\n\n\n

\\(\\displaystyle=-\\sin \\frac{2}{9}\\pi\\)<\/p>\n\n\n\n

\uff13\uff0e\\(\\displaystyle \\tan \\frac{13}{18}\\pi\\)<\/p>\n\n\n\n

\\(\\displaystyle =\\tan (\\frac{2}{9}\\pi+\\frac{\\pi}{2})\\)<\/p>\n\n\n\n

\\(\\displaystyle =-\\frac{1}{\\tan \\frac{2}{9}\\pi}\\)<\/p>\n\n\n\n

\u03b8\uff0b\u03c0\/2\uff0c\u03b8+\u03c0\u4e09\u89d2\u95a2\u6570 \u304a\u308f\u308a\u306b<\/h2>\n\n\n\n

\u4eca\u56de\u306f\u4e09\u89d2\u95a2\u6570\u304b\u3089\u03b8\uff0b\u03c0\/2\uff0c\u03b8+\u03c0\u306e\u4e09\u89d2\u95a2\u6570\u306e\u516c\u5f0f\u306b\u3064\u3044\u3066\u307e\u3068\u3081\u307e\u3057\u305f\u3002<\/p>\n\n\n\n

\u4ed6\u306b\u3082\u3001\u6559\u79d1\u66f8\u306b\u5185\u5bb9\u306b\u6cbf\u3063\u3066\u3069\u3093\u3069\u3093\u89e3\u8aac\u8a18\u4e8b\u3092\u6319\u3052\u3066\u3044\u304f\u306e\u3067\u3001<\/p>\n\n\n\n

\u304a\u6c17\u306b\u5165\u308a\u767b\u9332\u3057\u3066\u304a\u3044\u3066\u3082\u3089\u3048\u308b\u3068\u5b9a\u671f\u8a66\u9a13\u524d\u306b\u78ba\u8a8d\u3067\u304d\u308b\u3068\u601d\u3044\u307e\u3059\u3002<\/p>\n\n\n\n

\u3067\u306f\u3001\u3053\u3053\u307e\u3067\u8aad\u3093\u3067\u304f\u3060\u3055\u3063\u3066\u3042\u308a\u304c\u3068\u3046\u3054\u3056\u3044\u307e\u3057\u305f\u3002<\/p>\n\n\n\n

\u307f\u3093\u306a\u306e\u52aa\u529b\u304c\u5831\u308f\u308c\u307e\u3059\u3088\u3046\u306b\uff01<\/p>\n","protected":false},"excerpt":{"rendered":"

\u4e09\u89d2\u95a2\u6570\u306e\u516c\u5f0f\u3092\u7406\u89e3\u3057\u3066\u3001\u3084\u3063\u3068\u6163\u308c\u3066\u304d\u305f\u9803\u306b \\(\\sin (\\theta+\\pi)\\) \u3053\u3093\u306a\u306e\u3068\u304b \\(\\displaystyle \\cos (\\theta+\\frac{\\pi}{2})\\) \u3053\u3093\u306a\u306e\u304c\u51fa\u3066\u304f\u308b\u3093\u3067 […]<\/p>\n","protected":false},"author":1,"featured_media":2134,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"swell_btn_cv_data":"","footnotes":""},"categories":[35,224],"tags":[36,14,11],"class_list":["post-2119","post","type-post","status-publish","format-standard","has-post-thumbnail","hentry","category-sincos","category-math-2","tag-36","tag-b","tag-11"],"yoast_head":"\n\u4e09\u89d2\u95a2\u6570\u306e\u516c\u5f0f\uff08\u03b8\uff0b\u03c0\/2, \u03b8+\u03c0\uff09\u306e\u5c0e\u304d\u65b9\uff01\u5358\u4f4d\u5186\u3092\u4f7f\u3048\u3070\u4e38\u6697\u8a18\u306f\u4e0d\u8981<\/title>\n<meta name=\"robots\" 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