{"id":2005,"date":"2025-12-24T17:19:15","date_gmt":"2025-12-24T08:19:15","guid":{"rendered":"https:\/\/math-travel.com\/?p=2005"},"modified":"2026-03-06T16:38:16","modified_gmt":"2026-03-06T07:38:16","slug":"trigonometric-functions","status":"publish","type":"post","link":"https:\/\/math-travel.jp\/math-2\/trigonometric-functions\/","title":{"rendered":"\u4e09\u89d2\u95a2\u6570\u306e\u516c\u5f0f\u304c\u308f\u304b\u308b\uff01\u91cd\u8981\u516c\u5f0f\u306e\u4f7f\u3044\u65b9\u3092\u57fa\u790e\u304b\u3089\u4e01\u5be7\u306b\u89e3\u8aac"},"content":{"rendered":"\n
\u4eca\u56de\u89e3\u6c7a\u3059\u308b\u60a9\u307f<\/span><\/div>
\n

\u300c\u4e09\u89d2\u95a2\u6570\u3092\u3072\u3068\u901a\u308a\u5fa9\u7fd2\u3057\u305f\u3044\u300d <\/p>\n\n\n\n

\u300c\u4e09\u89d2\u95a2\u6570\u306e\u516c\u5f0f\u3092\u78ba\u8a8d\u3057\u305f\u3044\u300d<\/p>\n<\/div><\/div>\n\n\n\n

\u4e09\u89d2\u95a2\u6570\u306f\u899a\u3048\u308b\u516c\u5f0f\u304c\u591a\u304f\u3001\u7fd2\u3063\u305f\u3070\u304b\u308a\u3060\u3068\u96e3\u3057\u304f\u611f\u3058\u308b\u5358\u5143\u306e1\u3064\u3067\u3059\u3002<\/p>\n\n\n\n

\u5b9a\u671f\u30c6\u30b9\u30c8\u3060\u3051\u3067\u306a\u304f\u3001\u5171\u901a\u30c6\u30b9\u30c8\u306b\u3082\u5fc5\u305a\u51fa\u984c\u3055\u308c\u308b<\/span>\u306e\u3067\u3057\u3063\u304b\u308a\u7406\u89e3\u3057\u3066\u304d\u307e\u3057\u3087\u3046\u3002<\/p>\n\n\n\n

2024\u5e74\u5171\u901a\u30c6\u30b9\u30c8\u6570\u5b66\u2161B<\/th><\/tr><\/thead>
\u7b2c1\u554f<\/th>[1]<\/td>\u4e09\u89d2\u95a2\u6570<\/span><\/td><\/tr>
[2]<\/td>\u6307\u6570\u95a2\u6570\u30fb\u5bfe\u6570\u95a2\u6570<\/td><\/tr>
\u7b2c2\u554f<\/th>[1][2]<\/td>\u5fae\u5206\u6cd5\u3068\u7a4d\u5206\u6cd5<\/td><\/tr>
\u7b2c3\u554f<\/th>\u78ba\u7387\u5206\u5e03\u3068\u7d71\u8a08\u7684\u306a\u63a8\u6e2c<\/td><\/tr>
\u7b2c4\u554f<\/th>\u6570\u5217<\/td><\/tr>
\u7b2c5\u554f<\/th>\u30d9\u30af\u30c8\u30eb<\/td><\/tr><\/tbody><\/table><\/figure>\n\n\n\n

\u672c\u8a18\u4e8b\u3067\u306f\u3001\u4e09\u89d2\u95a2\u6570\u3067\u4f7f\u3046\u516c\u5f0f\u3092\u7db2\u7f85\u7684\u306b\u5b66\u3079\u308b\u3088\u3046<\/span>\u306b\u307e\u3068\u3081\u307e\u3057\u305f\u3002<\/p>\n\n\n\n

\u82e6\u624b\u306a\u90e8\u5206\u3060\u3051\u3067\u306a\u304f\u3001\u5206\u304b\u3063\u305f\u3064\u3082\u308a\u3067\u3044\u308b\u90e8\u5206\u3082\u78ba\u8a8d\u3057\u3066\u307f\u3066\u304f\u3060\u3055\u3044\u3002<\/p>\n\n\n\n

\u4e09\u89d2\u95a2\u6570\u306e\u57fa\u672c<\/h2>\n\n\n\n

\u307e\u305a\u306f\u8d85\u57fa\u672c\u306e\u4e09\u89d2\u6bd4\u306e\u516c\u5f0f<\/span>\u304b\u3089\u78ba\u8a8d\u3057\u307e\u3059\u3002<\/p>\n\n\n\n

\u307e\u305a\u5358\u4f4d\u5186\u3068\u547c\u3070\u308c\u308b\u539f\u70b9\\(O\\)\u3092\u4e2d\u5fc3\u3068\u3057\u305f\u534a\u5f84\\(r\\)\u306e\u5186\u3092\u63cf\u304d\u307e\u3059\u3002<\/p>\n\n\n

\n
\"\u4e09\u89d2\u95a2\u6570\u306e\u516c\u5f0f\"<\/figure>\n<\/div>\n\n\n

\\(x\\)\u8ef8\u306e\u6b63\u306e\u65b9\u5411\u306b\u5bfe\u3057\u3066\u3001\u7dda\u5206\\(OA\\)\u306b\u3088\u308b\u89d2\u306e\u5927\u304d\u3055\u3092\\(\\angle AOB=\\theta \\)\u3068\u3059\u308b\u3068\u304d\u3001<\/p>\n\n\n\n

\u4e09\u89d2\u6bd4\u306e\u516c\u5f0f<\/span><\/div>
\n

\\[\\sin \\theta = \\frac{y}{r}, \\cos \\theta = \\frac{x}{r}, \\tan \\theta = \\frac{y}{x}\\]<\/p>\n<\/div><\/div>\n\n\n\n

\u4e0a\u8a18\u306e\u4e09\u89d2\u6bd4\u3092\u542b\u3093\u3060\u95a2\u6570\u3092\u4e09\u89d2\u95a2\u6570<\/span>\u3068\u3044\u3044\u307e\u3059\u3002<\/p>\n\n\n\n

\u4e09\u89d2\u6bd4\u306e\u6c42\u3081\u65b9\u306f\u4ee5\u4e0b\u306e3\u901a\u308a\u306e\u52d5\u304d\u3067\u899a\u3048\u307e\u3057\u3087\u3046\u3002<\/p>\n\n\n

\n
\"\u4e09\u89d2\u95a2\u6570\u306e\u899a\u3048\u65b9\"<\/figure>\n<\/div>\n\n
\n
\"\u4e09\u89d2\u95a2\u6570\u306e\u899a\u3048\u65b9\"<\/figure>\n<\/div>\n\n\n

\u8a73\u3057\u304f\u306f\u300c\u4e09\u89d2\u6bd4(sin,cos,tan)\u306e\u516c\u5f0f\u3068\u899a\u3048\u65b9\u300d\u3067\u89e3\u8aac\u3057\u3066\u3044\u308b\u306e\u3067\u3001\u5408\u308f\u305b\u3066\u3069\u3046\u305e\u3002<\/p>\n\n\n\n

\u5f27\u5ea6\u6cd5\uff08\u30e9\u30b8\u30a2\u30f3\uff09\u3068\u306f\uff1f<\/h3>\n\n\n\n

\u4e09\u89d2\u95a2\u6570\u3092\u7fd2\u3046\u3068\u89d2\u5ea6\u3092\u5f27\u5ea6\u6cd5\u3067\u8868\u3059\u3088\u3046\u306b\u306a\u308a\u307e\u3059\u3002<\/p>\n\n\n\n

\n

\u300c\u5f27\u5ea6\u6cd5\u3063\u3066\u306a\u3093\u3060\u3088\u3002\u300d<\/span>
\u300c\u30e9\u30b8\u30a2\u30f3\u3063\u3066\u306a\u306b\uff01\uff1f\u300d<\/span><\/p>\n<\/div>\n\n\n\n

\u305d\u3093\u306a\u58f0\u304c\u805e\u3053\u3048\u3066\u304d\u305d\u3046\u3067\u3059\u306d(\u7b11)<\/p>\n\n\n\n

\u5f27\u5ea6\u6cd5\u3068\u3044\u3046\u306e\u306f\u3001\u201d\u5f27\u201d\u306b\u6ce8\u76ee\u3057\u3066\u89d2\u5ea6\u3092\u8868\u73fe\u3059\u308b\u65b9\u6cd5<\/span>\u306e\u3053\u3068\u3067\u3059\u3002<\/p>\n\n\n\n

\u5186\u306e\u534a\u5f84\u3068\u5f27\u306e\u9577\u3055\u304c\u7b49\u3057\u304f\u306a\u308b\u89d2\u5ea6\u30921rad\uff08\u30e9\u30b8\u30a2\u30f3\uff09\u3068\u3044\u3044\u307e\u3059\u3002<\/span><\/p>\n\n\n

\n
\"\u5f27\u5ea6\u6cd5\u3068\u306f\uff1f\"<\/figure>\n<\/div>\n\n\n

\u534a\u5f84\\(r\\)\u306e\u5186\u306b\u304a\u3044\u3066\u3001\u5186\u5468\u306e\u9577\u3055\u306f\\(2\\pi r\\)\u3068\u306a\u308a\u3001\u3053\u306e\u6642\u306e\u4e2d\u5fc3\u89d2\u3092\\(2\\pi\\)\u30e9\u30b8\u30a2\u30f3\u3068\u3044\u3044\u307e\u3059\u3002<\/p>\n\n\n

\n
\"\u5f27\u5ea6\u6cd5\u3068\u306f\uff1f\"<\/figure>\n<\/div>\n\n\n

\u8a73\u3057\u304f\u306f\u300c\u5f27\u5ea6\u6cd5\u3068\u306f\uff1f\u5f27\u5ea6\u6cd5\u306e\u5909\u63db\u3084\u9762\u7a4d\u516c\u5f0f\u3059\u3079\u3066\u89e3\u8aac\uff01\u300d<\/p>\n\n\n\n

\u4e09\u89d2\u6bd4\u306e\u76f8\u4e92\u95a2\u4fc2<\/h2>\n\n\n
\n
\"\u4e09\u89d2\u95a2\u6570\u306e\u76f8\u4e92\u95a2\u4fc2\"<\/figure>\n<\/div>\n\n\n

\u4e09\u89d2\u6bd4\u306f\\(\\sin,\\cos,\\tan\\)\u306e\u3044\u305a\u308c\u304b1\u3064\u304c\u5206\u304b\u308b\u3060\u3051\u3067\u3001\u305d\u306e\u4ed6\u306e\u4e09\u89d2\u6bd4\u3082\u5206\u304b\u308a\u307e\u3059\u3002<\/p>\n\n\n\n

\u305d\u308c\u306b\u306f\u4ee5\u4e0b\u306e\u4e09\u89d2\u6bd4\u306e\u76f8\u4e92\u95a2\u4fc2\u304c\u3068\u3066\u3082\u91cd\u8981\u306b\u306a\u3063\u3066\u304d\u307e\u3059\u3002<\/p>\n\n\n\n

\u4e09\u89d2\u6bd4\u306e\u76f8\u4e92\u95a2\u4fc2\u306f\u5fc5\u305a\u62bc\u3055\u3048\u3066\u304a\u304d\u305f\u3044\u516c\u5f0f\u3067\u3059\u3002<\/span><\/p>\n\n\n\n

\u4e09\u89d2\u6bd4\u306e\u76f8\u4e92\u95a2\u4fc2<\/span><\/div>
\n

\\(\\sin^{2} \\theta+\\cos^{2} \\theta = 1\\)
\\(\\displaystyle \\tan \\theta = \\frac{\\sin \\theta}{\\cos \\theta}\\)
\\(\\displaystyle 1+\\tan ^{2} \\theta = \\frac{1}{\\cos ^{2} \\theta}\\)<\/p>\n<\/div><\/div>\n\n\n\n

\u4e09\u89d2\u95a2\u6570\u306e\u76f8\u4e92\u95a2\u4fc2\u306b\u3064\u3044\u3066\u306f\u8a73\u3057\u304f\u77e5\u308a\u305f\u3044\u65b9\u306f\u300c\u4e09\u89d2\u95a2\u6570\u306e\u76f8\u4e92\u95a2\u4fc2\u300d\u3092\u3054\u89a7\u304f\u3060\u3055\u3044\u3002<\/p>\n\n\n\n

\\(\\theta+\\pi\\)\u306e\u516c\u5f0f<\/h2>\n\n\n\n

\\(sin(\\theta+\\pi)\\)\u306e\u3088\u3046\u306a\u89d2\u5ea6\u306e\u90e8\u5206\u306b\\(\\pi\\)\u3092\u542b\u3080\u516c\u5f0f\u3092\u307e\u3068\u3081\u307e\u3057\u305f\u3002<\/p>\n\n\n\n

\u516c\u5f0f\u2460<\/span><\/div>
\n

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

\u516c\u5f0f\u2461<\/span><\/div>
\n

\\(\\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<\/div><\/div>\n\n\n\n

\u516c\u5f0f\u2462<\/span><\/div>
\n

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

\u8a73\u3057\u304f\u306f\u300c\u03b8\uff0b\u03c0\/2\uff0c\u03b8+\u03c0\u4e09\u89d2\u95a2\u6570\u306e\u516c\u5f0f\u3068\u5c0e\u304d\u65b9\u300d<\/p>\n\n\n\n

\u52a0\u6cd5\u5b9a\u7406\u3092\u6d3b\u7528\u3057\u305f\u516c\u5f0f<\/h2>\n\n\n\n

\u6b21\u306f\u4e09\u89d2\u5f62\u306e\u52a0\u6cd5\u5b9a\u7406<\/span>\u306b\u3064\u3044\u3066\u307e\u3068\u3081\u307e\u3059\u3002<\/p>\n\n\n\n

\u52a0\u6cd5\u5b9a\u7406\u3092\u6d3b\u7528\u3057\u3066\u69d8\u3005\u306a\u516c\u5f0f\u304c\u6210\u308a\u7acb\u3063\u3066\u3044\u308b\u306e\u3067\u3001\u52a0\u6cd5\u5b9a\u7406\u3092\u7406\u89e3\u3057\u3066\u304a\u304f\u3068\u8003\u3048\u65b9\u306e\u5e45\u304c\u5e83\u304c\u308a\u307e\u3059\u3002<\/p>\n\n\n\n

\u52a0\u6cd5\u5b9a\u7406<\/h3>\n\n\n\n

\u307e\u305a\u306f\u52a0\u6cd5\u5b9a\u7406\u304b\u3089\u78ba\u8a8d\u3057\u307e\u3057\u3087\u3046\u3002<\/p>\n\n\n\n

\u52a0\u6cd5\u5b9a\u7406\u3092\u4f7f\u3046\u3053\u3068\u3067\u3001\\(\\displaystyle \\sin \\frac{5}{12}\\pi\\)\u306a\u3069\u306e\u4e09\u89d2\u6bd4\u3092\u6c42\u3081\u308b\u3053\u3068\u304c\u3067\u304d\u307e\u3059\u3002<\/p>\n\n\n\n

\u52a0\u6cd5\u5b9a\u7406<\/span><\/div>
\n

\\begin{eqnarray}
\\sin(\\alpha+\\beta)&=&\\sin \\alpha \\cos \\beta + \\cos \\alpha \\sin \\beta\\\\
\\sin(\\alpha-\\beta)&=&\\sin \\alpha \\cos \\beta-\\cos \\alpha \\sin \\beta\\\\
\\cos(\\alpha+\\beta)&=&\\cos \\alpha \\cos \\beta-\\sin \\alpha \\sin \\beta\\\\
\\cos(\\alpha-\\beta)&=&\\cos \\alpha \\cos \\beta+\\sin \\alpha \\sin \\beta\\\\
\\displaystyle \\tan(\\alpha+\\beta)&=&\\frac{\\tan \\alpha+\\tan \\beta}{1-\\tan \\alpha \\tan \\beta}\\\\
\\displaystyle \\tan(\\alpha-\\beta)&=&\\frac{\\tan \\alpha -\\tan \\beta}{1+\\tan \\alpha \\tan \\beta}
\\end{eqnarray}<\/p>\n<\/div><\/div>\n\n\n\n

\u52a0\u6cd5\u5b9a\u7406\u306e\u91cd\u8981\u30dd\u30a4\u30f3\u30c8\u306f\u300c\u52a0\u6cd5\u5b9a\u7406\u306e\u516c\u5f0f\u307e\u3068\u3081\uff01\u52a0\u6cd5\u5b9a\u7406\u306e\u91cd\u8981\u30dd\u30a4\u30f3\u30c8\u3092\u5fb9\u5e95\u89e3\u8aac\uff01\u300d\u306b\u307e\u3068\u3081\u307e\u3057\u305f\u3002<\/p>\n\n\n\n

\u5f0f\u304c\u9577\u304f\u52a0\u6cd5\u5b9a\u7406\u304c\u899a\u3048\u3089\u308c\u306a\u3044\uff01\u3068\u3044\u3046\u65b9\u306f\u3001\u8a9e\u5442\u5408\u308f\u305b\u3067\u899a\u3048\u3066\u3057\u307e\u3044\u307e\u3057\u3087\u3046\u3002<\/p>\n\n\n\n

\u21d2 \u52a0\u6cd5\u5b9a\u7406\u306e\u899a\u3048\u65b9\u30925\u3064\u7d39\u4ecb\uff01<\/p>\n\n\n\n

2\u500d\u89d2\u306e\u516c\u5f0f<\/h3>\n\n\n\n
2\u500d\u89d2\u306e\u516c\u5f0f<\/span><\/div>
\n

\\begin{eqnarray}
\\sin 2 \\theta &=& 2 \\sin \\theta \\cos \\theta\\\\
\\cos 2 \\theta &=& \\cos ^{2} \\theta-\\sin ^{2} \\theta\\\\
&=& 2 \\cos ^{2} \\theta-1\\\\
&=& 1-2 \\sin ^{2} \\theta\\\\
\\displaystyle \\tan 2 \\theta &=& \\frac{2 \\tan \\theta}{1-\\tan ^{2} \\theta}
\\end{eqnarray}<\/p>\n<\/div><\/div>\n\n\n\n

2\u500d\u89d2\u306e\u5b9a\u7406\u306f\u5148\u307b\u3069\u7d39\u4ecb\u3057\u305f\u52a0\u6cd5\u5b9a\u7406\u3092\u5909\u5f62\u3057\u3066\u8a3c\u660e\u3067\u304d\u307e\u3059\u3002<\/p>\n\n\n\n

\u975e\u5e38\u306b\u3088\u304f\u4f7f\u3046\u516c\u5f0f\u306a\u306e\u3067\u3001\u516c\u5f0f\u3092\u4e38\u6697\u8a18\u3057\u3066\u3057\u307e\u3046\u3053\u3068\u3092\u30aa\u30b9\u30b9\u30e1\u3057\u307e\u3059\u3002<\/p>\n\n\n\n

3\u500d\u89d2\u306e\u516c\u5f0f<\/h3>\n\n\n\n

3\u500d\u89d2\u306e\u516c\u5f0f\u3082\u8f09\u305b\u3066\u304a\u304d\u307e\u3057\u3087\u3046\u3002<\/p>\n\n\n\n

3\u500d\u89d2\u306e\u516c\u5f0f<\/span><\/div>
\n

\\begin{eqnarray}
\\sin 3 \\theta&=&-4\\sin ^{3} \\theta+3 \\sin \\theta\\\\
\\cos 3 \\theta&=&4\\cos ^{3} \\theta-3 \\cos \\theta\\\\
\\displaystyle \\tan 3 \\theta&=&\\frac{3 \\tan \\theta – \\tan ^{3} \\theta}{1-3 \\tan ^{2} \\theta}
\\end{eqnarray}<\/p>\n<\/div><\/div>\n\n\n\n

\u534a\u89d2\u306e\u516c\u5f0f<\/h3>\n\n\n\n

\u534a\u89d2\u306e\u516c\u5f0f\u306f2\u500d\u89d2\u306e\u516c\u5f0f\u3092\u5229\u7528\u3057\u3066\u534a\u89d2\u306e\u4e09\u89d2\u95a2\u6570\u3092\u5c0e\u304f\u516c\u5f0f\u3067\u3059\u3002<\/p>\n\n\n\n

\u305f\u3060\u3057\u3001\uff12\u500d\u89d2\u3084\uff13\u500d\u89d2\u306e\u516c\u5f0f\u3068\u9055\u3063\u3066\u3001\uff12\u4e57\u306e\u5f62\u3067\u3042\u308b\u3053\u3068\u306b\u6ce8\u610f\u304c\u5fc5\u8981\u3067\u3059\u3002<\/span><\/p>\n\n\n\n

\u534a\u89d2\u306e\u516c\u5f0f<\/span><\/div>
\n

\\begin{eqnarray}
\\displaystyle \\sin ^{2} \\frac{\\theta}{2}=\\frac{1-\\cos \\theta}{2}\\\\
\\displaystyle \\cos ^{2} \\frac{\\theta}{2}=\\frac{1+\\cos \\theta}{2}\\\\
\\displaystyle \\tan ^{2} \\frac{\\theta}{2}=\\frac{1-\\cos \\theta}{1+\\cos \\theta}
\\end{eqnarray}<\/p>\n<\/div><\/div>\n\n\n\n

\u4e09\u89d2\u95a2\u6570\u306e\u5408\u6210<\/h2>\n\n\n
\n
\"\u4e09\u89d2\u95a2\u6570\u306e\u5408\u6210\"<\/figure>\n<\/div>\n\n\n


\u4e09\u89d2\u95a2\u6570\u306e\u5408\u6210\u306f\u521d\u3081\u3066\u898b\u305f\u3068\u304d\u9a5a\u304d\u307e\u3059\u3088\u306d\u3002<\/p>\n\n\n\n

\u300c\u3069\u3046\u3057\u3066\u305d\u3046\u306a\u3063\u305f\uff01\uff1f\u300d<\/span><\/p>\n\n\n\n

\u305d\u3093\u306a\u98a8\u306b\u611f\u3058\u307e\u3057\u305f\u3002<\/p>\n\n\n\n

\u4e09\u89d2\u95a2\u6570\u306e\u5408\u6210\u516c\u5f0f<\/span><\/div>
\n

\\(a\\)\u3068\\(b\\)\u306e\u3044\u305a\u308c\u304b\u304c\\(0\\)\u3067\u306a\u3044\u3068\u304d<\/p>\n\n\n\n

\\(a \\sin \\theta+b \\cos \\theta=\\sqrt{a^{2}+b^{2}} \\sin (\\theta+\\alpha)\\)
\\(a \\sin \\theta+b \\cos \\theta=\\sqrt{a^{2}+b^{2}} \\cos (\\theta-\\alpha)\\)
\u305f\u3060\u3057, \\(\\alpha\\)\u306f\\(\\displaystyle \\sin \\alpha=\\frac{b}{\\sqrt{a^{2}+b^{2}}},\\cos \\alpha=\\frac{a}{\\sqrt{a^{2}+b^{2}}}\\) \u3092\u6e80\u305f\u3059\u89d2\u5ea6\u3068\u3059\u308b\u3002<\/p>\n<\/div><\/div>\n\n\n\n

\u4e09\u89d2\u95a2\u6570\u306e\u5408\u6210\u306e\u8a3c\u660e\u3084\u7df4\u7fd2\u554f\u984c\u306f\u300c\u4e09\u89d2\u95a2\u6570\u306e\u5408\u6210\u516c\u5f0f\u3068\u8a3c\u660e\uff01sin\u30fbcos\u306e\u5408\u6210\u3092\u5fb9\u5e95\u89e3\u8aac\uff01\u300d\u306b\u307e\u3068\u3081\u307e\u3057\u305f\u3002<\/p>\n\n\n\n

\u4e09\u89d2\u95a2\u6570\u306e\u548c\u7a4d\u30fb\u7a4d\u548c\u306e\u516c\u5f0f<\/h2>\n\n\n\n

\u4e09\u89d2\u95a2\u6570\u306e\u548c\u3084\u7a4d\u306e\u5f62\u3092\u5909\u63db\u3059\u308b\u516c\u5f0f\u3092\u548c\u7a4d\u306e\u516c\u5f0f\u3084\u7a4d\u548c\u306e\u516c\u5f0f\u3068\u3044\u3044\u307e\u3059\u3002<\/p>\n\n\n\n

\u7a4d\u548c\u306e\u516c\u5f0f<\/h3>\n\n\n\n

\u307e\u305a\u306f\u7a4d\u548c\u306e\u516c\u5f0f\u304b\u3089\uff01<\/p>\n\n\n\n

\u7a4d\u548c\u306e\u516c\u5f0f<\/span><\/div>
\n

\\begin{eqnarray}
\\sin \u03b1 \\cos \u03b2 &=& \\frac{1}{2}\\{\\sin (\u03b1+\u03b2)+\\sin (\u03b1-\u03b2)\\}\\\\
\\sin \u03b1 \\sin \u03b2 &=& \\frac{1}{2}\\{-\\cos (\u03b1+\u03b2)+\\cos (\u03b1-\u03b2)\\}\\\\
\\cos \u03b1 \\cos \u03b2 &=& \\frac{1}{2}\\{\\cos (\u03b1+\u03b2)+\\cos (\u03b1-\u03b2)\\}
\\end{eqnarray}<\/p>\n<\/div><\/div>\n\n\n\n

\u7a4d\u548c\u306e\u516c\u5f0f\u306f\u52a0\u6cd5\u5b9a\u7406\u3092\u7528\u3044\u3066\u3001\u5c0e\u304f\u3053\u3068\u304c\u3067\u304d\u307e\u3059\u3002<\/p>\n\n\n\n

\u548c\u7a4d\u306e\u516c\u5f0f<\/h3>\n\n\n\n

\u6b21\u306f\u4e09\u89d2\u6bd4\u306e\u548c\u3092\u7a4d\u3067\u8868\u3059\u3001\u548c\u7a4d\u306e\u516c\u5f0f\u3067\u3059\u3002<\/p>\n\n\n\n

\u548c\u7a4d\u306e\u516c\u5f0f\u306f\u5148\u307b\u3069\u7d39\u4ecb\u3057\u305f\u7a4d\u548c\u306e\u516c\u5f0f\u304b\u3089\u5c0e\u304b\u308c\u307e\u3059\u3002<\/p>\n\n\n\n

\u548c\u7a4d\u306e\u516c\u5f0f<\/span><\/div>
\n

\\begin{eqnarray}
\\sin A+\\sin B &=& 2 \\sin \\frac{A+B}{2} \\cos \\frac{A-B}{2}\\\\
\\cos A+\\cos B &=& 2 \\cos \\frac{A+B}{2} \\cos \\frac{A-B}{2}\\\\
\\cos A-\\cos B &=& -2 \\sin \\frac{A+B}{2} \\sin \\frac{A-B}{2}
\\end{eqnarray}<\/p>\n<\/div><\/div>\n\n\n\n

\u548c\u7a4d\u306e\u516c\u5f0f\u30fb\u7a4d\u548c\u306e\u516c\u5f0f\u306f\u672c\u5f53\u306b\u899a\u3048\u3065\u3089\u3044\u516c\u5f0f\u306a\u306e\u3067\u3001\u3069\u3046\u3057\u3066\u3082\u899a\u3048\u3089\u308c\u306a\u3044\u65b9\u306f\u300c\u548c\u7a4d\uff06\u7a4d\u548c\u306e\u516c\u5f0f\u3068\u899a\u3048\u65b9\u300d\u3092\u53c2\u8003\u306b\u3057\u3066\u307f\u3066\u304f\u3060\u3055\u3044\u3002<\/p>\n\n\n\n

\u4e09\u89d2\u95a2\u6570\u3092\u5229\u7528\u3057\u305f\u516c\u5f0f<\/h2>\n\n\n
\n
\"\u4e09\u89d2\u95a2\u6570\u3092\u5229\u7528\u3057\u305f\u516c\u5f0f\"<\/figure>\n<\/div>\n\n\n

\u305d\u306e\u4ed6\u306b\u3082\u4e09\u89d2\u95a2\u6570\u3092\u5229\u7528\u3057\u305f\u516c\u5f0f\u304c\u3044\u304f\u3064\u304b\u3042\u308b\u306e\u3067\u7d39\u4ecb\u3057\u307e\u3059\u3002<\/p>\n\n\n\n

\u6b63\u5f26\u5b9a\u7406<\/h3>\n\n\n\n

\u6b63\u5f26\u5b9a\u7406\u306f\u4e09\u89d2\u5f62\u306b\u4f7f\u3046\u5b9a\u7406\u3067\u3059\u3002<\/p>\n\n\n\n

\u5404\u9802\u70b9A,B,C\u3068\u3057\u3066\u3001\u5411\u304b\u3044\u5408\u3046\u8fba\u3092a,b,c\u3068\u3059\u308b\u3002<\/p>\n\n\n

\n
\"\u6b63\u5f26\u5b9a\u7406\"<\/figure>\n<\/div>\n\n\n
\u6b63\u5f26\u5b9a\u7406<\/span><\/div>
\n

\u25b3ABC\u306e\u5916\u63a5\u5186\u306e\u534a\u5f84\u3092R\u3068\u3059\u308b\u3068\u3001\u6b21\u304c\u6210\u308a\u7acb\u3064
\\[\\displaystyle \\frac{a}{sin A}=\\frac{b}{sin B}=\\frac{c}{sin C}=2R\\]<\/p>\n<\/div><\/div>\n\n\n\n

\u4f59\u5f26\u5b9a\u7406<\/h3>\n\n\n\n

\u4f59\u5f26\u5b9a\u7406\u3082\u4e09\u89d2\u5f62\u306b\u8fba\u3084\u89d2\u3092\u6c42\u3081\u3089\u308c\u308b\u5b9a\u7406\u3067\u3059\u3002<\/p>\n\n\n\n

\u5404\u9802\u70b9A,B,C\u3068\u3057\u3066\u3001\u5411\u304b\u3044\u5408\u3046\u8fba\u3092a,b,c\u3068\u3059\u308b\u3002<\/p>\n\n\n

\n
\"\u4f59\u5f26\u5b9a\u7406\"<\/figure>\n<\/div>\n\n\n
\u4f59\u5f26\u5b9a\u7406<\/span><\/div>
\n

\\begin{eqnarray}
a^{2} &=& b^{2}+c^{2}-2bc \\cos \\angle A\\\\
b^{2} &=& a^{2}+c^{2}-2ac \\cos \\angle B\\\\
c^{2} &=& a^{2}+b^{2}-2ab \\cos \\angle C
\\end{eqnarray}<\/p>\n<\/div><\/div>\n\n\n\n

sin\u3092\u4f7f\u3063\u305f\u9762\u7a4d\u516c\u5f0f<\/h3>\n\n\n\n

\u4e09\u89d2\u95a2\u6570\u3092\u4f7f\u3063\u3066\u4e09\u89d2\u5f62\u306e\u9762\u7a4d\u3092\u6c42\u3081\u308b\u3053\u3068\u3082\u3067\u304d\u308b\u3093\u3067\u3059\u3002<\/span><\/p>\n\n\n\n

sin\uff08\u30b5\u30a4\u30f3\uff09\u3092\u7528\u3044\u305f\u9762\u7a4d\u516c\u5f0f\u306f\u4e09\u89d2\u5f62\u306e2\u8fba\u3068\u305d\u306e\u9593\u306e\u89d2\u304c\u5206\u304b\u3063\u3066\u308b\u3068\u304d\u306b\u4f7f\u3046\u3053\u3068\u304c\u3067\u304d\u307e\u3059\u3002<\/p>\n\n\n\n

\"\"<\/figure>\n\n\n\n
sin\u3092\u7528\u3044\u305f\u9762\u7a4d\u516c\u5f0f<\/span><\/div>
\n

2\u8fba\u306e\u9577\u3055\u3068\u305d\u306e\u9593\u306e\u89d2\u304c\u5206\u304b\u308c\u3070\u4e09\u89d2\u5f62\\(ABC\\)\u306e\u9762\u7a4d\\(S\\)\u3092\u6c42\u3081\u308b\u3053\u3068\u304c\u3067\u304d\u307e\u3059\u3002
\\begin{eqnarray}
S &=& \\frac{1}{2}bc \\sin A \\\\
&=& \\frac{1}{2}ca \\sin B \\\\
&=& \\frac{1}{2}ab \\sin C
\\end{eqnarray}<\/p>\n<\/div><\/div>\n\n\n\n

2\u76f4\u7dda\u306e\u306a\u3059\u89d2\u3068\u50be\u304d\u306e\u95a2\u4fc2<\/h3>\n\n\n\n

tan\uff08\u30bf\u30f3\u30b8\u30a7\u30f3\u30c8\uff09\u3092\u7528\u3044\u30662\u76f4\u7dda\u306e\u306a\u3059\u89d2\u306e\u5927\u304d\u3055\u3092\u6c42\u3081\u308b\u3053\u3068\u3082\u3067\u304d\u307e\u3059\u3002<\/span><\/p>\n\n\n\n

\n

2\u76f4\u7dda\u306e\u306a\u3059\u89d2\u3068\u50be\u304d\u4e92\u3044\u306b\u5782\u76f4\u3067\u306a\u30442\u76f4\u7dda<\/p>\n\n\n\n

\\[y=m_{1} x+n_{1}, \\quad y=m_{2} x+n_{2}\\]<\/p>\n\n\n\n

\u306e\u306a\u3059\u89d2\u3092 \\(\\theta\\) \u3068\u3057\u3066<\/p>\n\n\n\n

\\[\\displaystyle \\tan \\theta=|\\frac{m_{1}-m_{2}}{1+m_{1} m_{2}}|\\]<\/p>\n<\/div><\/div>\n\n\n\n

\u4e09\u89d2\u95a2\u6570\u306e\u307e\u3068\u3081<\/h2>\n\n\n\n

\u4eca\u56de\u306f\u4e09\u89d2\u95a2\u6570\u306b\u3064\u3044\u3066\u305d\u308c\u305e\u308c\u307e\u3068\u3081\u307e\u3057\u305f\u3002<\/span><\/p>\n\n\n\n

\u4e09\u89d2\u95a2\u6570\u4ee5\u5916\u306e\u5358\u5143\u306b\u3064\u3044\u3066\u3082\u307e\u3068\u3081\u8a18\u4e8b\u3092\u51fa\u3057\u3066\u3044\u307e\u3059\u3002<\/p>\n\n\n\n

\u6700\u5f8c\u307e\u3067\u3054\u89a7\u3044\u305f\u3060\u304d\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\u306f\u899a\u3048\u308b\u516c\u5f0f\u304c\u591a\u304f\u3001\u7fd2\u3063\u305f\u3070\u304b\u308a\u3060\u3068\u96e3\u3057\u304f\u611f\u3058\u308b\u5358\u5143\u306e1\u3064\u3067\u3059\u3002 \u5b9a\u671f\u30c6\u30b9\u30c8\u3060\u3051\u3067\u306a\u304f\u3001\u5171\u901a\u30c6\u30b9\u30c8\u306b\u3082\u5fc5\u305a\u51fa\u984c\u3055\u308c\u308b\u306e\u3067\u3057\u3063\u304b\u308a\u7406\u89e3\u3057\u3066\u304d\u307e\u3057\u3087\u3046\u3002 2024\u5e74\u5171\u901a\u30c6\u30b9\u30c8\u6570\u5b66\u2161B \u7b2c1\u554f [1] \u4e09\u89d2\u95a2\u6570 [2] […]<\/p>\n","protected":false},"author":1,"featured_media":6144,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"swell_btn_cv_data":"","footnotes":""},"categories":[35,224],"tags":[36,10,14,11],"class_list":["post-2005","post","type-post","status-publish","format-standard","has-post-thumbnail","hentry","category-sincos","category-math-2","tag-36","tag-a","tag-b","tag-11"],"yoast_head":"\n\u4e09\u89d2\u95a2\u6570\u306e\u516c\u5f0f\u304c\u308f\u304b\u308b\uff01\u91cd\u8981\u516c\u5f0f\u306e\u4f7f\u3044\u65b9\u3092\u57fa\u790e\u304b\u3089\u4e01\u5be7\u306b\u89e3\u8aac<\/title>\n<meta name=\"robots\" content=\"index, follow, max-snippet:-1, max-image-preview:large, max-video-preview:-1\" \/>\n<link rel=\"canonical\" href=\"https:\/\/math-travel.jp\/math-2\/trigonometric-functions\/\" \/>\n<meta property=\"og:locale\" content=\"ja_JP\" \/>\n<meta property=\"og:type\" content=\"article\" \/>\n<meta property=\"og:title\" content=\"\u4e09\u89d2\u95a2\u6570\u306e\u516c\u5f0f\u304c\u308f\u304b\u308b\uff01\u91cd\u8981\u516c\u5f0f\u306e\u4f7f\u3044\u65b9\u3092\u57fa\u790e\u304b\u3089\u4e01\u5be7\u306b\u89e3\u8aac\" \/>\n<meta property=\"og:description\" content=\"\u4e09\u89d2\u95a2\u6570\u306f\u899a\u3048\u308b\u516c\u5f0f\u304c\u591a\u304f\u3001\u7fd2\u3063\u305f\u3070\u304b\u308a\u3060\u3068\u96e3\u3057\u304f\u611f\u3058\u308b\u5358\u5143\u306e1\u3064\u3067\u3059\u3002 \u5b9a\u671f\u30c6\u30b9\u30c8\u3060\u3051\u3067\u306a\u304f\u3001\u5171\u901a\u30c6\u30b9\u30c8\u306b\u3082\u5fc5\u305a\u51fa\u984c\u3055\u308c\u308b\u306e\u3067\u3057\u3063\u304b\u308a\u7406\u89e3\u3057\u3066\u304d\u307e\u3057\u3087\u3046\u3002 2024\u5e74\u5171\u901a\u30c6\u30b9\u30c8\u6570\u5b66\u2161B \u7b2c1\u554f [1] \u4e09\u89d2\u95a2\u6570 [2] […]\" \/>\n<meta property=\"og:url\" content=\"https:\/\/math-travel.jp\/math-2\/trigonometric-functions\/\" \/>\n<meta property=\"og:site_name\" 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