{"id":2189,"date":"2025-12-24T17:19:15","date_gmt":"2025-12-24T08:19:15","guid":{"rendered":"https:\/\/math-travel.com\/?p=2189"},"modified":"2026-02-11T16:38:31","modified_gmt":"2026-02-11T07:38:31","slug":"sanbaikakun-kousiki","status":"publish","type":"post","link":"https:\/\/math-travel.jp\/math-2\/sanbaikakun-kousiki\/","title":{"rendered":"3\u500d\u89d2\u306e\u516c\u5f0f\u306e\u899a\u3048\u65b9\uff08\u8a9e\u5442\u5408\u308f\u305b\uff09\u3068\u5c0e\u304d\u65b9\uff01\u516c\u5f0f\u3092\u30de\u30b9\u30bf\u30fc\u3057\u3066\u5f97\u70b9\u30a2\u30c3\u30d7"},"content":{"rendered":"\n
\u300c3\u500d\u89d2\u306e\u516c\u5f0f\u3063\u3066\u3069\u3093\u306a\u306e\uff1f\u300d<\/span> 3\u500d\u89d2\u306e\u516c\u5f0f\u3092\u3059\u3050\u5fd8\u308c\u3061\u3083\u3044\u307e\u3059\u2026<\/p>\n<\/span><\/span><\/span><\/div><\/div><\/div><\/div>\n\n\n \u4e09\u89d2\u95a2\u6570\u306e3\u500d\u89d2\u306e\u516c\u5f0f\u3092\u77e5\u3063\u3066\u3044\u307e\u3059\u304b\uff1f<\/p>\n\n\n\n 3\u500d\u89d2\u306e\u516c\u5f0f\u306f\u4ee5\u4e0b\u306e\u3088\u3046\u306a\u5f62\u3092\u3057\u3066\u3044\u307e\u3059\u3002<\/span><\/p>\n\n\n\n \\begin{eqnarray} \u3068\u3066\u3082\u8907\u96d1\u306a\u516c\u5f0f\u306a\u306e\u3067\u3001\u8a9e\u5442\u5408\u308f\u305b\u3067\u899a\u3048\u3061\u3083\u3044\u307e\u3057\u3087\u3046\u3002<\/p>\n\n\n\n \u672c\u8a18\u4e8b\u3067\u306f\uff13\u500d\u89d2\u306e\u516c\u5f0f\u3068\u899a\u3048\u65b9\u306b\u3064\u3044\u3066\u89e3\u8aac<\/span>\u3057\u307e\u3059\u3002<\/p>\n\n\n\n \u5f8c\u534a\u306b\u7df4\u7fd2\u554f\u984c\u3082\u7528\u610f\u3057\u305f\u306e\u3067\u3001\u305c\u3072\u3054\u6d3b\u7528\u304f\u3060\u3055\u3044\u3002<\/p>\n\n\n \u6c17\u306b\u306a\u308b\u898b\u51fa\u3057\u3092\u30af\u30ea\u30c3\u30af\u3057\u3066\u3001 3\u500d\u89d2\u306e\u516c\u5f0f\u306f\u3081\u3063\u305f\u306b\u4f7f\u3044\u307e\u305b\u3093\u304c\u3001\u3053\u3093\u306a\u516c\u5f0f\u304c\u3042\u308b\u3053\u3068\u306f\u77e5\u3063\u3066\u304a\u304d\u307e\u3057\u3087\u3046\u3002<\/p>\n\n\n\n \\begin{eqnarray} \uff13\u500d\u89d2\u306e\u516c\u5f0f\u3068\u3044\u3046\u306e\u306f\u3001\u89d2\u304c\uff13\u500d\u306e\u5f62\u3092\u3057\u3066\u3044\u308b\u4e09\u89d2\u95a2\u6570\u306e\u516c\u5f0f<\/span>\u3067\u3059\u3002<\/p>\n\n\n\n \\[\\sin 3 \\theta =3 \\sin \\theta-4 \\sin ^{3} \\theta\\]<\/p>\n\n\n \u3068\u3066\u3082\u8907\u96d1\u306a\u516c\u5f0f\u306a\u306e\u3067\u3059\u3050\u5fd8\u308c\u3061\u3083\u3044\u307e\u3059<\/p>\n<\/span><\/span><\/span><\/div><\/div><\/div><\/div>\n\n 3\u500d\u89d2\u306e\u516c\u5f0f\u306e\u899a\u3048\u65b9\u3092\u7d39\u4ecb\u3059\u308b\u3088\uff01<\/p>\n<\/span><\/span><\/span><\/div><\/div><\/div><\/div>\n\n\n 3\u500d\u89d2\u306e\u516c\u5f0f\u306f\u8907\u96d1\u306a\u306e\u3067\u5fd8\u308c\u3066\u3057\u307e\u3044\u307e\u3059\u3088\u306d\u3002<\/p>\n\n\n\n \u305d\u3053\u30673\u500d\u89d2\u306e\u516c\u5f0f\u306e\u899a\u3048\u65b9<\/span>\u3092\u7d39\u4ecb\u3057\u307e\u3059\u3002<\/p>\n\n\n\n \u307e\u305a\u306f\\(\\sin\\)\u306e3\u500d\u89d2\u306e\u516c\u5f0f\u3092\u8a9e\u5442\u5408\u308f\u305b\u3067\u899a\u3048\u307e\u3057\u3087\u3046\u3002<\/p>\n\n\n\n \\[\\sin 3 \\theta =3 \\sin \\theta-4 \\sin^{3} \\theta\\] 3\u500d\u89d2\u306e\u516c\u5f0f\u306f\u8a9e\u5442\u5408\u308f\u305b\u3059\u3089\u899a\u3048\u3065\u3089\u3044\u3067\u3059\u306d\u3002<\/p>\n\n\n\n \u6b21\u306b\\(\\cos\\)\u306e\u8a9e\u5442\u5408\u308f\u305b\u3082\u7d39\u4ecb\u3057\u307e\u3059\u3002<\/p>\n\n\n\n \\(\\tan\\)\u306e\u8a9e\u5442\u5408\u308f\u305b\u306f\u8abf\u3079\u3066\u3082\u898b\u3064\u304b\u3089\u306a\u304b\u3063\u305f\u306e\u3067\u3001\u6c17\u5408\u3067\u899a\u3048\u307e\u3057\u3087\u3046…\uff08\u7b11\uff09<\/p>\n\n\n \u8a9e\u5442\u5408\u308f\u305b\u3082\u899a\u3048\u3065\u3089\u3044\u6c17\u304c\u3057\u307e\u3059\u2026<\/p>\n<\/span><\/span><\/span><\/div><\/div><\/div><\/div>\n\n \u3054\u3081\u3093\u306d\u3002\u307b\u3093\u3068\u306b\u826f\u3044\u306e\u304c\u898b\u3064\u304b\u3089\u306a\u304b\u3063\u305f\u3093\u3060\u2026<\/p>\n<\/span><\/span><\/span><\/div><\/div><\/div><\/div>\n\n\n \uff13\u500d\u89d2\u306e\u516c\u5f0f\u306f\u52a0\u6cd5\u5b9a\u7406\u3092\u5fdc\u7528\u3057\u3066\u8a3c\u660e\u3057\u307e\u3059\u3002<\/p>\n\n\n \u305d\u308c\u3067\u306f\u3001\u305d\u308c\u305e\u308c\u306e\u516c\u5f0f\u306e\u8a3c\u660e\u3092\u3057\u3066\u3044\u304d\u307e\u3059\u3002<\/p>\n\n\n\n \\(\\sin\\)\u306e\u52a0\u6cd5\u5b9a\u7406\u3092\u4f7f\u3044\u307e\u3059\u3002<\/p>\n\n\n\n \\[\\sin(\u03b1+\u03b2)=\\sin \u03b1 \\cos \u03b2+\\cos \u03b1 \\sin \u03b2\\]<\/p>\n\n\n\n \u3053\u3053\u3067\\(\u03b1=2 \\theta,\u03b2=\\theta\\)\u306b\u7f6e\u304d\u63db\u3048\u308b\u3068\u3001<\/p>\n\n\n\n \\begin{eqnarray} \u3057\u305f\u304c\u3063\u3066\u3001<\/p>\n\n\n\n \\[\\sin 3 \\theta=3 \\sin \\theta-4 \\sin ^{3} \\theta\\]<\/span><\/p>\n\n\n\n \\(\\cos\\)\u3082\u540c\u69d8\u306e\u624b\u9806\u3067\u8a3c\u660e\u3057\u307e\u3059\u3002<\/p>\n\n\n\n \\(\\cos\\)\u306e\u52a0\u6cd5\u5b9a\u7406\u3092\u4f7f\u3063\u3066\u3001<\/p>\n\n\n\n \\[\\cos(\u03b1+\u03b2)=\\cos \u03b1 \\cos \u03b2 – \\sin \u03b1 \\sin \u03b2\\]<\/p>\n\n\n\n \\(\u03b1=2\\theta,\u03b2=\\theta\\)\u3068\u3059\u308b\u3068\u3001<\/p>\n\n\n\n \\begin{eqnarray} \u3057\u305f\u304c\u3063\u3066\u3001<\/p>\n\n\n\n \\[\\cos 3 \\theta =4 \\cos^{3} \\theta-3 \\cos \\theta\\]<\/span><\/p>\n\n\n\n \u6700\u5f8c\u306b\\(\\tan\\)\u306e3\u500d\u89d2\u306e\u516c\u5f0f\u3092\u8a3c\u660e\u3057\u307e\u3059\u3002<\/p>\n\n\n\n \\(\\tan\\)\u306e\u52a0\u6cd5\u5b9a\u7406\u3092\u7528\u3044\u3066\u3001<\/p>\n\n\n\n \\[\\displaystyle \\tan(\u03b1+\u03b2)=\\frac{\\tan \u03b1 + \\tan \u03b2}{1-\\tan \u03b1 \\tan \u03b2}\\]<\/p>\n\n\n\n \\(\u03b1=2\\theta,\u03b2=\\theta\\)\u3068\u3059\u308b\u3068<\/p>\n\n\n\n \\begin{eqnarray} \u5206\u6bcd\u5206\u5b50\u306b \\(1-\\tan ^{2} \\theta\\) \u3092\u304b\u3051\u308b\u3068<\/p>\n\n\n\n \\[\\displaystyle \\frac{3 \\tan \\theta-\\tan ^{3} \\theta}{1-3 \\tan ^{2} \\theta}\\]<\/span><\/p>\n\n\n\n \u3068\u306a\u308a\u3001\u8a3c\u660e\u7d42\u4e86\u3002<\/p>\n\n\n\n \uff13\u500d\u89d2\u306e\u516c\u5f0f\u306f<\/p>\n\n\n\n \\[\\sin 3 \\theta =3 \\sin \\theta-4 \\sin ^{3} \\theta\\]<\/p>\n\n\n\n \u306e\u3088\u3046\u306a\u89d2\u304c\uff13\u500d\u306e\u5f62\u3092\u3057\u3066\u3044\u308b\u3068\u304d\u306b\u6d3b\u8e8d\u3057\u307e\u3059\u3002<\/p>\n\n\n\n \u4f8b\u984c\u3092\u3082\u3068\u306b3\u500d\u89d2\u306e\u516c\u5f0f\u306e\u4f7f\u3044\u65b9\u3092\u78ba\u8a8d\u3057\u307e\u3057\u3087\u3046\u3002<\/span><\/p>\n\n\n\n \\(\\displaystyle \\sin \\theta=\\frac{1}{3} \\)\u306e\u3068\u304d\u3001\\(\\sin 3 \\theta\\)\u3092\u6c42\u3081\u3088\u3002<\/p>\n\n\n\n \u305f\u3060\u3057,\\(\\displaystyle 0<\\theta<\\frac{\\pi}{2}\\)\u3068\u3059\u308b\u3002<\/p>\n<\/div><\/div>\n\n\n\n \u89e3\u7b54<\/span><\/p>\n\n\n\n \\(\\sin 3 \\theta =3 \\sin \\theta-4 \\sin ^{3} \\theta\\)\u3092\u4f7f\u3044\u305f\u3044\u306e\u3067\u3001<\/p>\n\n\n\n \\(\\displaystyle \\sin \\theta=\\frac{1}{3} \\)\u3092\u4ee3\u5165\u3057\u307e\u3057\u3087\u3046\u3002<\/p>\n\n\n\n \\begin{eqnarray} \u3057\u305f\u304c\u3063\u3066\u3001<\/p>\n\n\n\n \\[\\sin 3 \\theta=\\frac{23}{27}\\]<\/span><\/p>\n\n\n \u516c\u5f0f\u3055\u3048\u899a\u3048\u3066\u3057\u307e\u3048\u3070\u96e3\u3057\u304f\u306f\u306a\u3044\u3088\uff01<\/p>\n<\/span><\/span><\/span><\/div><\/div><\/div><\/div>\n\n\n 3\u500d\u89d2\u306e\u516c\u5f0f\u3092\u4f7f\u3063\u3066\u7df4\u7fd2\u554f\u984c\u306b\u6311\u6226\u3057\u307e\u3057\u3087\u3046\u3002<\/p>\n\n\n\n \\(\\displaystyle 0<\\theta<\\frac{\\pi}{2}, \\sin \\theta=\\frac{4}{5}\\)\u306e\u3068\u304d\u3001<\/p>\n\n\n\n \\(\\sin 3 \\theta,\\cos 3 \\theta,\\tan 3 \\theta\\)\u306e\u503c\u3092\u6c42\u3081\u3088\u3046\u3002<\/p>\n<\/div><\/div>\n\n\n\n \u89e3\u7b54<\/span><\/p>\n\n\n\n \\(\\sin,\\cos,\\tan\\)\u305d\u308c\u305e\u308c\u306e3\u500d\u89d2\u306e\u516c\u5f0f\u3092\u4f7f\u3046\u305f\u3081\u306b\u3001\\(\\cos \\theta ,\\tan \\theta\\)\u3092\u6c42\u3081\u307e\u3057\u3087\u3046\u3002<\/p>\n\n\n\n \u4e09\u89d2\u5f62\u306e\u76f8\u4e92\u95a2\u4fc2\u3088\u308a\u3001<\/p>\n\n\n\n \\(\\sin^{2} \\theta +\\cos^{2} \\theta=1\\)<\/p>\n\n\n\n \u306a\u306e\u3067\u3001<\/p>\n\n\n\n \\begin{eqnarray} \\(\\displaystyle 0<\\theta<\\frac{\\pi}{2}\\)\u3088\u308a\u3001<\/p>\n\n\n\n \\[\\displaystyle cos \\theta=\\frac{3}{5}\\]<\/p>\n\n\n\n \u307e\u305f\u3001<\/p>\n\n\n\n \\begin{eqnarray} \u3057\u305f\u304c\u3063\u3066\u3001<\/p>\n\n\n\n \\(\\displaystyle \\sin \\theta=\\frac{4}{5}\\),\\(\\displaystyle \\cos \\theta=\\frac{3}{5}\\),\\(\\displaystyle \\tan \\theta=\\frac{4}{3}\\)<\/p>\n\n\n\n \u3053\u3053\u304b\u3089\u304c\u672c\u984c\u3067\u3059\uff01<\/span><\/p>\n\n\n\n \u6c42\u3081\u305f\u5024\u30923\u500d\u89d2\u306e\u516c\u5f0f\u306b\u4ee3\u5165\u3057\u307e\u3059\u3002<\/p>\n\n\n\n \\begin{eqnarray} \\begin{eqnarray} \u6700\u5f8c\u306b\\(\\tan 3 \\theta\\)\u3092\u6c42\u3081\u307e\u3059\u3002<\/p>\n\n\n\n \\(\\tan 3\\theta\\)\u306f\\(\\displaystyle \\tan 3 \\theta =\\frac{\\sin 3 \\theta}{\\cos 3 \\theta}\\)\u304b\u3089\u6c42\u3081\u307e\u3057\u3087\u3046\u3002<\/p>\n\n\n\n \u203b\\(\\tan\\)\u306e3\u500d\u89d2\u306e\u516c\u5f0f\u3082\u5b58\u5728\u3059\u308b\u3088\uff01<\/span><\/p>\n\n\n\n \\begin{eqnarray} \u3057\u305f\u304c\u3063\u3066\u3001<\/p>\n\n\n\n \\begin{eqnarray} \u8a08\u7b97\u304c\u5927\u5909\u3060\u3063\u305f\u3051\u3069\u3001\u306a\u3093\u3068\u304b\u89e3\u3051\u307e\u3057\u305f<\/p>\n<\/span><\/span><\/span><\/div><\/div><\/div><\/div>\n\n \u8a08\u7b97\u304c\u8907\u96d1\u306a\u306e\u3067\u3001\u8a08\u7b97\u30df\u30b9\u306b\u6c17\u3092\u4ed8\u3051\u3088\u3046\uff01<\/p>\n<\/span><\/span><\/span><\/div><\/div><\/div><\/div>\n\n\n \u4eca\u56de\u306f3\u500d\u89d2\u306e\u516c\u5f0f\u306b\u3064\u3044\u3066\u307e\u3068\u3081\u307e\u3057\u305f\u3002<\/span><\/p>\n\n\n\n \\begin{eqnarray} \u4eca\u56de\u306f3\u500d\u89d2\u306e\u516c\u5f0f\u3092\u4e2d\u5fc3\u306b\u89e3\u8aac\u3057\u307e\u3057\u305f\u3002<\/p>\n\n\n\n 3\u500d\u89d2\u306e\u516c\u5f0f\u306f\u4f7f\u3046\u6a5f\u4f1a\u304c\u5c11\u306a\u3044\u306e\u3067\u5fd8\u308c\u304c\u3061\u3067\u3059\u3088\u306d\u3002<\/p>\n","protected":false},"excerpt":{"rendered":" \u300c3\u500d\u89d2\u306e\u516c\u5f0f\u3063\u3066\u3069\u3093\u306a\u306e\uff1f\u300d\u300c\u899a\u3048\u65b9\u304c\u77e5\u308a\u305f\u3044\u300d\u4eca\u56de\u306f3\u500d\u89d2\u306e\u516c\u5f0f\u306b\u95a2\u3059\u308b\u60a9\u307f\u3092\u89e3\u6c7a\u3057\u307e\u3059\u3002 \u4e09\u89d2\u95a2\u6570\u306e3\u500d\u89d2\u306e\u516c\u5f0f\u3092\u77e5\u3063\u3066\u3044\u307e\u3059\u304b\uff1f 3\u500d\u89d2\u306e\u516c\u5f0f\u306f\u4ee5\u4e0b\u306e\u3088\u3046\u306a\u5f62\u3092\u3057\u3066\u3044\u307e\u3059\u3002 \u3068\u3066\u3082\u8907\u96d1\u306a\u516c\u5f0f\u306a\u306e\u3067\u3001\u8a9e\u5442\u5408\u308f\u305b\u3067\u899a […]<\/p>\n","protected":false},"author":1,"featured_media":6849,"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-2189","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
\u300c\u899a\u3048\u65b9\u304c\u77e5\u308a\u305f\u3044\u300d<\/span>
\u4eca\u56de\u306f3\u500d\u89d2\u306e\u516c\u5f0f\u306b\u95a2\u3059\u308b\u60a9\u307f\u3092\u89e3\u6c7a\u3057\u307e\u3059\u3002<\/p>\n\n\n
\u9ad8\u6821\u751f<\/span><\/div>
\\sin 3 \\theta &=&3 \\sin \\theta-4 \\sin ^{3} \\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
\u30b7\u30fc\u30bf<\/span><\/div>
\u305c\u3072\u6700\u5f8c\u307e\u3067\u3054\u89a7\u304f\u3060\u3055\u3044\u3002<\/p>\n<\/span><\/span><\/span><\/div><\/div><\/div><\/div>\n\n\n3\u500d\u89d2\u306e\u516c\u5f0f<\/h2>\n\n\n\n
\\sin 3 \\theta &=&3 \\sin \\theta-4 \\sin ^{3} \\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
\u9ad8\u6821\u751f<\/span><\/div>
\u30b7\u30fc\u30bf<\/span><\/div>3\u500d\u89d2\u306e\u516c\u5f0f\u306e\u899a\u3048\u65b9<\/h2>\n\n\n\n
\u30b5\u30f3\u30b7\u30e3\u30a4\u30f3\u5f15\u3044\u3066\u53f8\u796d\u304c\u53c2\u4e0a\u3059<\/p>\n<\/div><\/div>\n\n\n\n
\\[\\cos 3 \\theta =4 \\cos^{3} \\theta-3 \\cos \\theta\\]
\u826f\u3044\u5b50\u306e\u307f\u3093\u306a\u3067\u5f15\u3063\u5f35\u308b\u795e\u8f3f\u307f\u3053\u3057<\/p>\n<\/div><\/div>\n\n\n\n
\u9ad8\u6821\u751f<\/span><\/div>
\u30b7\u30fc\u30bf<\/span><\/div>\uff13\u500d\u89d2\u306e\u516c\u5f0f\u3000\u8a3c\u660e<\/h2>\n\n\n\n
<\/figure>\n<\/div>\n\n\n\\(\\sin\\)\u306e\uff13\u500d\u89d2\u306e\u516c\u5f0f<\/h3>\n\n\n\n
\\sin 3 \\theta &=&\\sin (2 \\theta+\\theta)\\\\
&=&\\sin 2 \\theta \\cos \\theta+\\cos 2 \\theta \\sin \\theta\\\\
&=&2 \\sin \\theta \\cos \\theta \\cdot \\cos \\theta+(1-2 \\sin ^{2} \\theta) \\sin \\theta\\\\
&=&2 \\sin \\theta \\cos ^{2} \\theta+\\sin \\theta-2 \\sin ^{3} \\theta\\\\
&=&2 \\sin \\theta(1-\\sin ^{2} \\theta)+\\sin \\theta-2 \\sin ^{3} \\theta\\\\
&=&3 \\sin \\theta-4 \\sin ^{3} \\theta
\\end{eqnarray}<\/p>\n\n\n\n\\(\\cos\\)\u306e\uff13\u500d\u89d2\u306e\u516c\u5f0f<\/h3>\n\n\n\n
\\cos 3 \\theta &=&\\cos (2 \\theta+\\theta)\\\\
&=&\\cos 2 \\theta \\cos \\theta-\\sin 2 \\theta \\sin \\theta\\\\
&=&(2 \\cos ^{2} \\theta-1) \\cos \\theta-2 \\sin \\theta \\cos \\theta \\cdot \\sin \\theta\\\\
&=&2 \\cos ^{3} \\theta-\\cos \\theta-2 \\sin ^{2} \\theta \\cos \\theta\\\\
&=&2 \\cos ^{3} \\theta-\\cos \\theta-2(1-\\cos ^{2} \\theta) \\cos \\theta\\\\
&=&4 \\cos ^{3} \\theta-3 \\cos \\theta
\\end{eqnarray}<\/p>\n\n\n\n\\(\\tan\\)\u306e\uff13\u500d\u89d2\u306e\u516c\u5f0f<\/h3>\n\n\n\n
\\tan 3 \\theta&=&\\tan (2 \\theta+\\theta)\\\\
\\displaystyle &=&\\frac{\\tan 2 \\theta+\\tan \\theta}{1-\\tan 2 \\theta \\tan \\theta}\\\\
\\displaystyle &=&\\frac{\\frac{2 \\tan \\theta}{1-\\tan ^{2} \\theta}+\\tan \\theta}{1-\\frac{2 \\tan \\theta \\cdot \\tan \\theta}{1-\\tan ^{2} \\theta}}
\\end{eqnarray}<\/p>\n\n\n\n3\u500d\u89d2\u306e\u516c\u5f0f\u306e\u4f7f\u3044\u65b9<\/h2>\n\n\n\n
\\sin 3 \\theta &=&3 \\sin \\theta-4 \\sin ^{3} \\theta\\\\
\\displaystyle &=&3 \\frac{1}{3}-4 \\left(\\frac{1}{3}\\right)^{3}\\\\
\\displaystyle &=&1-4 \\frac{1}{27}\\\\
\\displaystyle &=&\\frac{23}{27}
\\end{eqnarray}<\/p>\n\n\n\n
\u30b7\u30fc\u30bf<\/span><\/div>3\u500d\u89d2\u306e\u516c\u5f0f\u300a\u7df4\u7fd2\u554f\u984c\u300b<\/h2>\n\n\n\n
\\cos^{2} \\theta&=&1-\\sin^{2} \\theta\\\\
\\displaystyle &=&1-(\\frac{4}{5})^{2}\\\\
\\displaystyle &=&\\frac{9}{25}
\\end{eqnarray}<\/p>\n\n\n\n
\\displaystyle \\tan \\theta&=&\\frac{\\sin \\theta}{\\cos \\theta}\\\\
\\displaystyle &=&\\frac{\\frac{4}{5}}{\\frac{3}{5}}\\\\
\\displaystyle &=&\\frac{4}{3}
\\end{eqnarray}<\/p>\n\n\n\n
\\sin 3 \\theta &=&3 \\sin \\theta-4 \\sin ^{3} \\theta\\\\
\\displaystyle &=&3 \\cdot \\frac{4}{5}-4 \\left(\\frac{4}{5}\\right)^{3}\\\\
\\displaystyle &=&\\frac{12}{5}-\\frac{192}{125}\\\\
\\displaystyle &=&\\frac{108}{125}
\\end{eqnarray}<\/p>\n\n\n\n
\\cos 3 \\theta&=&4 \\cos ^{3} \\theta-3 \\cos \\theta\\\\
\\displaystyle &=&4 \\left(\\frac{3}{5}\\right)^{3}-3 \\cdot \\frac{3}{5}\\\\
\\displaystyle &=&\\frac{108}{125}-\\frac{9}{5}\\\\
\\displaystyle &=&-\\frac{107}{125}
\\end{eqnarray}<\/p>\n\n\n\n
\\displaystyle \\tan 3 \\theta &=&\\frac{\\sin 3 \\theta}{\\cos 3 \\theta}\\\\
\\displaystyle &=&\\frac{\\frac{108}{125}}{-\\frac{107}{125}}\\\\
\\displaystyle &=&-\\frac{108}{107}
\\end{eqnarray}<\/p>\n\n\n\n
\\displaystyle \\sin 3 \\theta&=&\\frac{108}{125}\\\\
\\displaystyle \\cos 3 \\theta&=&-\\frac{107}{125}\\\\
\\displaystyle \\tan 3 \\theta&=&-\\frac{108}{107}
\\end{eqnarray}<\/span><\/p>\n\n\n
\u9ad8\u6821\u751f<\/span><\/div>
\u30b7\u30fc\u30bf<\/span><\/div>\uff13\u500d\u89d2\u306e\u516c\u5f0f\u3000\u307e\u3068\u3081<\/h2>\n\n\n\n
\\sin 3 \\theta &=&3 \\sin \\theta-4 \\sin ^{3} \\theta\\\\
\\cos 3 \\theta&=&4 \\cos ^{3} \\theta-3 \\cos \\theta\\\\
\\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