\n
\\begin{eqnarray}
\\cos 2\\theta&=&\\cos^{2} \\theta-\\sin^{2} \\theta\\\\
&=&1-2\\sin^{2} \\theta \\\\
&=&2 \\cos^{2} \\theta -1
\\end{eqnarray}<\/p>\n<\/div><\/div>\n\n\n\n
2\u500d\u89d2\u306e\u516c\u5f0f\u3088\u308a\u3001<\/p>\n\n\n\n
\\[\\cos 2\\theta=1-2\\sin^{2} \\theta\\]<\/p>\n\n\n\n
\u3053\u3053\u3067\\(\\theta\\)\u3092\\(\\displaystyle \\frac{\\theta}{2}\\)\u306b\u7f6e\u304d\u63db\u3048\u308b\u3068\u3001<\/p>\n\n\n\n
\\[\\displaystyle \\cos 2 \\cdot \\frac{\\theta}{2}=1-2\\sin^{2} \\frac{\\theta}{2}\\]<\/p>\n\n\n\n
\u3088\u3063\u3066\u3001<\/p>\n\n\n\n
\\[\\displaystyle \\cos \\theta=1\u22122 \\sin^{2} \\frac{\\theta}{2}\\]<\/p>\n\n\n\n
\u5f0f\u3092\u6574\u7406\u3059\u308b\u3053\u3068\u3067\u3001<\/p>\n\n\n\n
\\[\\displaystyle \\sin^{2} \\frac{\\theta}{2}=\\frac{1-\\cos \\theta}{2}\\]<\/p>\n\n\n\n
\u8a3c\u660e\u7d42\u4e86\u3002<\/p>\n\n\n\n
\\(\\cos\\)\u306e\u534a\u89d2\u306e\u516c\u5f0f\u3000\u8a3c\u660e<\/h3>\n\n\n\n
\u540c\u69d8\u306b2\u500d\u89d2\u306e\u516c\u5f0f\u3088\u308a<\/p>\n\n\n\n
\\[\\cos 2\\theta=2\\cos^{2} \\theta -1\\]<\/p>\n\n\n\n
\\(\\sin\\)\u3068\u540c\u69d8\u306b\\(\\theta\\)\u3092\\(\\displaystyle \\frac{\\theta}{2}\\)\u306b\u7f6e\u304d\u63db\u3048\u3066\u3001<\/p>\n\n\n\n
\\[\\displaystyle \\cos 2 \\cdot \\frac{\\theta}{2}=2\\cos^{2} \\frac{\\theta}{2}-1\\]<\/p>\n\n\n\n
\u3088\u3063\u3066\u3001<\/p>\n\n\n\n
\\[\\displaystyle \\cos \\theta=2 \\cos^{2} \\frac{\\theta}{2}-1\\]<\/p>\n\n\n\n
\u5f0f\u3092\u6574\u7406\u3059\u308b\u3053\u3068\u3067\u3001<\/p>\n\n\n\n
\\[\\displaystyle \\cos^{2} \\frac{\\theta}{2}=\\frac{1+\\cos \\theta}{2}\\]<\/p>\n\n\n\n
\u8a3c\u660e\u7d42\u4e86\u3002<\/p>\n\n\n\n
\\(\\tan\\)\u306e\u534a\u89d2\u306e\u516c\u5f0f\u3000\u8a3c\u660e<\/h3>\n\n\n\n
\\(\\tan\\)\u306e\u534a\u89d2\u306e\u516c\u5f0f\u306f<\/p>\n\n\n\n
\\[\\displaystyle \\tan \\theta=\\frac{\\sin \\theta}{\\cos \\theta}\\]<\/p>\n\n\n\n
\u3092\u7528\u3044\u308b\u3068\u7c21\u5358\u306b\u8a3c\u660e\u304c\u3067\u304d\u307e\u3059\u3002<\/p>\n\n\n\n
\\begin{eqnarray}
\\displaystyle \\tan^{2} \\frac{\\theta}{2}&=&\\frac{\\sin^{2} \\frac{\\theta}{2}}{\\cos^{2} \\frac{\\theta}{2}}\\\\
\\displaystyle &=&\\frac{\\frac{1-\\cos \\theta}{2}}{\\frac{1+\\cos \\theta}{2}}\\\\
\\displaystyle &=&\\frac{1-\\cos \\theta}{1+\\cos \\theta}
\\end{eqnarray}<\/p>\n\n\n\n
\u3053\u308c\u3067\u534a\u89d2\u306e\u516c\u5f0f\u3092\u8a3c\u660e\u3059\u308b\u3053\u3068\u304c\u3067\u304d\u307e\u3057\u305f\u3002<\/p>\n\n\n\n
\u30dd\u30a4\u30f3\u30c8\u306f\u52a0\u6cd5\u5b9a\u7406\u304b\u3089\u306e\u5f0f\u5909\u5f62<\/span>\u3067\u3059\u3002<\/p>\n\n\n![\"\"](\"https:\/\/math-travel.jp\/wp-content\/uploads\/2024\/05\/math-travel-hukidashi7-150x150.webp\")
\u9ad8\u6821\u751f<\/span><\/div>\n
\u52a0\u6cd5\u5b9a\u7406\u3092\u899a\u3048\u308b\u5fc5\u8981\u304c\u3042\u308b\u3093\u3067\u3059\u306d\uff01<\/p>\n<\/span><\/span><\/span><\/div><\/div><\/div><\/div>\n\n\n\u534a\u89d2\u306e\u516c\u5f0f\u306e\u5c0e\u304d\u65b9<\/h2>\n\n\n\n
\u300c\u534a\u89d2\u306e\u516c\u5f0f\u306f\u8907\u96d1\u306a\u306e\u3067\u3001\u3088\u304f\u5fd8\u308c\u3066\u3057\u307e\u3044\u307e\u3059…\u300d<\/span><\/p>\n\n\n\n\u305d\u3093\u306a\u3068\u304d\u306b\u79c1\u304c\u3084\u3063\u3066\u3044\u308b\u534a\u89d2\u306e\u516c\u5f0f\u306e\u5c0e\u304d\u65b9\u3092\u7d39\u4ecb\u3057\u307e\u3059\u3002<\/p>\n\n\n\n
\u534a\u89d2\u306e\u516c\u5f0f\u3092\u5c0e\u304f<\/span><\/div>\n
\n- \u52a0\u6cd5\u5b9a\u7406\u3092\u601d\u3044\u51fa\u3059<\/li>\n\n\n\n
- \u5f0f\u5909\u5f62\u3092\u3059\u308b<\/li>\n\n\n\n
- \u6570\u5b57\u3092\u4ee3\u5165\u3059\u308b<\/li>\n<\/ol>\n<\/div><\/div>\n\n\n\n
\u4ee5\u4e0b\u306e\u554f\u984c\u3092\u4f8b\u3068\u3057\u3066\u5c0e\u3044\u3066\u307f\u307e\u3057\u3087\u3046\u3002<\/p>\n\n\n\n
\u4f8b\u984c<\/span><\/div>\n
\u6b21\u306e\u5024\u3092\u6c42\u3081\u3066\u307f\u3088\u3046\u3002<\/p>\n\n\n\n
\\[\\displaystyle \\sin^{2} \\frac{\\pi}{8}\\]<\/p>\n<\/div><\/div>\n\n\n\n
\\(\\displaystyle \\frac{\\pi}{8}\\)\u306a\u306e\u3067\u534a\u89d2\u306e\u516c\u5f0f\u3092\u4f7f\u3044\u305f\u3044\u3067\u3059\u304c\u3001\u516c\u5f0f\u3092\u5fd8\u308c\u3066\u3057\u307e\u3063\u305f\u3068\u3057\u307e\u3057\u3087\u3046\u3002<\/p>\n\n\n\n
STEP1\u52a0\u6cd5\u5b9a\u7406\u3092\u601d\u3044\u51fa\u3059<\/p>\n\n\n\n
\u307e\u305a\\(\\cos\\)\u306e\u52a0\u6cd5\u5b9a\u7406\u3092\u66f8\u304d\u307e\u3059\u3002<\/p>\n\n\n\n
\\[\\cos 2\\theta=\\cos^{2}\\theta-\\sin^{2}\\theta\\]<\/p>\n\n\n\n
\u4eca\u56de\u306f\\(\\displaystyle \\sin \\frac{\\pi}{8}\\)\u3092\u6c42\u3081\u305f\u3044\u306e\u3067\u3001<\/p>\n\n\n\n
\\[\\cos 2\\theta=1-2\\sin^{2}\\theta \\cdots \u2460\\]<\/p>\n\n\n\n
\u3092\u5c0e\u304d\u307e\u3059\u3002<\/p>\n\n\n\n
STEP2\u5f0f\u5909\u5f62\u3092\u3059\u308b<\/p>\n\n\n\n
\u2460\u3092\u6574\u7406\u3059\u308b\u3068\u3001<\/p>\n\n\n\n
\\[2\\sin^{2}\\theta=1-\\cos 2\\theta\\]<\/p>\n\n\n\n
\u5f0f\u5909\u5f62\u3057\u3066\u3001<\/p>\n\n\n\n
\\[\\displaystyle \\sin^{2} \\theta=\\frac{1-\\cos 2 \\theta}{2} \\cdots \u2461\\]<\/p>\n\n\n\n
STEP3\u6570\u5b57\u3092\u4ee3\u5165\u3059\u308b<\/p>\n\n\n\n
\u2461\u306e\\(\\theta\\)\u306b\\(\\displaystyle \\frac{\\pi}{8}\\)\u3092\u4ee3\u5165\u3057\u307e\u3059\u3002<\/p>\n\n\n\n
\\begin{eqnarray}
\\displaystyle \\sin^{2} \\frac{\\pi}{8}&=&\\frac{1-\\cos \\frac{\\pi}{4}}{2}\\\\
\\displaystyle &=&\\frac{1-\\frac{\\sqrt{2}}{2}}{2}\\\\
\\end{eqnarray}<\/p>\n\n\n\n
\u3057\u305f\u304c\u3063\u3066\u3001<\/p>\n\n\n\n
\\[\\displaystyle \\sin^{2} \\frac{\\pi}{8}=\\frac{2-\\sqrt{2}}{4}\\]<\/p>\n\n\n\n
\u3053\u306e\u624b\u9806\u306a\u3089\u534a\u89d2\u306e\u516c\u5f0f\u3092\u5fd8\u308c\u3066\u3082\u3001\u516c\u5f0f\u3092\u4f5c\u308b\u3053\u3068\u304c\u3067\u304d\u307e\u3059\u3002<\/p>\n\n\n
![\"\"](\"https:\/\/math-travel.jp\/wp-content\/uploads\/2024\/05\/math-travel-hukidashi1-150x150.webp\")
\u30b7\u30fc\u30bf<\/span><\/div>\n
\u516c\u5f0f\u3092\u899a\u3048\u3089\u308c\u308b\u306a\u3089\u899a\u3048\u305f\u65b9\u304c\u826f\u3044\u3088\uff01<\/p>\n<\/span><\/span><\/span><\/div><\/div><\/div><\/div>\n\n\n\u534a\u89d2\u306e\u516c\u5f0f\uff1c\u7df4\u7fd2\u554f\u984c\uff1e<\/h2>\n\n\n\n
\u534a\u89d2\u306e\u516c\u5f0f\u3092\u4f7f\u3063\u3066\u7df4\u7fd2\u554f\u984c\u306b\u30c1\u30e3\u30ec\u30f3\u30b8\u3057\u3066\u307f\u307e\u3057\u3087\u3046\u3002<\/p>\n\n\n\n
\u7df4\u7fd2\u554f\u984c<\/span><\/div>\n
\\(\\displaystyle \\frac{\\pi}{2}<\\theta<\\pi\\)\u3067\\(\\displaystyle \\sin \\theta=\\frac{3}{5}\\)\u306e\u3068\u304d\u3001\\(\\displaystyle \\sin \\frac{\\theta}{2}\\)\u306e\u503c\u3092\u6c42\u3081\u3088\u3002<\/p>\n<\/div><\/div>\n\n\n\n
\u534a\u89d2\u306e\u516c\u5f0f\u3092\u4f7f\u3046\u305f\u3081\u306b\u3001\\(\\cos \\theta \\)\u304b\u3089\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}
\\cos^{2} \\theta&=&1-\\sin^{2} \\theta\\\\
\\displaystyle &=&1-(\\frac{3}{5})^{2}\\\\
\\displaystyle &=&\\frac{16}{25}
\\end{eqnarray}<\/p>\n\n\n\n
\\(\\displaystyle \\frac{\\pi}{2} < \\theta < \\pi \\)\u306e\u3068\u304d\u3001\\(cos \\theta < 0 \\)\u306a\u306e\u3067\u3001<\/p>\n\n\n\n
\\[\\displaystyle cos \\theta =-\\frac{4}{5}\\]<\/p>\n\n\n\n
\u3088\u3063\u3066\u3001sin \u306e\u534a\u89d2\u306e\u516c\u5f0f\u3092\u7528\u3044\u308b\u3068<\/p>\n\n\n\n
\\begin{eqnarray}
\\displaystyle \\sin ^{2} \\frac{\\theta}{2} &=& \\frac{1-\\cos \\theta}{2}\\\\
\\displaystyle &=&\\frac{1-(-\\frac{4}{5})}{2}\\\\
\\displaystyle &=&\\frac{\\frac{9}{5}}{2}\\\\
\\displaystyle &=&\\frac{9}{10}
\\end{eqnarray}<\/p>\n\n\n\n
\\(\\displaystyle \\frac{\\pi}{2}<\\theta<{\\pi}\\)\u3088\u308a\u3001\\(\\displaystyle \\frac{\\pi}{4}<\\frac{\\theta}{2}<\\frac{\\pi}{2}\\)\u3067\u3042\u308b\u304b\u3089\u3001<\/p>\n\n\n\n
\u3086\u3048\u306b\u3001\\(\\displaystyle \\sin \\frac{\\theta}{2}>0\\)\u3067\u3042\u308b\u3002<\/p>\n\n\n\n
\u3057\u305f\u304c\u3063\u3066\u3001<\/p>\n\n\n\n
\\[\\displaystyle \\sin \\frac{\\theta}{2}=\\frac{3\\sqrt{10}}{10}\\]<\/p>\n\n\n\n
\u3068\u306a\u308a\u307e\u3059\u3002<\/p>\n\n\n
\u9ad8\u6821\u751f<\/span><\/div>\n
\u306a\u3093\u3068\u304b\u89e3\u304f\u3053\u3068\u304c\u3067\u304d\u307e\u3057\u305f\uff01\uff01<\/p>\n<\/span><\/span><\/span><\/div><\/div><\/div><\/div>\n\n\n\u534a\u89d2\u306e\u516c\u5f0f\u306e\u8a3c\u660e\u3000\u307e\u3068\u3081<\/h2>\n\n\n\n
\u4eca\u56de\u306f\u534a\u89d2\u306e\u516c\u5f0f\u306e\u8a3c\u660e\u306b\u3064\u3044\u3066\u307e\u3068\u3081\u307e\u3057\u305f\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
\u8a3c\u660e\u306e\u30dd\u30a4\u30f3\u30c8<\/span><\/div>\n
2\u500d\u89d2\u306e\u516c\u5f0f\u3092\u6d3b\u7528\u3057\u3066\u8a3c\u660e\u3059\u308b\u3002<\/p>\n\n\n\n
\\begin{eqnarray}
\\cos 2\\theta&=&\\cos^{2}-\\sin^{2}\\\\
&=&1-2\\sin^{2}\\\\
&=&2\\cos^{2}-1
\\end{eqnarray}<\/p>\n<\/div><\/div>\n\n\n\n
\u534a\u89d2\u306e\u516c\u5f0f\u3092\u5fd8\u308c\u305f\u3068\u304d\u306f\u4ee5\u4e0b\u306e\u624b\u9806\u3067\u5c0e\u304d\u307e\u3057\u3087\u3046\u3002<\/p>\n\n\n\n
\u534a\u89d2\u306e\u516c\u5f0f\u3092\u5c0e\u304f<\/span><\/div>\n
\n- \u52a0\u6cd5\u5b9a\u7406\u3092\u601d\u3044\u51fa\u3059<\/li>\n\n\n\n
- \u5f0f\u5909\u5f62\u3092\u3059\u308b<\/li>\n\n\n\n
- \u6570\u5b57\u3092\u4ee3\u5165\u3059\u308b<\/li>\n<\/ol>\n<\/div><\/div>\n\n\n\n
\u4eca\u56de\u306f\u534a\u89d2\u306e\u516c\u5f0f\u306e\u8a3c\u660e\u3092\u4e2d\u5fc3\u306b\u89e3\u8aac\u3057\u3066\u304d\u307e\u3057\u305f\u3002<\/p>\n","protected":false},"excerpt":{"rendered":"
\u300c\u306a\u3093\u3067\u534a\u89d2\u306e\u516c\u5f0f\u306f\u6210\u308a\u7acb\u3064\u306e\uff1f\u300d\u300c\u3059\u3050\u5fd8\u308c\u308b\u306e\u3067\u5c0e\u304d\u65b9\u3092\u77e5\u308a\u305f\u3044\u300d\u4eca\u56de\u306f\u534a\u89d2\u306e\u516c\u5f0f\u306b\u95a2\u3059\u308b\u3053\u3093\u306a\u60a9\u307f\u3092\u89e3\u6c7a\u3057\u307e\u3059\u3002 \u534a\u89d2\u306e\u516c\u5f0f\u306f\u4e09\u89d2\u95a2\u6570\u306e\u91cd\u8981\u306a\u516c\u5f0f\u306e1\u3064\u3067\u3059\u3002 \u534a\u89d2\u306e\u516c\u5f0f\u306f\u3001\\(\\displaystyle \\sin^ […]<\/p>\n","protected":false},"author":1,"featured_media":6751,"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-2201","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
\u534a\u89d2\u306e\u516c\u5f0f\u306e\u8a3c\u660e\u30fb\u5c0e\u304d\u65b9\u3092\u5fb9\u5e95\u89e3\u8aac\uff01\u4ed5\u7d44\u307f\u3092\u7406\u89e3\u3057\u3066\u516c\u5f0f\u5fd8\u308c\u3092\u30bc\u30ed\u306b<\/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\/hankaku\/\" \/>\n<meta property=\"og:locale\" content=\"ja_JP\" \/>\n<meta property=\"og:type\" content=\"article\" \/>\n<meta property=\"og:title\" content=\"\u534a\u89d2\u306e\u516c\u5f0f\u306e\u8a3c\u660e\u30fb\u5c0e\u304d\u65b9\u3092\u5fb9\u5e95\u89e3\u8aac\uff01\u4ed5\u7d44\u307f\u3092\u7406\u89e3\u3057\u3066\u516c\u5f0f\u5fd8\u308c\u3092\u30bc\u30ed\u306b\" \/>\n<meta property=\"og:description\" content=\"\u300c\u306a\u3093\u3067\u534a\u89d2\u306e\u516c\u5f0f\u306f\u6210\u308a\u7acb\u3064\u306e\uff1f\u300d\u300c\u3059\u3050\u5fd8\u308c\u308b\u306e\u3067\u5c0e\u304d\u65b9\u3092\u77e5\u308a\u305f\u3044\u300d\u4eca\u56de\u306f\u534a\u89d2\u306e\u516c\u5f0f\u306b\u95a2\u3059\u308b\u3053\u3093\u306a\u60a9\u307f\u3092\u89e3\u6c7a\u3057\u307e\u3059\u3002 \u534a\u89d2\u306e\u516c\u5f0f\u306f\u4e09\u89d2\u95a2\u6570\u306e\u91cd\u8981\u306a\u516c\u5f0f\u306e1\u3064\u3067\u3059\u3002 \u534a\u89d2\u306e\u516c\u5f0f\u306f\u3001(displaystyle sin^ […]\" \/>\n<meta property=\"og:url\" content=\"https:\/\/math-travel.jp\/math-2\/hankaku\/\" \/>\n<meta property=\"og:site_name\" content=\"\u30de\u30b9\u30c8\u30e9\u9ad8\u6821\u6570\u5b66\u307e\u3068\u3081\u30b5\u30a4\u30c8\" \/>\n<meta property=\"article:published_time\" content=\"2025-12-24T08:19:15+00:00\" \/>\n<meta property=\"article:modified_time\" content=\"2026-02-11T07:39:15+00:00\" \/>\n<meta property=\"og:image\" 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