\\(\\sin(180\u00b0-\\theta)=\\sin\\theta\\)<\/div>\n<\/div>\n<\/div>\n
\u3053\u308c\u3089\u3092\u4f7f\u3044, \u5b9f\u969b\u306b\u8a08\u7b97\u3057\u3066\u307f\u307e\u3059\u3002<\/p>\n
\\(\\theta=36\u00b0\\)\u3068\u304a\u304f\u3068, \\(5\\theta=180\u00b0\\)\u3068\u306a\u308a\u307e\u3059\u3002<\/p>\n
\u3053\u3053\u3067, $108^\\circ =180^\\circ -72^\\circ$\u3067\u3059\u304b\u3089<\/p>\n
\\(3\\theta=180\u00b0-2\\theta\\)<\/p>\n
\u3068\u306a\u308a\u307e\u3059\u3002\u3088\u3063\u3066,<\/p>\n
\\(\\sin3\\theta=\\sin(180\u00b0-2\\theta)=\\sin2\\theta\\)<\/p>\n
\u304c\u6210\u308a\u7acb\u3061\u307e\u3059\u3002<\/p>\n
$2$\u500d\u89d2, $3$\u500d\u89d2\u306e\u516c\u5f0f\u304b\u3089<\/p>\n
\\(3\\sin\\theta-4\\sin^3\\theta=2\\sin\\theta\\cos\\theta\\)<\/p>\n
\\(\\sin\\theta=\\sin36\u00b0\\neq0\\)\u3067\u3059\u304b\u3089, \u4e21\u8fba\\(\\sin\\theta\\)\u3067\u5272\u308b\u3068<\/p>\n
\\(3-4\\sin^2\\theta=2\\cos\\theta\\)<\/p>\n
\\(\\sin^2\\theta=1-\\cos^2\\theta\\)\u306a\u306e\u3067<\/p>\n
\\(3-4(1-\\cos^2\\theta)=2\\cos\\theta\\)<\/p>\n
\\(4\\cos^2\\theta-2\\cos\\theta-1=0\\)<\/p>\n
\\(\\cos\\theta=\\cfrac{1\\pm\\sqrt{5}}{4}\\)<\/p>\n
\\(\\cos\\theta=\\cos36\u00b0>0\\)\u3067\u3059\u304b\u3089<\/p>\n
\\(\\cos\\theta=\\cfrac{1+\\sqrt{5}}{4}\\)<\/p>\n
\u3068\u6c42\u3081\u3089\u308c\u307e\u3059\u3002<\/p>\n\n
\u6570\u5b66\u2162C\u300c\u8907\u7d20\u6570\u5e73\u9762\u300d\u306e\u77e5\u8b58\u3092\u4f7f\u3063\u3066\u6c42\u3081\u308b\u65b9\u6cd5<\/h2>\n
![\"\u6570\u5b66\u306e\u5206\u539a\u3044\u554f\u984c\u96c6\u306f\u300c\u554f\u984c\u8f9e\u66f8\u300d\u3068\u3057\u3066\u5229\u7528\u3057\u3088\u3046\"]()
<\/p>\n
\u6700\u5f8c\u306f\u6570\u5b66\u2162C\u300c\u8907\u7d20\u6570\u5e73\u9762\u300d\u306e\u77e5\u8b58\u3067\\(\\cos36\\)\u00b0\u306e\u5024\u3092\u6c42\u3081\u3066\u307f\u307e\u3059\u3002<\/p>\n
\u30c9\u30fb\u30e2\u30a2\u30d6\u30eb\u306e\u5b9a\u7406\u3092\u7528\u3044\u308b<\/h3>\n
\u3053\u3053\u3067\u306f\u30c9\u30fb\u30e2\u30a2\u30d6\u30eb\u306e\u5b9a\u7406\u3092\u4f7f\u3044\u307e\u3059\u3002<\/p>\n
\n
fa-lightbulb-o<\/span><\/i><\/span>\u30c9\u30fb\u30e2\u30a2\u30d6\u30eb\u306e\u5b9a\u7406<\/div>\n\u6574\u6570\\(n\\)\u306b\u5bfe\u3057\u3066
\n$(\\cos\\theta+i\\sin\\theta)^n=\\cos n\\theta+i\\sin n\\theta$
\n\u304c\u6210\u308a\u7acb\u3064\u3002<\/div>\n<\/div>\n
\u3055\u3089\u306b, \u7b49\u6bd4\u6570\u5217\u306e\u548c\u306e\u516c\u5f0f\u304b\u3089\\(z\\neq1\\)\u306e\u3068\u304d<\/p>\n
\\(1-z+z^2-z^3+z^4=\\frac{1-z^5}{1-z}\\)<\/p>\n
\u3068\u306a\u308b\u304b\u3089,<\/p>\n
\\(1-z^5=(1-z)(1-z+z^2-z^3+z^4)\\)<\/p>\n
\u3088\u3063\u3066,<\/p>\n
\\(z^5-1=(z-1)(z^4-z^3+z^2-z+1)\\)<\/p>\n
\u3068\u56e0\u6570\u5206\u89e3\u3067\u304d\u308b\u3053\u3068\u304c\u5206\u304b\u308a\u307e\u3059\u3002\u7d50\u679c\u306f\u3088\u304f\u4f7f\u3046\u306e\u3067\u899a\u3048\u3066\u3082\u3088\u3044\u3067\u3057\u3087\u3046\u3002<\/p>\n\n
4\u6b21\u306e\u76f8\u53cd\u65b9\u7a0b\u5f0f<\/h3>\n
\u307e\u305f, $\\color{red}{a}$$x^4$$+\\color{blue}{b}$$x^3 +cx^2 +$$\\color{blue}{b}$$x+\\color{red}{a}$$=0$\u306e\u3088\u3046\u306a\u65b9\u7a0b\u5f0f\u3092$4$\u6b21\u306e\u76f8\u53cd\u65b9\u7a0b\u5f0f\u3068\u547c\u3073\u307e\u3059\u3002<\/p>\n
\n
\n
4\u6b21\u306e\u76f8\u53cd\u65b9\u7a0b\u5f0f\u306f, \\(x\\neq0\\)\u3092\u89e3\u306b\u3082\u305f\u306a\u3044\u3068\u304d,\\(x^2\\)\u3067\u5272\u308a,
\n\\(x+\\frac{1}{x}=t\\)\u3068\u304a\u304f\u3068\u89e3\u3051\u307e\u3059\u3002<\/div>\n<\/div>\n<\/div>\n
\u3055\u3066, \u5b9f\u969b\u306b\u8a08\u7b97\u3057\u3066\u307f\u307e\u3057\u3087\u3046\u3002<\/p>\n
\\(z=\\cos36\u00b0+i\\sin36\u00b0\\)\u3068\u304a\u304f\u3068,<\/p>\n
\\(z^5=\\cos36\u00b0\\times5+i\\sin36\u00b0\\times5=\\cos360\u00b0+i\\sin360\u00b0=1\\)<\/p>\n
\u3088\u3063\u3066,<\/p>\n
\\(z^5-1=0\\)<\/p>\n
\\((z-1)(z^4-z^3+z^2-z+1)=0\\)<\/p>\n
\\(z\\neq1\\)\u3067\u3042\u308b\u304b\u3089<\/p>\n
\\(z^4-z^3+z^2-z+1=0\\)<\/p>\n
\\(z=\\cos36\u00b0+i\\sin36\u00b0\\)\u3067\u3042\u308b\u304b\u3089\u4e21\u8fba\\(z^2\\)\u3067\u5272\u308b\u3068<\/p>\n
\\(z^2-z+1-\\frac{1}{z}+\\frac{1}{z^2}=0\\)<\/p>\n
\\(z^2+\\frac{1}{z^2}-\\left(z+\\frac{1}{z}\\right)+1=0\\)<\/p>\n
\\(t=z+\\frac{1}{z}\\)\u3068\u304a\u304f\u3068\\(z^2+\\frac{1}{z^2}=t^2-2\\)\u3068\u306a\u308b\u304b\u3089<\/p>\n
\\(t^2-2-t+1=0\\)<\/p>\n
\\(t^2-t-1=0\\)<\/p>\n
\\(t=\\frac{1\\pm\\sqrt{5}}{2}\\)<\/p>\n
\u3053\u3053\u3067,<\/p>\n
\\(t=z+\\frac{1}{z}=z+z^{-1}=\\cos36\u00b0+i\\sin36\u00b0+\\cos(-36\u00b0)+i\\sin(-36\u00b0)=2\\cos36\u00b0\\)<\/span><\/p>\n\u3068\u306a\u308b\u304b\u3089, \\(t>0\\)\u306a\u306e\u3067<\/p>\n
\\(t=\\frac{1+\\sqrt{5}}{2}\\)<\/p>\n
\u3088\u3063\u3066, \\(2\\cos36\u00b0=\\frac{1+\\sqrt{5}}{2}\\)\u304b\u3089\\(\\cos36\u00b0=\\frac{1+\\sqrt{5}}{4}\\)\u3068\u6c42\u3081\u3089\u308c\u307e\u3059\u3002<\/p>\n\n
\u304a\u308f\u308a\u306b<\/h2>\n
![\"\"]()
\n\u4eca\u56de\u306f\u3044\u308d\u3044\u308d\u306a\u89e3\u6cd5\u3067\\(\\cos36\u00b0\\)\u306e\u5024\u3092\u6c42\u3081\u3066\u307f\u307e\u3057\u305f\u3002
\n\u3069\u306e\u89e3\u6cd5\u3082\u983b\u51fa\u30c6\u30fc\u30de\u3067\u3068\u3066\u3082\u5927\u4e8b\u306a\u30dd\u30a4\u30f3\u30c8\u304c\u542b\u307e\u308c\u3066\u3044\u307e\u3059\u3002\u5c0e\u51fa\u904e\u7a0b\u3092\u7406\u89e3\u3057, \u5b9f\u969b\u306b\u624b\u3092\u52d5\u304b\u3057\u3066\u6c42\u3081\u3066\u307f\u3066\u304f\u3060\u3055\u3044\u3002<\/p>\n
\u307e\u305f, \u540c\u69d8\u306e\u65b9\u6cd5\u3067\\(\\cos72\u00b0\\)\u3084\\(\\sin18\u00b0\\)\u306e\u5024\u3092\u8a08\u7b97\u3067\u304d\u307e\u3059\u3002\u3053\u3061\u3089\u3082\u662f\u975e\u6311\u6226\u3057\u3066\u307f\u3066\u304f\u3060\u3055\u3044\u3002<\/p>\n
\u305d\u308c\u3067\u306f,\u4eca\u56de\u306f\u3053\u306e\u8fba\u3067\uff01
\n
![\"\"](\"https:\/\/www.educational-lounge.com\/wp-content\/uploads\/2020\/06\/pexels-photo-3781338-300x199.jpeg\")
![\"\"](\"https:\/\/www.educational-lounge.com\/wp-content\/uploads\/2024\/06\/pentagon1.png\")
<\/a><\/p>\n