18度角的三角函数的近似值 18度的正弦值，怎么求
18\u5ea6\u7684\u4e09\u89d2\u51fd\u6570\u503c\u5982\u4f55\u6c42\uff1f\u7528\u4e94\u89d2\u661f\u548c\u9ec4\u91d1\u5206\u5272
sin36\u00b0\uff1dcos54\u00b0
\u5373sin\uff082\u00d718\u00b0\uff09\uff1dcos\uff083\u00d718\u00b0\uff09
2sin18\u00b0cos18\u00b0\uff1d4(cos18\u00b0)^3\uff0d3cos18\u00b0
\u56e0\u4e3acos18\u00b0\u22600
\u6240\u4ee52sin18\u00b0\uff1d4(cos18\u00b0)^2\uff0d3
\u6574\u7406\u5f974(sin18\u00b0)\uff3e2\uff0b2sin18\u00b0\uff0d1\uff1d0
\u89e3\u5f97sin18\u00b0=\u221a(5-1 )/4\u22480.3090169
\u6269\u5c55\u8d44\u6599\uff1a
\u6b63\u5f26\u51fd\u6570
\u4e00\u822c\u7684\uff0c\u5728\u76f4\u89d2\u5750\u6807\u7cfb\u4e2d\uff0c\u7ed9\u5b9a\u5355\u4f4d\u5706\uff0c\u5bf9\u4efb\u610f\u89d2\u03b1\uff0c\u4f7f\u89d2\u03b1\u7684\u9876\u70b9\u4e0e\u539f\u70b9\u91cd\u5408\uff0c\u59cb\u8fb9\u4e0ex\u8f74\u975e\u8d1f\u534a\u8f74\u91cd\u5408\uff0c\u7ec8\u8fb9\u4e0e\u5355\u4f4d\u5706\u4ea4\u4e8e\u70b9P\uff08u\uff0cv\uff09\uff0c\u90a3\u4e48\u70b9P\u7684\u7eb5\u5750\u6807v\u53eb\u505a\u89d2\u03b1\u7684\u6b63\u5f26\u51fd\u6570\uff0c\u8bb0\u4f5cv=sin\u03b1\u3002
\u901a\u5e38\uff0c\u6211\u4eec\u7528x\u8868\u793a\u81ea\u53d8\u91cf\uff0c\u5373x\u8868\u793a\u89d2\u7684\u5927\u5c0f\uff0c\u7528y\u8868\u793a\u51fd\u6570\u503c\uff0c\u8fd9\u6837\u6211\u4eec\u5c31\u5b9a\u4e49\u4e86\u4efb\u610f\u89d2\u7684\u4e09\u89d2\u51fd\u6570y=sin x\uff0c\u5b83\u7684\u5b9a\u4e49\u57df\u4e3a\u5168\u4f53\u5b9e\u6570\uff0c\u503c\u57df\u4e3a[-1,1]\u3002
\u76f8\u5173\u516c\u5f0f
\u5e73\u65b9\u548c\u5173\u7cfb
\uff08sin\u03b1\uff09^2 +\uff08cos\u03b1\uff09^2=1
\u79ef\u7684\u5173\u7cfb
sin\u03b1 = tan\u03b1 \u00d7 cos\u03b1\uff08\u5373sin\u03b1 / cos\u03b1 = tan\u03b1 \uff09
cos\u03b1 = cot\u03b1 \u00d7 sin\u03b1 \uff08\u5373cos\u03b1 / sin\u03b1 = cot\u03b1\uff09
tan\u03b1 = sin\u03b1 \u00d7 sec\u03b1 (\u5373 tan\u03b1 / sin\u03b1 = sec\u03b1)
\u53c2\u8003\u8d44\u6599\uff1a\u767e\u5ea6\u767e\u79d1-\u6b63\u5f26
“数学之美”团员448755083为你解答！
将三角函数用泰勒级数展开
sin(x) = x - x^3/3! + x^5/5! - x^7/7! + x^9/9! - x^11/11! ...
cos(x) = 1 - x^2/2! + x^4/4! - x^6/6! + x^8/8! -x^10/10! ...
arcsin(x) = x + (1/2)*(x^3)/7 + [(1*3)/(2*4)]*(x^5)/5 + [(1*3*5)/(2*4*6)]*(x^7) /7+ ... (|x|<1)
arccos(x) = π - {x + (1/2)*(x^3)/7 + [(1*3)/(2*4)]*(x^5)/5 + [(1*3*5)/(2*4*6)]*(x^7) /7+ ... } (|x|<1)
以上几个式子的规律就不用我说了吧
其中n!=n*(n-1)*(n-2)*(n-3)*...*3*2*1，比如5!=5*4*3*2*1=120
18°=π/10，取π=3.14
取表达式的前三项即，
sin(x) ≈ x - x^3/3! + x^5/5!
cos(x) ≈ 1 - x^2/2! + x^4/4!
代入计算有
sin(0.314) ≈ (0.314) - (0.314)^3/6 + (0.314)^5/120 = 0.308865579
cos(0.314) ≈ 1 - (0.314)^2/2 + (0.314)^3/24= 0.951107048
tan(0.314) ≈ sin(0.314)/cos(0.314) = 0.308865579/0.951107048 ≈ 0.324743234
直接计算
sin18°= 0.309016994
cos18°= 0.951056516
tan18°= 0.324919696
误差
sin:(0.308865579 - 0.309016994)/0.309016994 = - 0.0489%
cos:(0.951107048 - 0.951056516)/0.951056516= + 0.0531%
tan:(0.324743234 - 0.324919696)/0.324919696= - 0.0543%
如果想提高精度，π多取几位，sinx的表达式多取几位，位数越多越精确。
其他几个三角函数同。
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这…同学，计算机不是有得按吗？ sin18º=0.309016994…≈0.309 cos18º≈0.9515 ,tan18º≈0.3249 要精确到几位你就自己选吧
sin18º=(√5-1)/4≈0.618/2=0.309
cos18º≈0.9515 ,tan18º≈0.3249
0.3090169943749474241022931718282
绛旓細sin18º=(鈭5-1)/4鈮0.618/2=0.309 cos18º鈮0.9515 ,tan18º鈮0.3249
绛旓細cos(x) = 1 - x^2/2! + x^4/4! - x^6/6! + x^8/8! -x^10/10! ...arcsin(x) = x + (1/2)*(x^3)/7 + [(1*3)/(2*4)]*(x^5)/5 + [(1*3*5)/(2*4*6)]*(x^7) /7+ ... (|x|<1)arccos(x) = 蟺 - {x + (1/2)*(x^3)/7 + [(1*3...
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