求三个角以上的正、余弦和积互化公式
\u6b63\u4f59\u5f26\u548c\u5dee\u5316\u79ef\u516c\u5f0fsinx+siny=2sin((x+y)/2)*cos((x-y)/2)
sinx-siny=2cos((x+y)/2)*sin((x-y)/2)
cosx+cosy=2cos((x+y)/2)*cos((x-y)/2)
cosx-cosy=-2sin((x+y)/2)*sin((x-y)/2)
\u5bf9\u4e8e\u548c\u5dee\u5316\u79ef\u516c\u5f0f\u6765\u8bf4\uff0c\u82e5\u7b49\u53f7\u5de6\u8fb9\u5168\u662fsin\uff0c\u5219\u53f3\u8fb9\u5f02\u540d\uff0c\u82e5\u7b49\u53f7\u5de6\u8fb9\u5168\u662fcos\uff0c\u5219\u7b49\u53f7\u53f3\u8fb9\u540c\u540d\uff0c\u82e5\u7b49\u53f7\u5de6\u8fb9\u4e2d\u95f4\u7684\u6b63\u8d1f\u53f7\u51b3\u5b9a\u4e86\u53f3\u8fb9\u7b2c\u4e8c\u9879\uff0c\u82e5\u662f\u6b63\uff0c\u5219\u662fcos\uff0c\u82e5\u662f\u8d1f\uff0c\u5219\u662fsin\uff0c\u53ef\u4ee5\u6839\u636e\u7b2c\u4e00\u6761\u539f\u5219\u5199\u51fa\u5b8c\u6574\u7684\u53f3\u8fb9\u5f0f\u5b50\uff0c\u6700\u540e\u8bb0\u5f97cos-cos\u8981\u6dfb\u4e00\u4e2a\u8d1f\u53f7\u3002
\u6269\u5c55\u8d44\u6599\uff1a
\u4e09\u89d2\u51fd\u6570\u6982\u5ff5\u6ce8\u610f\u7684\u95ee\u9898\uff1a
1\u3001\u521d\u4e2d\u9636\u6bb5\u7684\u6240\u8bf4\u7684\u9510\u89d2\u4e09\u89d2\u51fd\u6570\u662f\u9510\u89d2\u7684\u6b63\u5f26\u3001\u4f59\u5f26\u3001\u6b63\u5207\u3001\u4f59\u5207\u56db\u79cd\u51fd\u6570\u7684\u7edf\u79f0\u3002
2\u3001\u9510\u89d2\u4e09\u89d2\u51fd\u6570\u8868\u793a\u7684\u662f\u4e24\u4e2a\u6b63\u6570\u7684\u6bd4\u503c\uff0c\u56e0\u800c\u9510\u89d2\u4e09\u89d2\u51fd\u6570\u6ca1\u6709\u5355\u4f4d\u3002
3\u3001\u7406\u6e05\u9510\u89d2\u4e09\u89d2\u51fd\u6570\u4e2d\u7684\u81ea\u53d8\u91cf\u4e0e\u56e0\u53d8\u91cf\uff0c\u5bf9\u4e8e\u56db\u79cd\u51fd\u6570\u6765\u8bf4\uff0c\u4ee5\u2220A\u4e3a\u4f8b\uff0c\u81ea\u53d8\u91cf\u90fd\u662f\u9510\u89d2A\uff0c\u56e0\u53d8\u91cf\u5c31\u662f\u9510\u89d2A\u7684\u56db\u79cd\u4e09\u89d2\u51fd\u6570\uff0c\u8fd9\u8bf4\u660e\u5f53\u9510\u89d2A\u7684\u5927\u5c0f\u4e0d\u53d8\u65f6\uff0c\u9510\u89d2A\u7684\u6b63\u5f26\u503c\u3001\u4f59\u5f26\u503c\u3001\u6b63\u5207\u503c\u3001\u4f59\u5207\u503c\u4e5f\u5c06\u4fdd\u6301\u4e0d\u53d8\u3002
4\u3001\u9510\u89d2\u4e09\u89d2\u51fd\u6570\u4e2d\u81ea\u53d8\u91cf\u7684\u53d6\u503c\u8303\u56f4\uff0c\u9510\u89d2\u4e09\u89d2\u51fd\u6570\u7684\u81ea\u53d8\u91cf\u662f\u9510\u89d2\uff0c\u6240\u4ee5\u81ea\u53d8\u91cf\u2220A\u7684\u8303\u56f4\u5c31\u662f0\u00b0\uff1c\u2220A\uff1c90\u00b0\u3002
\u53c2\u8003\u8d44\u6599\u6765\u6e90\uff1a\u767e\u5ea6\u767e\u79d1-\u4e09\u89d2\u51fd\u6570
\u53c2\u8003\u8d44\u6599\u6765\u6e90\uff1a\u767e\u5ea6\u767e\u79d1-\u548c\u5dee\u5316\u79ef
1.\u8bf1\u5bfc\u516c\u5f0f
sin(-a)=-sin(a)
cos(-a)=cos(a)
sin(\u03c02-a)=cos(a)
cos(\u03c02-a)=sin(a)
sin(\u03c02+a)=cos(a)
cos(\u03c02+a)=-sin(a)
sin(\u03c0-a)=sin(a)
cos(\u03c0-a)=-cos(a)
sin(\u03c0+a)=-sin(a)
cos(\u03c0+a)=-cos(a)
2.\u4e24\u89d2\u548c\u4e0e\u5dee\u7684\u4e09\u89d2\u51fd\u6570
sin(a+b)=sin(a)cos(b)+cos(\u03b1)sin(b)
cos(a+b)=cos(a)cos(b)-sin(a)sin(b)
sin(a-b)=sin(a)cos(b)-cos(a)sin(b)
cos(a-b)=cos(a)cos(b)+sin(a)sin(b)
tan(a+b)=tan(a)+tan(b)1-tan(a)tan(b)
tan(a-b)=tan(a)-tan(b)1+tan(a)tan(b)
3.\u548c\u5dee\u5316\u79ef\u516c\u5f0f
sin(a)+sin(b)=2sin(a+b2)cos(a-b2)
sin(a)?sin(b)=2cos(a+b2)sin(a-b2)
cos(a)+cos(b)=2cos(a+b2)cos(a-b2)
cos(a)-cos(b)=-2sin(a+b2)sin(a-b2)
4.\u79ef\u5316\u548c\u5dee\u516c\u5f0f (\u4e0a\u9762\u516c\u5f0f\u53cd\u8fc7\u6765\u5c31\u5f97\u5230\u4e86)
sin(a)sin(b)=-12?[cos(a+b)-cos(a-b)]
cos(a)cos(b)=12?[cos(a+b)+cos(a-b)]
sin(a)cos(b)=12?[sin(a+b)+sin(a-b)]
5.\u4e8c\u500d\u89d2\u516c\u5f0f
sin(2a)=2sin(a)cos(b)
cos(2a)=cos2(a)-sin2(a)=2cos2(a)-1=1-2sin2(a)
6.\u534a\u89d2\u516c\u5f0f
sin2(a2)=1-cos(a)2
cos2(a2)=1+cos(a)2
tan(a2)=1-cos(a)sin(a)=sina1+cos(a)
7.\u4e07\u80fd\u516c\u5f0f
sin(a)=2tan(a2)1+tan2(a2)
cos(a)=1-tan2(a2)1+tan2(a2)
tan(a)=2tan(a2)1-tan2(a2)
8.\u5176\u5b83\u516c\u5f0f(\u63a8\u5bfc\u51fa\u6765\u7684 )
a?sin(a)+b?cos(a)=a2+b2sin(a+c) \u5176\u4e2d tan(c)=ba
a?sin(a)+b?cos(a)=a2+b2cos(a-c) \u5176\u4e2d tan(c)=ab
1+sin(a)=(sin(a2)+cos(a2))2
1-sin(a)=(sin(a2)-cos(a2))2
=sinxcosycosz+cosxsinycosz+cosxcosysinz-sinxsinysinz
=cosxcosycosz(tanx+tany+tanz-tanxtanytanz)
cos(x+y+z)
=cosxcosycosz-cosxsinysinz-sinxcosysinz-sinxsinycosz
=cosxcosycosz(1-tanxtany-tanytanz-tanztanx)
tan(x+y+z)
=[tanx+tany+tanz-tanxtanytanz]/[1-tanxtany-tanytanz-tanztanx]
cot(x+y+z)
=[cotxcotycotz-cotx-coty-cotz]/[cotxcoty+cotycotz+cotzcotx-1]
已知sin(x+y+z)
=sinxcosycosz+cosxsinycosz+cosxcosysinz-sinxsinysinz
所以
sin(x+y-z)
=sinxcosycosz+cosxsinycosz-cosxcosysinz+sinxsinysinz
sin(x-y+z)
=sinxcosycosz-cosxsinycosz+cosxcosysinz+sinxsinysinz
sin(-x+y+z)
=-sinxcosycosz+cosxsinycosz+cosxcosysinz+sinxsinysinz
sin(x+y+z)
=sinxcosycosz+cosxsinycosz+cosxcosysinz-sinxsinysinz
所以4sinxsinysinz ＝sin(x+y-z) ＋sin(x-y+z) ＋sin(-x+y+z) －sin(x+y+z)
sin(x－y-z)
=sinxcosycosz－cosxsinycosz-cosxcosysinz－sinxsinysinz
sin(－x-y+z)
=－sinxcosycosz-cosxsinycosz+cosxcosysinz－sinxsinysinz
sin(-x+y+z)
=-sinxcosycosz+cosxsinycosz+cosxcosysinz+sinxsinysinz
sin(x+y+z)
=sinxcosycosz+cosxsinycosz+cosxcosysinz-sinxsinysinz
全相加
2cosxcosysinz－2sinxsinysinz ＝sin(x－y-z) ＋sin(－x-y+z) ＋sin(-x+y+z) ＋sin(x+y+z)
再利用4sinxsinysinz ＝sin(x+y-z) ＋sin(x-y+z) ＋sin(-x+y+z) －sin(x+y+z)
得到4cosxcosysinz＝ ＋sin(－x-y+z) ＋sin(-x+y+z) ＋sin(x+y-z) ＋sin(x-y+z)
其他自己仿照这2个，推理吧！
sinθ+sinφ=2sin(θ/2+θ/2)cos(θ/2-φ/2)
sinθ-sinφ=2cos(θ/2+φ/2)sin(θ/2-φ/2)
cosθ+cosφ=2cos(θ/2+φ/2)cos(θ/2-φ/2)
cosθ-cosφ=-2sin(θ/2+φ/2)sin(θ/2-φ/2)
sinαsinβ=-1/2[cos(α+β)-cos(α-β)]
cosαcosβ= 1/2[cos(α+β)+cos(α-β)]
sinαcosβ= 1/2[sin(α+β)+sin(α-β)]
cosαsinβ= 1/2[sin(α+β)-sin(α-β)]
据我所知没有，我用的都是2个角三角函数公式，涉及多个角的都是2个角的变化形式。
sinθ+sinφ=2sin(θ/2+θ/2)cos(θ/2-φ/2)
sinθ-sinφ=2cos(θ/2+φ/2)sin(θ/2-φ/2)
cosθ+cosφ=2cos(θ/2+φ/2)cos(θ/2-φ/2)
cosθ-cosφ=-2sin(θ/2+φ/2)sin(θ/2-φ/2)
sinαsinβ=-1/2[cos(α+β)-cos(α-β)]
cosαcosβ= 1/2[cos(α+β)+cos(α-β)]
sinαcosβ= 1/2[sin(α+β)+sin(α-β)]
cosαsinβ= 1/2[sin(α+β)-sin(α-β)]
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绛旓細2銆侀泦鍚堢殑涓厓绱犵殑涓変釜鐗规: 1.鍏冪礌鐨勭‘瀹氭; 2.鍏冪礌鐨勪簰寮傛; 3.鍏冪礌鐨勬棤搴忔 璇存槑:(1)瀵逛簬...瑙扐鐨勬寮﹀煎氨绛変簬瑙扐鐨勫杈规瘮鏂滆竟, 浣欏鸡绛変簬瑙扐鐨勯偦杈规瘮鏂滆竟 姝ｅ垏绛変簬瀵硅竟姣旈偦杈, 路[1]涓夎
