为什么sin（X–2派）=sinX。 求大神指导，真心不明白！！ 求sin(x+△x)-sinx的转换原理，多谢
\u5df2\u77e5\u51fd\u6570fx=1\u20132sin(x+\u03c0/8(sinx+\u03c0/8\u2013cos(x+\u03c0/8)))\u6c42\u51fd\u6570\u6700\u5c0f\u6b63\u54682\u03c0
\u89e3\uff1a
f(x+2\u03c0)
=1\u20132sin(x+2\u03c0+\u03c0/8(sin(x+2\u03c0)+\u03c0/8\u2013cos(x+2\u03c0+\u03c0/8)))
=1\u20132sin(x+\u03c0/8(sinx+\u03c0/8\u2013cos(x+\u03c0/8)))
=f(x)
\u2234 \u6700\u5c0f\u6b63\u5468\u671f\u662f2\u03c0
sin(x0+\u25b3x)-sinx0
=sinx0cos\u25b3x+sin\u25b3xcosx0-sinx0
=sinx0cos\u25b3x-sinx0 +sin\u25b3xcosx0
=sinx0(cos\u25b3x-1) +2sin(\u25b3x/2)cos(\u25b3x/2)cosx0
=sinx0{cos(\u25b3x/2)-sin(\u25b3x/2)-1}+2sin(\u25b3x/2)cos(\u25b3x/2)cosx0
=-sinx0*2sin(\u25b3x/2) +2sin(\u25b3x/2)cos(\u25b3x/2)cosx0
=2sin(\u25b3x/2){cos(\u25b3x/2)cosx0-sinx0sin(\u25b3x/2)}
=2sin(\u25b3x/2)cos(x0+\u25b3x/2)
\u4e09\u89d2\u51fd\u6570
90\u00b0\u7684\u5947\u6570\u500d+\u03b1\u7684\u4e09\u89d2\u51fd\u6570\uff0c\u5176\u7edd\u5bf9\u503c\u4e0e\u03b1\u4e09\u89d2\u51fd\u6570\u7684\u7edd\u5bf9\u503c\u4e92\u4e3a\u4f59\u51fd\u6570\u300290\u00b0\u7684\u5076\u6570\u500d+\u03b1\u7684\u4e09\u89d2\u51fd\u6570\u4e0e\u03b1\u7684\u4e09\u89d2\u51fd\u6570\u7edd\u5bf9\u503c\u76f8\u540c\u3002\u4e5f\u5c31\u662f\u201c\u5947\u4f59\u5076\u540c\uff0c\u5947\u53d8\u5076\u4e0d\u53d8\u201d\u3002
\u6bd4\u5982\uff1a90\u00b0+\u03b1\u3002\u5b9a\u540d\uff1a90\u00b0\u662f90\u00b0\u7684\u5947\u6570\u500d\uff0c\u6240\u4ee5\u5e94\u53d6\u4f59\u51fd\u6570\uff1b\u5b9a\u53f7\uff1a\u5c06\u03b1\u770b\u505a\u9510\u89d2\uff0c\u90a3\u4e4890\u00b0+\u03b1\u662f\u7b2c\u4e8c\u8c61\u9650\u89d2\uff0c\u7b2c\u4e8c\u8c61\u9650\u89d2\u7684\u6b63\u5f26\u4e3a\u6b63\uff0c\u4f59\u5f26\u4e3a\u8d1f\u3002\u6240\u4ee5sin\uff0890\u00b0+\u03b1\uff09=cos\u03b1 , cos\uff0890\u00b0+\u03b1\uff09=-sin\u03b1 \u8fd9\u4e2a\u975e\u5e38\u795e\u5947\uff0c\u5c61\u8bd5\u4e0d\u723d~
\u8fd8\u6709\u4e00\u4e2a\u53e3\u8bc0\u201c\u7eb5\u53d8\u6a2a\u4e0d\u53d8\uff0c\u7b26\u53f7\u770b\u8c61\u9650\u201d\uff0c\u4f8b\u5982\uff1asin\uff0890\u00b0+\u03b1\uff09\uff0c90\u00b0\u7684\u7ec8\u8fb9\u5728\u7eb5\u8f74\u4e0a\uff0c\u6240\u4ee5\u51fd\u6570\u540d\u53d8\u4e3a\u76f8\u53cd\u7684\u51fd\u6570\u540d\uff0c\u5373cos\uff0c\u6240\u4ee5sin\uff0890\u00b0+\u03b1\uff09=cos\u03b1\u3002
π就是一圈儿，2π就是两圈，转完两圈以后还在那，和没转一样。所以xin(x-2π)=sinx
因为sinx是一个周期为2派的三角函数，所以只要是2派的整数倍，都等于sinx
绛旓細X-2娲撅紝杩欎釜瑙掑氨鏄疿杩欎釜瑙掗『鏃堕拡杞袱鍛紝鍏剁粓杈逛笌X杩欎釜瑙掗噸鍚堬紝鎵浠ュ叾姝ｅ鸡鍊间笌X杩欎釜瑙掔殑姝ｅ鸡鍊肩浉绛夛紝鍗硈in锛圶鈥2娲撅級=sinX銆
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