sin2x等于多少? sin2x等于什么呢？
sin2x\u7b49\u4e8e\u591a\u5c11\uff1fsin2x=2sinxcosx\u3002\u5982\u679cX\u662f\u4e00\u4e2a\u89d2\u5ea6\u7684\u8bdd,\u90a3\u4e48\u5b83\u7684\u539f\u516c\u5f0f\u662f\uff1asin\uff08X+Y\uff09=sinXcosY+cosXsinY\u3002
\u8fd9\u5176\u5b9e\u662f\u7531\u4e24\u89d2\u548c\u7684\u6b63\u5f26\u516c\u5f0f\uff0c\u7531sin\uff08x+y\uff09=sinxcosy+cosxsiny\u5f97\u5230\u3002
\u6b64\u5916,\u8fd8\u6709\u51e0\u4e2a\u4e09\u89d2\u6052\u7b49\u5f0f\uff1a
cos\uff08x-y\uff09=cosxcosy+sinxsiny
sin\uff08x-y\uff09=sinxcosy-cosxsiny
\u60f3\u63a8\u5bfc\u51fa\u5404\u79cd\u4e8c\u500d\u89d2\u516c\u5f0f\uff0c\u53ea\u9700\u5c06\u548c\u89d2\u516c\u5f0f\u4e2d\u7684y\u66ff\u6362\u4e3ax\u5373\u53ef\u3002
\u6ce8\u610f\uff1a\u4e24\u89d2\u548c\u5dee\u7684\u6b63\u5207\u516c\u5f0f\u5fc5\u987b\u5728\u7b49\u5f0f\u4e24\u8fb9\u90fd\u6709\u610f\u4e49\u65f6\u65b9\u53ef\u6210\u7acb\u3002
\u4e09\u89d2\u51fd\u6570\u4e2d\u548c\u5dee\u5316\u79ef\u516c\u5f0f
1\u3001sin\u03b8+sin\u03c6=2sin[(\u03b8+\u03c6)/2]cos[(\u03b8-\u03c6)/2]
2\u3001sin\u03b8-sin\u03c6=2cos[(\u03b8+\u03c6)/2]sin[(\u03b8-\u03c6)/2]
3\u3001cos\u03b8+cos\u03c6=2cos[(\u03b8+\u03c6)/2]cos[(\u03b8-\u03c6)/2]
4\u3001cos\u03b8-cos\u03c6=-2sin[(\u03b8+\u03c6)/2]sin[(\u03b8-\u03c6)/2]
5\u3001tanA+tanB=sin(A+B)/cosAcosB=tan(A+B)(1-tanAtanB)
6\u3001tanA-tanB=sin(A-B)/cosAcosB=tan(A-B)(1+tanAtanB)
sin2x\u7b49\u4e8e2sinxcosx\u3002\u8fd9\u5176\u5b9e\u662f\u7531\u4e24\u89d2\u548c\u7684\u6b63\u5f26\u516c\u5f0fsin(x+y)=sinxcosy+cosxsiny\u5f97\u5230\u3002\u6b64\u5916\uff0c\u8fd8\u6709\u51e0\u4e2a\u4e09\u89d2\u6052\u7b49\u5f0fcos(x+y)=cosxcosy-sinxsinycos(x-y)=cosxcosy+sinxsinysin(x-y)=sinxcosy-cosxsinytan(x+y)=(tanx+tany)/(1-tanxtany)tan(x-y)=(tanx-tany)/(1+tanxtany)\u60f3\u63a8\u5bfc\u51fa\u5404\u79cd\u4e8c\u500d\u89d2\u516c\u5f0f\uff0c\u53ea\u9700\u5c06\u548c\u89d2\u516c\u5f0f\u4e2d\u7684y\u66ff\u6362\u4e3ax\u5373\u53ef\u3002
sin2x\u7684\u53d6\u503c\u8303\u56f4
\u51fd\u6570y=sin2x\u662f\u6b63\u5f26\u51fd\u6570\uff0c\u5b83\u7684\u81ea\u53d8\u91cf\u7684\u53d6\u503c\u8303\u56f4\u662f\u5168\u4f53\u5b9e\u6570\uff0c\u5b83\u7684\u503c\u57df\u662f-1\u52301\uff0c\u5b83\u7684\u5bfc\u51fd\u6570\u5e94\u533a\u5206\u5916\u5c42\u4e0e\u5185\u5c42\u51fd\u6570\u5206\u522b\u6c42\u5bfc\u5c14\u540e\u6c42\u79ef\u3002\u90a3\u4e48\u6211\u4eec\u77e5\u9053\uff0c\u5b83\u7684\u5916\u5c42\u51fd\u6570\u7684\u5bfc\u6570\u662fcos2x\uff0c\u5b83\u7684\u5185\u5c42\u51fd\u6570\u662f2x\uff0c\u5b83\u7684\u5bfc\u6570\u662f2\uff0c\u90a3\u4e48\u539f\u51fd\u6570\u7684\u5bfc\u6570\u5c31\u662f\u7b49\u4e8e2cos2x\u3002
sin2x=2sinxcosx。
分析过程如下：
sin(α+β)=sinαcosβ+ sinβcosα
sin(α-β)=sinαcosβ-sinB*cosα
根据sin(α+β)=sinαcosβ+ sinβcosα可得：
sin2x=sin（x+x）=sinxcosx+sinxcosx=2sinxcosx
扩展资料：
二倍角公式
tan2α=2tanα/(1-tan^2(α))
cos2α=cos^2(α)-sin^2(α)=2cos^2(α)-1=1-2sin^2(α)
半角公式
sin^2(α/2)=(1-cosα)/2
cos^2(α/2)=(1+cosα)/2
tan^2(α/2)=(1-cosα)/(1+cosα)
tan(α/2)=sinα/(1+cosα)=(1-cosα)/sinα
sin2x=2sinxcosx
这个是倍角公式。
sin2x
=2sinxcosx
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