COS(A-30度)+SINA=4/5 乘根号3 求SIN(A+210度)?

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COS(A-30度)+SINA=4/5 乘根号3 求SIN(A+210度)?
COS(A-30度)+SINA=4/5 乘根号3 求SIN(A+210度)?

COS(A-30度)+SINA=4/5 乘根号3 求SIN(A+210度)?
根号3用[3]代替
COS(A-30)+SINA=COSA*[3]/2+SINA*1/2+SINA=4*[3]/5
两边同时约去[3]
COSA*1/2+SINA*[3]/2=4/5
COS(A-60)=4/5
COS(A-60+180)=-4/5
COS(A+120)=-4/5
COS(A+120)=SIN(A+120+90)=-4/5
SIN(A+210)=-4/5

用和差化积公式
cos(A-30)+sinA=sin(A+60)+sinA=2sin(A+30)cos(30)=根号3sin(A+30)=4/5乘根号3
所以sin(A+30)=4/5
所以sin(A+210)=-sin(A+30)=-4/5

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