已知sin(六分之π+a)=五分之三,三分之π

Question

已知sin(六分之π+a)=五分之三,三分之π

数学

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Answer 1

三分之π∴ π/2∴ cos(a+π/6)<0
∵ cos²(a+π/6)=1-sin²(a+π/6)=1-(3/5)²=16/25
∴ cos(a+π/6)=-4/5
∴ cosa
= cos[(a+π/6)-π/6)]
= cos(a+π/6)cos(π/6)+sin(a+π/6)sin(π/6)
= (-4/5)*(√3/2)+(3/5)*(1/2)
= (-4√3+3)/10