
已知cosa=1/2,0<a<派/2,求sin(a+派/3)的值
2个回答
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法一:cosa=1/2,0<a<π/2,a=π/3
sin(a+π/3)=sin(π/3+π/3)=sin(2π/3)=sin(π-π/3)=sin(π/3)=根号3/2
法二:cosa=1/2,
0<a<π/2,sina=根号下(1-cosa的平方)=根号3/2,
sin(a+π/3)
=sina*cos(π/3)+cosa*sin(π/3)
=(根号3/2)*(1/2)+(1/2)*(根号3/2)
=根号3/2
sin(a+π/3)=sin(π/3+π/3)=sin(2π/3)=sin(π-π/3)=sin(π/3)=根号3/2
法二:cosa=1/2,
0<a<π/2,sina=根号下(1-cosa的平方)=根号3/2,
sin(a+π/3)
=sina*cos(π/3)+cosa*sin(π/3)
=(根号3/2)*(1/2)+(1/2)*(根号3/2)
=根号3/2
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