已知sinacos(π/3)-cosasin(π/3)=1/2,a∈【0,2π),则a等于( )

来源:学生作业帮助网 编辑:作业帮 时间:2024/04/30 13:22:05
已知sinacos(π/3)-cosasin(π/3)=1/2,a∈【0,2π),则a等于( )

已知sinacos(π/3)-cosasin(π/3)=1/2,a∈【0,2π),则a等于( )
已知sinacos(π/3)-cosasin(π/3)=1/2,a∈【0,2π),则a等于( )

已知sinacos(π/3)-cosasin(π/3)=1/2,a∈【0,2π),则a等于( )
应用公式sinAcosB-cosAsinB=sin(A-B)可得:
sinacos(π/3)-cosasin(π/3)=sin(a-π/3),
又sinacos(π/3)-cosasin(π/3)=1/2,
∴sin(a-π/3)=1/2,
所以a-π/3=π/6+2kπ或a-π/3=5π/6+2kπ
即a=π/2+2kπ或a=7π/6+2kπ
又a∈【0,2π),
故a=π/2或a=7π/6.

1)sin(a-π/3)=sin(π/6)
a-π/3=π/6
a=1/2π
2)sin(a-π/3)=sin(2π/3)
a-π/3=2π/3
a=π

π/2或7/6π