f(x)=根号3(wx+Φ)-cos(wx+Φ)(0<Φ<π,w>0)为偶函数,周期为二分之派.求 f(π/8)

来源:学生作业帮助网 编辑:作业帮 时间:2024/05/15 13:05:06
f(x)=根号3(wx+Φ)-cos(wx+Φ)(0<Φ<π,w>0)为偶函数,周期为二分之派.求 f(π/8)

f(x)=根号3(wx+Φ)-cos(wx+Φ)(0<Φ<π,w>0)为偶函数,周期为二分之派.求 f(π/8)
f(x)=根号3(wx+Φ)-cos(wx+Φ)(0<Φ<π,w>0)为偶函数,周期为二分之派.求 f(π/8)

f(x)=根号3(wx+Φ)-cos(wx+Φ)(0<Φ<π,w>0)为偶函数,周期为二分之派.求 f(π/8)
f(x)=√3sin(wx+Φ)-cos(wx+Φ)(0<Φ<π,w>0)
=2[√3/2sin(wx+Φ)-1/2cos(wx+Φ)]
=2sin(wx+Φ-π/6)
∵f(x)是偶函数∴f(-x)=f(x)
∴Φ-π/6=kπ+π/2,k∈Z
∵0<Φ<π∴Φ=2π/3
∵周期T=π/2∴2π/w=π/2,w=4
∴f(x)=2sin(4x+π/2)=2cos4x
∴f(π/8)=2cos(π/2)=0