- 数学求φ使函数y=√3cos(3x
- 求φ使y=√3cos(3x-φ)-sin(3x-φ)是奇函数
- 求φ使y=√3cos(3x-φ)-sin(3x-φ)是奇函数
令f(x)=y=√3cos(3x-φ)-sin(3x-φ)
=2*[(√3/2)*cos(3x-φ)-(1/2)sin(3x-φ)]
=2*[sin(π/3)*cos(3x-φ)-cos(π/3)*sin(3x-φ)]
=2*sin[(π/3)-(3x-φ)]
所以,f(-x)=2*sin[(π/3)-(-3x-φ)]=2*sin[(π/3)+(3x+φ)]
要满足f(x)为奇函数,则就有:f(-x)=-f(x)
所以:
2*sin[(π/3)+(3x+φ)]=-2*sin[(π/3)-(3x-φ)]
===> sin[(π/3)+(3x+φ)]=-sin[(π/3)-(3x-φ)]
===> sin[(π/3)+(3x+φ)]=sin[(-π/3)+(3x-φ)]
===> (π/3)+(3x+φ)=(-π/3)+(3x-φ)+2kπ(k∈Z)
===> 2φ=2kπ-(2π/3)(k∈Z)
===> φ=kπ-(π/3)(k∈Z)