(1)原式=cos(π/4)cosφ –sin(π/4)sinφ=0
=cos(π/4+φ)=0
π/4+φ=π/2
φ=π/4
(2)两对称轴之间的距离=π/3
该函数的周期为T=2π/3
T=2π/ω ω=3
∴f(x)=sin(3x+π/4)即为所求.