设有函数f(x)=asin(kx-π/3)和函数g(x）=bcos(2kx-π/6),(a>0,b>0,k>o),若它们的最小正周期之和

Question

设有函数f(x)=asin(kx-π/3)和函数g(x）=bcos(2kx-π/6),(a>0,b
>0,k>o),若它们的最小正周期之和

Answer 1

T1+T2=2π/|k|+2π/|2k|=3π/k=3π/2
k=2
f(x)=asin(2x-π/3)
g(x)=bcos(4x-π/6)
f(π/2)=asin(2π/3)=asin(π-π/3)=asin(π/3)=acos(π/2-π/6)=acos(π/6)=g(π/2)=bcos(-π/6)=bcos(π/6)
所以a=bf(π/4)=asin(π/6)=-√3g(π/4)-1=-√3bcos(5π/6)-1
所以a/2=-√3*b(-√3/2)-1=3b/2-1
a=3b-2
a=b
所以a=b=1
f(x)=sin(2x-π/3)
g(x)=cos(4x-π/6)