已知函数f(x)=asin(kx+π/3),g(x)=btan(kx-π/3),k>0,它们的周期之和为3π/2,且f(π/2)=g(π/2),f(π/4)=-

问题描述:

已知函数f(x)=asin(kx+π/3),g(x)=btan(kx-π/3),k>0,它们的周期之和为3π/2,且f(π/2)=g(π/2),f(π/4)=-

f(x)周期为T1,g(x)周期为T2.T1+T2=2π/k+2π/k=4π/k=3π/2,k=8/3
f(x)=asin((8/3)x+π/3),g(x)=btan((8/3)x-π/3)
f(π/2)=-(1/2)a=g(x)=0,a=0,
f(π/4)=0