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_数学解答

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
为（3π）/2,且f(π/2)=g(π/2),f(π/4)=-√3g(π/4)-1,求这两个函数的解析式.

人气：168 ℃　时间：2019-12-20 23:01:38

解答

T1+T2=2π/|k|+2π/|2k|=3π/k=3π/2k=2f(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)...