已知函数f(X)=sin(wx+A)—根3cos(wx+A)(w>0,0

题目

已知函数f(X)=sin(wx+A)—根3cos(wx+A)(w>0,0相邻对称轴的距离为π/3,则函数的解析式为?

答案

∵f(x)＝sin(wx＋A)－√3cos(wx＋A)＝2[1/2sin(wx＋A)－√3/2cos(wx＋A)]＝2sin(wx＋A－π/3)
∵函数Y=f(x)的图像相邻对称轴的距离为π/3 ∴T＝2×π/3＝2π/w ∴w＝3
∴f(x)＝2sin(3x＋A－π/3)
∵函数f(X)＝sin(wx＋A)－√3cos(wx＋A)(w>0,0