问题描述: 已知f(x)=根号3sin(wx+b)-cos(wx+b)且为偶函数,图像的两相邻对称轴的距离为π/2,求f(π/6) 1个回答 分类:综合 2014-10-27 问题解答: 我来补答 f(x)=√3sin(wx+b)-cos(wx+b)f(x)=2[sin(wx+b)cosπ/6-cos(wx+b)sinπ/6]f(x)=2sin(wx+b-π/6)因为f(x)为偶函数,所以:f(-x)=f(x),即:2sin(-wx+b-π/6)=2sin(wx+b-π/6);所以:b-π/6=π/6-b+π,得到:b=2π/3.又因为图像的两相邻对称轴的距离为π/2,有:(1/2)T=π/2;所以T=π,所以w=2.所以:f(x)=2sin(2x+π/2)=2cos2x.f(π/6) =2cos(π/3) =√3. 展开全文阅读