把函数f(x)=sin(7π/8-x)*cos(x+π/8)的图象向右平移a(a>0)的单位,得函数g(x)图象,且g(X)图象
问题描述:
把函数f(x)=sin(7π/8-x)*cos(x+π/8)的图象向右平移a(a>0)的单位,得函数g(x)图象,且g(X)图象
且g(X)图象关于直线x=π/4对称
(1)求a的最小值
(2)已知当x∈[(2b+1)π/8,(3b+2)π/8](b∈N)时,过函数f(x)图象上任意两点的直线的斜率恒大于零,求b的值
答
解 (1)f(x)=sin(7π/8-x)*cos(x+π/8)=sin[π-(π/8+x)]cos(x+π/8) =sin(x+π/8)cos(x+π/8)=1/2sin(2x+π/4) 则g(x)=f(x-a)=1/2sin(2x-2a+π/4)由于g(X)图象关于直线x=π/4对称 ...