Question

已知函数f(x)=2cosωx(ω>0),且函数y=f(x)图像的两条相邻对称轴间的距离为π/2.

(1）求f(π/8)的值
(2)将函数y=f(x)向右π/6，横坐标伸长4倍，得y=g(x)的图像，求g(x)的单调递减区间

Answer 1

两条相邻对称轴间的距离为π/2
T=π/2*2=π
ω=2π/T=2
f(x)=2cos2x
(1)f(π/8)=2cosπ/4=√2
(2) g(x)=2cos(x/2-π/3)
2kπ≤x/2-π/3≤π+2kπ
g(x)的单调递减区间
2π/3+4kπ≤x≤8π/3+4kπ