Question

已知函数f（x）=sin（wx+φ）（w＞0,0＜φ＜π）为偶函数,其图像上相邻的两个最高点间的距离为2π,则函数f（x

Answer 1

图像上相邻的两个最高点间的距离为2π=>T=2π

w=1

f(x)=sin(x+φ)

对称轴x+φ=kπ+(π/2)

φ=kπ+(π/2)

φ=π/2

f(x)=sin(x+(π/2))

=cosx

单调递减区间[2kπ,2kπ+π]