已知函数f(x)=sin(x-π/2)+sin(x-π)

问题描述:

已知函数f(x)=sin(x-π/2)+sin(x-π)
(1)求函数f(x)的最值和最小正周期;(2)求函数f(x)的对称轴和单调增区间

(1)f(x)=sin(x-π/2)+sin(x-π)=-sin(π/2-x)+sinx=sinx-cosx=√2(√2/2sinx-√2/2cosx)=√2sin(x-π/4)f(x)最大值为√2,最小值为-√2周期T=2π(2)由x-π/4=kπ+π/2,k∈Z得f(x)的对称轴方程x=kπ+3π/4,k∈Z由2kπ-...