已知函数f(x)=sin(π/2-x)+sinx
问题描述:
已知函数f(x)=sin(π/2-x)+sinx
(1)求函数y=f(x)的单调递增区间
(2)若f(a-π/4)=根号2/3,求f(2a+π/4)的值
答
f(x)=cosx+sinxf(x)=√2sin(x+π/4)(1)递增区间:2kπ-π/2≤x+π/4≤2kπ+π/2得:2kπ-3/4π≤x≤2kπ+π/4递增区间是:[2kπ-3π/4,2kπ+π/4],其中k∈Z(2)f(a-π/4)=√2sina=√2/3则:sina=1/3f(2a+...