求f(x)=sin(x/2)+cos(x/2)的单调增区间

来源:学生作业帮助网 编辑:六六作业网 时间:2024/07/04 23:03:47
求f(x)=sin(x/2)+cos(x/2)的单调增区间求f(x)=sin(x/2)+cos(x/2)的单调增区间求f(x)=sin(x/2)+cos(x/2)的单调增区间f(x)=sin(x/2)

求f(x)=sin(x/2)+cos(x/2)的单调增区间
求f(x)=sin(x/2)+cos(x/2)的单调增区间

求f(x)=sin(x/2)+cos(x/2)的单调增区间
f(x)=sin(x/2)+cos(x/2)
=√2sin(x/2+π/4)
单增:
x/2+π/4∈[2kπ-π/2,2kπ+π/2]
x∈[4kπ-3π/2,4kπ+π/2] k∈z

2kπ-1.5π