求y=sin(1/2x+π/3)的单调区间,对称中心及对称轴

来源:学生作业帮助网 编辑:作业帮 时间:2024/05/10 03:00:15
求y=sin(1/2x+π/3)的单调区间,对称中心及对称轴

求y=sin(1/2x+π/3)的单调区间,对称中心及对称轴
求y=sin(1/2x+π/3)的单调区间,对称中心及对称轴

求y=sin(1/2x+π/3)的单调区间,对称中心及对称轴
y=sin(1/2x+π/3)
(1)增区间
2kπ-π/2≤1/2x+π/3≤2kπ+π/2
2kπ-5π/6≤1/2x≤2kπ+π/6
4kπ-5π/3≤x≤4kπ+π/3
增区间[ 4kπ-5π/3,4kπ+π/3],k∈Z
减区间
2kπ+π/2≤1/2x+π/3≤2kπ+3π/2
2kπ+π/6≤1/2x≤2kπ+7π/6
4kπ+π/3≤x≤4kπ+7π/3
增区间[ 4kπ+π/3,4kπ+7π/3],k∈Z
(2)对称中心
1/2x+π/3=kπ
1/2x=kπ-π/3
x=2kπ-π/6
对称中心为 (2kπ-π/6,0),k∈Z
(3)对称轴
1/2x+π/3=kπ+π/2
1/2x=kπ+π/6
x=2kπ+π/3
对称轴为 x=2kπ+π/3,k∈Z