Question

求y=sin（1/2x+π/3)的单调区间,对称中心及对称轴

Answer 1

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