写出函数Y=sin(π/3-X)的轴对称中心对称

1个回答

因为Y=sin(π/3-X)=-sin(x-π/3)
令x-π/3=kπ得x=kπ+π/3,所以对称中心为（kπ+π/3,0）
令x-π/3=kπ+π/2得x=kπ+5π/6,所以对称轴为x=kπ+5π/6
由2kπ+π/2≤x-π/3≤2kπ+3π/2得到,单调递增区间[2kπ+5π/6,2kπ+11π/6]
由2kπ-π/2≤x-π/3≤2kπ+π/2得到,单调递减区间[2kπ+π/6,2kπ+5π/6]