Question

函数Y=2sin(2X+pai/3)的图像关于?对称.？

Answer 1

Y = 2sin(2X+π/3) = 2sin{2(X+π/6)}
(1)
当x=kπ/2-π/6时,Y=0,关于x=kπ/2-π/6中心对称,其中k∈Z
(2)
当x=kπ/4-π/6时,Y=-2,或+2,关于x=kπ/4-π/6轴对称,其中k∈Z,4,∵Y = 2sin(2X+π/3)
2X+π/3=kπX=kπ/2-π/6
Y关于x=kπ/2-π/6中心对称，其中k∈Z
2X+π/3=2kπ+π/2==>X=kπ+π/12
2X+π/3=2kπ-π/2==>X=kπ-5π/12
y关于x=kπ-5π/12或X=kπ+π/12轴对称，其中k∈Z,1,∵Y = 2sin(2X+π/3)
2X+π/3=kπX=kπ/2-π/6
Y关于x=kπ/2-π/6中心对称，其中k∈Z
2X+π/3=kπ+π/2==>X=kπ/2+π/12
y关于X=kπ/2+π/12轴对称，其中k∈Z,0,