Question

把函数y=sin(x+（π/6))图像上各点的横坐标x缩短到原来的1/2，再将图像向右平移π/3个单位

求所得图像的对称轴

Answer 1

y=sin(x+（π/6))---y=sin(2x+（π/6))---y=sin(2(x-π/3)+（π/6))=y=sin(2x-(π/2))=-cos2x,所以对称轴为x=π/2+kπ/2

Answer 2

y=sin[2(x-π/3)+π/6]
=sin(2x-π/2)
设2x-π/2=π/2+kπ (k∈Z)
2x=π+kπ
x=π/2+kπ/2 (k∈Z)

Answer 3

缩短sin(x/2+pi/12)
平移sin(x/2-pi/4)
对称轴pi/2