要得到函数y=cos(x/2-π/4)的图像,只需将y=sin(x/2)的图像怎样移动
解析:∵sin((x+π/2)/2)=sin(x/2+π/4)=sin[(x/2+π/2)-π/4]
=sin(x/2+π/2)cosπ/4-cos(x/2+π/2)sinπ/4
=cosx/2cosπ/4+sinx/2sinπ/4=cos(x/2-π/4)
∴要得到函数y=cos(x/2-π/4)的图像,只需将y=sin(x/2)的图像向左平移π/2个坐标单位即可
要得到函数y=cos(x/2-π/4)的图像,只需将y=sin(x/2)的图像怎样移动
解析:∵sin((x+π/2)/2)=sin(x/2+π/4)=sin[(x/2+π/2)-π/4]
=sin(x/2+π/2)cosπ/4-cos(x/2+π/2)sinπ/4
=cosx/2cosπ/4+sinx/2sinπ/4=cos(x/2-π/4)
∴要得到函数y=cos(x/2-π/4)的图像,只需将y=sin(x/2)的图像向左平移π/2个坐标单位即可