已知函数f(x)=sin(wx+pi/4)(x属于R,w>0),为了得到函数g(×)=coswx的图象,只需将f(x)的图象如何变动?

Question

已知函数f(x)=sin(wx+pi/4)(x属于R,w>0),为了得到函数g(×)=coswx的图象,只需将f(x)的图象如何变动?

Answer 1

f(x)=sin(wx+pi/4)=cos(pi/2-wx-pi/4)=cos(pi/4-wx)=cos(wx-pi/4)
=cos{w[x-pi/(4w)]}
从cos{w[x-pi/(4w)]}到coswx即图像向左平移pi/(4w)