已知函数f(x)=sin(wx+π/4)(x属于R,w大于0)的最小正周期为π将y=f(x)的图像向左平移绝对值fai

f(x)=sin(wx+π/4)(x属于R,w大于0)的最小正周期为πT=2π/w=π,w=2y=f(x)的图像向左平移|α|,所得图像关于y轴对称,y=f(x+|α|)=sin(2(x+|α|)+π/4)=sin(2x+2|α|+π/4)=±cos2x2|α|+π/4=kπ+π/22|α|=kπ+π/4|...y=f(x+|α|)=sin(2(x+|α|)+π/4)=sin(2x+2|α|+π/4)=±cos2x中的sin(2x+2|α|+π/4)=±cos2x这一步不懂！求解？y=f(x)的图像向左平移|α|,所得图像关于y轴对称即：y=f(x+|α|)=sin(2x+2|α|+π/4)图像关于y轴对称说明y=f(x+|α|)=sin(2x+2|α|+π/4)是偶函数，y=cos2x或者y=-cos2x是偶函数所以sin(2x+2|α|+π/4)=±cos2x这样就有2|α|+π/4=kπ+π/2因为sin(2x±π/2）=±cos2x