向量a=(sin x,1),b=(cos x,-1/2),函数f(x)=a*(b-a)的图像可由y=√2/2sin 2x 经过怎样的变化得到

f(x)=a*(b-a)=(sin x,1)*(cos x-sinx,-3/2)
=sinx(cosx-sinx)-3/2
=sinxcosx-(sinx)^2-3/2
=sin2x/2-(1-cos2x)/2-3/2
=(sin2x+cos2x)/2-2
=√2/2*sin(2x+π/4)-2
可由y=√2/2sin 2x 纵坐标不变,横坐标向左移动π/8个单位,再向下平移2个单位.