為了得到函數(shù)y=cos2x的圖像,
即是Y=cos2x=sin(2x+π/2)的圖像.
令,點(diǎn)P(X,Y)在Y=sin(2x-π/6)的圖像上,按向量a(h,k)平移后,得到函數(shù)y=cos2x的圖像,即Y=sin(2x+π/2)的圖像.
點(diǎn)P按向量a(h,k)平移后,得到點(diǎn)P'(X'Y').則有
X'=X+h,y'=y+k.
即有,
X=X'-h,y=y'-k.
把X,Y代入Y=sin(2x-π/6)中,得到,
y'-k=sin[2(x'-h)-π/6]=sin(2x'-2h-π/6),
即,y'=sin(2x'-2h-π/6)+k.
而,y'=sin(2x'-2h-π/6)+k.與Y=sin(2x+π/2)的圖像.是恒等的,則有
-2h-π/6=π/2, h=-π/3.
0=k.
即,按向量a(-π/3,0)平移后,得到
Y=cos2x圖象.
或是按向量a(2Kπ-π/3,0)平移后,得到
Y=cos2x圖象.(K屬于Z).