Question

已知向量a=(sin(+),cos),b=(cos(+),-cos),x∈［,π］,函數f(x)=a·b.

（1）若cosx=-,求函數f(x)的值;

（2）將函數f(x)的圖象按向量c=(M,n)(0＜M＜π)平移,使得平移后的圖象關于原點對稱,求向量c.

Answer 1

解:由題意,得?

f(x)=sin(+)cos(+)-cos²?

=sin(x+)-(1+cosx)?

=sinx-cosx-?

=(sinx-cosx)-

=sin(x-)-.                                                                                             ?

(1)∵x∈［,π］,cosx=-,∴sinx=.?

∴f(x)=sinx-cosx-=-.                                                                     ?

(2)由圖象變換得平移后的函數為g(x)=sin(x--M)+n-,而平移后的圖象關于原點對稱，

∴g(0)=0且n-=0,                                                                                                ?

即sin(M+)=0且n=，?

∵0＜M＜π,∴M=,即c=(,).