已知函数f(x)=cos^2x-2sinxcosx-sin^2x+1化简问题已知函数f(x)=cos^2x-2sinxcosx-sin^2x+1,求f(x)对称轴方程和对称中心坐标.顺便化简下.

问题描述:

已知函数f(x)=cos^2x-2sinxcosx-sin^2x+1化简问题
已知函数f(x)=cos^2x-2sinxcosx-sin^2x+1,求f(x)对称轴方程和对称中心坐标.顺便化简下.

f(x)=cos^2x-2sinxcosx-sin^2x+1=(cos2x+1)/2-sin2x+1/2-sin^2x+1/2=(1/2)*cos2x+1/2-sin2x+(1/2)*cos2x+1/2=cos2x-sin2x+1=-(sin2x-cos2x)+1=-√2sin(2x-π/4)+1对称轴:2x-π/4=π/2+kπ(k∈Z)2x=3π/4+kπx=3π...