Question

已知函数f(x)=cos(2x-π/3)+sin^2x-cos^2x 1.求f(x)的对称轴及对称

已知函数f(x)=cos(2x-π/3)+sin^2x-cos^2x
1.求f(x)的对称轴及对称中心

Answer 1

f(x)=cos(2x-π/3)+sin^2x-cos^2x
=cos2xcosπ/3+sin2xsinπ/3-cos2x
=1/2cos2x+sin2xsinπ/3-cos2x
=-1/2cos2x+sin2xsinπ/3
=-cosπ/3cos2x+sin2xsinπ/3
=-cos(2x+π/3)
对称轴：
2x+π/3=kπ
2x=kπ-π/3
x=kπ/2-π/6
对称中心：
2x+π/3=kπ＋π/2
2x=kπ-π/6
x=kπ/2-π/12
中心为（kπ/2-π/12，0）

追问

若f(a)=3/5,2a是第二象限角，求sin2a