Question

求大神学霸解答 急！！！！！

Answer 1

1. f(x)=cos(π/3x+π/3)-2cos^2(π/6x)

        =cos(π/3x)*cos(π/3)-sin(π/3x)*sin(π/3)-1+sin^2(π/6x)-cos^2(π/6x)

        =1/2cos(π/3x)-√3/2sin(π/3x)-1-cos(π/3x)

        =-1/2cos(π/3x)-√3/2sin(π/3x)-1

        =-(cos(π/3x)*cos(π/3)+sin(π/3x)*sin(π/3))-1

        =-cos(π/3x-π/3)-1

   所以周期为2π/(π/3)=6

2. 因为周期为6

   所以f(1)+f(2)+...+f(2013)=336(f(1)+f(2)+f(3))+335(f(4)+f(5)+f(6))

                                         =336(-2-3/2-1/2)+335(0-1/2-3/2)

                                         =336*(-4)+335*(-2)

                                         =-2014

追问

谢啦