f(x)=cos(Pi/2-Pix/6)x属于R求出f(1)+f(2)+f(3)+...+f(2007)

Question

f(x)=cos(Pi/2-Pix/6) x属于R求出f(1)+f(2)+f(3)+...+f(2007)

Answer 1

周期T=2π/|-π/6|=12
所以是12个一循环
f(1)=cosπ/3=1/2
f(2)=cosπ/6=√3/2
f(3)=cos0=1
f(4)=cos-π/6=√3/2
f(5)=cos-π/3=1/2
f(6)=-π/2=0
f(7)=-2π/3=-1/2
f(8)=-√3/2
f(9)=-1
f(10)=-√3/2
f(11)=-1/2
f(12)=0
所以f(1)+……+f(12)=0
2007/12余数=3
所以原式=f(1)+f(2)+f(3)=(3+√3)/2