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