y=2sin(πx4),求f(1)+f（2）+f(3)+f(4)+f(5）+f（6）+f(7）+f（8）+f(9)+f(10)+f（11）的值?

题目

y=2sin(πx4),求f(1)+f（2）+f(3)+f(4)+f(5）+f（6）+f(7）+f（8）+f(9)+f(10)+f（11）的值?
希望给出详细的解析

答案

f(x)=2sin(πx4),
最小正周期T=2π/(π/4)=8
f(1)=2sin(π/4)=根号2
f(2)=2sin(π/2)=2
f(3)=2sin(3π/4)=根号2
f(4)=2sin(4π/4)=0
f(5)=2sin(5π/4)=-根号2
f(6)=2sin(6π/4)=-2
f(7)=2sin(7π/4)=-根号2
f(8)=2sin(8π/4)=0
f(9)=f(8+1)=f(1)=根号2
f(10)=f(2)=2
f(11)=f(3)=根号2
所以,【f(1)+f（2）+f(3)+f(4)+f(5）+f（6）+f(7）+f（8）】+【f(9)+f(10)+f（11）】=0+2+2根号2
=2+2根号2