已知f(x)=sin(3.14/4*x),求f(0)+f(1)+f(2)+.+f(100) 的值上面的3.14是丌

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已知f(x)=sin(3.14/4*x),求f(0)+f(1)+f(2)+.+f(100) 的值上面的3.14是丌
已知f(x)=sin(3.14/4*x),求f(0)+f(1)+f(2)+.+f(100) 的值
上面的3.14是丌

已知f(x)=sin(3.14/4*x),求f(0)+f(1)+f(2)+.+f(100) 的值上面的3.14是丌
答:
在0~2π周期内:
sin(π/4)+sin(2π/4)+sin(3π/4)+sin(4π/4)+.+sin(8π/4)=0
100/8=12余4
f(x)=sin(πx/4)
f(0)+f(1)+f(2)+.+f(100)
=sin0+sin(π/4)+sin(2π/4)+sin(3π/4)+.+sin(100π/4)
=0+0+.+sin(97π/4)+sin(98π/4)+sin(99π/4)+sin(100π/4)
=sin(π/4)+sin(2π/4)+sin(3π/4)+sin(4π/4)
=√2/2+2+√2/2+0
=2+√2