设f(x)={sinπx x<0,f(x-1)+1 (x≥0) }和g(x)={cosxπ (x<1/2),g(x-1)+1 (x≥1/2)}求g(1/4)+f(1/3)+g(5/6)+f(3/4)

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设f(x)={sinπx x<0,f(x-1)+1 (x≥0) }和g(x)={cosxπ (x<1/2),g(x-1)+1 (x≥1/2)}求g(1/4)+f(1/3)+g(5/6)+f(3/4)
设f(x)={sinπx x<0,f(x-1)+1 (x≥0) }和
g(x)={cosxπ (x<1/2),g(x-1)+1 (x≥1/2)}
求g(1/4)+f(1/3)+g(5/6)+f(3/4)

设f(x)={sinπx x<0,f(x-1)+1 (x≥0) }和g(x)={cosxπ (x<1/2),g(x-1)+1 (x≥1/2)}求g(1/4)+f(1/3)+g(5/6)+f(3/4)
g(1/4)=cos(1/4)π =2分之根号2
f(1/3)=sin(-2/3)π +1=-sin(2/3)π +1=1-2分之根号3
g(5/6)=g(5/6-1)+1=g(-1/6)π +1=g(1/6)π +1=cos(1/6)π +1=1+2分之根号3
f(3/4)=f(-1/3)π +1=sin(-1/3)π +1=-sin(1/3)π +1=1-2分之根号2
所以,g(1/4)+f(1/3)+g(5/6)+f(3/4)=2分之根号2+1-2分之根号3+1+2分之根号3+1-2分之根号2=2