f(x)是周期为派的偶函数,当x属于[0,派/2)时,f(x)=根号3tanx-1,求f(8派/3)

题目

f(x)是周期为派的偶函数,当x属于[0,派/2)时,f(x)=根号3tanx-1,求f(8派/3)

答案

f(8π/3)=f(8π/3-2π)=f(2π/3)=f(-π+2π/3)=f(-π/3)=f(π/3)=√3tan(π/3)-1=(√3)²-1=3-1=2