函数f(x)是周期为派的偶函数,且当x属于[0,2/派)时,f(x)=根号3 tanx-1,则f(8派/3)的值是
问题描述:
函数f(x)是周期为派的偶函数,且当x属于[0,2/派)时,f(x)=根号3 tanx-1,则f(8派/3)的值是
答
解;因为函数的周期为π
所以f(8π/3)=f(2π/3+2π)=f(2π/3)=f(-π/3+π)=f(-π/3)
又因为f(x)为偶函数,所以f(-π/3)=f(π/3)
所以f(8π/3)=f(π/3)
=√3×√3-1
=2