Question

定义在r上的函数f(x)既是偶函数又是周期函数，若f(x)的最小正周期是π，切当x属于【0，π/2】时f(x)=sinx,

则f(5π/3）的值为

Answer 1

由于偶函数，所以f(5π/3)=f(-5π/3)
由于周期π，所以f(5π/3)=f(-5π/3)=f(-5π/3+2π)=f(π/3)=sin(π/3)=根号3/2