Question

定义在R上的函数f(x)既是奇函数又是周期函数,若函数f(x)的最小正周期是π，且当x属于[-π/2，0)时

f（x）=sinx，求f（-5π/3）的值

Answer 1

函数f(x)的最小正周期是π
f（-5π/3）=f(π/3) (加上两个周期)
且当x属于[-π/2，0)时 f(-π/3)=sin(-π/3)=-√3/2
奇函数 f(-x)=-f(x)
所以f(-π/3)=-f(π/3)
f(π/3)=-√3/2
f（-5π/3）=-√3/2

Answer 2

f(-x) = - f(x)
f(-5π/3) = - f(5π/3) = - f(π + 2π/3) = - f(2π/3)
= sin(2π/3) = (√3)/2

追问

这- =肯定错的 f要先在定义域内才可以转化成sin的