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)的最小正周期为π，且当x属于[0，π/2]时

f(x)=sinx,则f(5π/3)为什么等于根号3/2,为什么不是等于-根号3/2?

Answer 1

解答：
f(x)的周期是π
所以 f(5π/3)=f(5π/3-π)=f(2π/3)=f(2π/3-π)=f(-π/3)
又因为f(x)是偶函数
f(5π/3)=f(-π/3)=f(π/3)=sin(π/3)=√3/2

Answer 2

=f(2/3π）=f(-2/3π）=f(-2/3π+π）=sin(1/3π)=sin(60°）=根号3/2,

Answer 3

f(5π/3)=sin（5π/3）=sin(2π/3)=根号3/2