Question

y=|sinx|+|cosx|是周期函数吗?如果是,则周期是多少?

Answer 1

是周期函数,周期T=k*π/2,k为正整数,最小正周期为π/2.

f(x+π/2)=|sin(x+π/2)|+|cos(x+π/2)|=|cos(x)|+|-sin(x)|=|sin(x)|+|cos(x)|=f(x).

因此它的周期为π/2,“Lmy0217网友”不懂装懂并不可怕,怕的是误人子弟!