设函数f(x)=arc sin(cos(x)),则f(f(f(x)))的最小正周期为?

问题描述:

设函数f(x)=arc sin(cos(x)),则f(f(f(x)))的最小正周期为?

3.265

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