Question

求函数y=|sinx+cosx|的最小正周期

Answer 1

y=|sinx+cosx|=|√2sin(x+π/4)|
最小正周期是T=(2π/1)/2=π【加绝对值周期减半】
sinx+cosx
=√2*[sinx*(√2/2)+cos*(√2/2)]
=√2*[sinx*cos(π/4)+cos*sin(π/4)]
=√2sin(x+π/4)