函数在线急等f(x)=4cosxsin(x+30度)-1.求f(x)最小正周期和在-六分之派,四分之派的最值f(x)=4cosxsin(x+30度)-1

Answer 1

1.解:f(x)=2cosx(cosx+√3sinx)-1
=cos2x+√3sin2x
=2sin(2x+π/6)
因此f(x)的最小正周期是π.
2.解:易知f(x)在[-π/3,π/6]上递增,在[π/6,2π/3]上递减.求得
f(-π/6)=-1
f(π/6)=2
f(π/4)=√3/2
因此所求最大值为2,最小值为-1.