已知函数f(x)=根号3sinωx乘以cosωx-cos^2ωx(ω>0)的最小正周期为π/2(1)求ω的值(2)若0

Question

已知函数f(x)=根号3sinωx乘以cosωx-cos^2ωx(ω>0)的最小正周期为π/2
(1)求ω的值
(2)若0

Answer 1

1、
f(x)=(√3/2)sin2ωx-(1+cos2ωx)/2
=(√3/2)sin2ωx-(1/2)cos2ωx-1/2
=sin(2ωx-z)-1/2
tanz=(1/2)÷(√3/2)=1/√3
所以z=π/6
所以f(x)=sin(2ωx-π/6)-1/2
所以T=2π/2ω=π/2
ω=2
2、
f(x)=sin(4x-π/6)-1/2
00<4x<=4π/3
-π/6<4x-π/6<=7π/6
所以4x-π/6=7π/6,sin(4x-π/6)最小=-1/2
4x-π/6=π/2,sin(4x-π/6)最答=1
所以-1/2<=sin(4x-π/6)<=1
再减去1/2
所以最大值=1/2,最小值=-1