求三角函数值域 y=sin2x-根号3cos2x.x属于[派/6,派/2]
问题描述：
求三角函数值域 y=sin2x-根号3cos2x.x属于[派/6,派/2]
答
y=sin2x-√3cos2x
=2sin(2x-π/3)
因为 x∈[π/6,π/2]
所以 2x-π/3∈[0,2π/3]
所以
函数 y=2sin(2x-π/3)的值域为 [0,2]
答
y=sin2x-根号3cos2x
=2[sin2xcosπ/3-cos2xsinπ/3]
=2sin(2x-π/3)
x∈[π/6,π/2]
当x=5π/12；y有最大值=2
当x=π/6,y有最小值=0
函数值域为[0,2]