函数y=cos(x+π/3),x∈(0,π/3]的值域是

来源：学生作业帮助网编辑：作业帮时间：2024/05/09 04:39:18

函数y=cos(x+π/3),x∈(0,π/3]的值域是
函数y=cos(x+π/3),x∈(0,π/3]的值域是

函数y=cos(x+π/3),x∈(0,π/3]的值域是
y=cosx+cos(x+π/3)
=cosx+cosxcosπ/3-sinxsinπ/3
=3/2cosx-√3/2sinx
=√3(√3/2cosx-1/2sinx)
=√3cos(x+π/6)
∵x∈[0,π]
∴x+π/6∈[π/6,7π/6]
∴-1≤cos(x+π/6)≤√3/2
∴-√3≤√3cos(x+π/6)≤3/2
即函数值域为[-√3,3/2]
【中学生数理化】团队为您答题,
请点击下面的【选为满意回答】按钮.

根据Y=cosx的函数图像当x=0时 y=1/2 当x=π/3时 y=-1/2
所以函数y=cos(x+π/3),x∈(0,π/3]的值域y∈[-1/2,1/2)

函数y=cos(x+π/3),x∈(0,π/3]的值域是函数y=cos(x/2-π/3),x∈【0,2π】的值域是函数y=cos(x-π/6)(x∈[0,2/3π])的最大值是? 求函数y=cos^2x+3cos x+2,x属于【0,π/2)的值域? 函数y=-cos根号x(0 函数y=cos(x+b)(0 画出y=3cos+1,x∈[0,2π]的函数简图函数y=cos(3π/2-x)/cos(3π-x)最小正周期是函数y=cos(3π/2-x)/cos(3π-x)最小正周期是：判断下列函数y=cos(x+π/3)cos(x-π/3)的奇偶性函数y=2cos(x-π/3)(π/6 函数y=cos(x+π/6)(0 函数y=3cos(2x-π/3)最小值求函数y=cos(x+π/3)的定义域函数y=cos(x+π/3)的值域(其中x∈[-π/2,π/3]) 求函数y=4cos(x/3),0 求函数y=cos(x-π/3),x∈[-π/2,π/2]的值域, 函数y=cos(x-π/8)(x∈[π/6,2π/3]的最小值.