(1)求函数y=2sin(2x+π/3)(-π/6<x<π/6)的值域 (2)求函数y=2cos(1)求函数y=2sin(2x+π/3)(-π/6<x<π/6)的值域 (2)求函数y=2cos∧2x+5sinx-4的值域
来源:学生作业帮助网 编辑:作业帮 时间:2024/06/24 06:43:22
![(1)求函数y=2sin(2x+π/3)(-π/6<x<π/6)的值域 (2)求函数y=2cos(1)求函数y=2sin(2x+π/3)(-π/6<x<π/6)的值域 (2)求函数y=2cos∧2x+5sinx-4的值域](/uploads/image/z/1748894-14-4.jpg?t=%281%29%E6%B1%82%E5%87%BD%E6%95%B0y%EF%BC%9D2sin%282x%EF%BC%8B%CF%80%2F3%29%28-%CF%80%2F6%EF%BC%9Cx%EF%BC%9C%CF%80%2F6%29%E7%9A%84%E5%80%BC%E5%9F%9F+%282%29%E6%B1%82%E5%87%BD%E6%95%B0y%EF%BC%9D2cos%281%29%E6%B1%82%E5%87%BD%E6%95%B0y%EF%BC%9D2sin%282x%EF%BC%8B%CF%80%2F3%29%28-%CF%80%2F6%EF%BC%9Cx%EF%BC%9C%CF%80%2F6%29%E7%9A%84%E5%80%BC%E5%9F%9F+%282%29%E6%B1%82%E5%87%BD%E6%95%B0y%EF%BC%9D2cos%E2%88%A72x%EF%BC%8B5sinx-4%E7%9A%84%E5%80%BC%E5%9F%9F)
(1)求函数y=2sin(2x+π/3)(-π/6<x<π/6)的值域 (2)求函数y=2cos(1)求函数y=2sin(2x+π/3)(-π/6<x<π/6)的值域 (2)求函数y=2cos∧2x+5sinx-4的值域
(1)求函数y=2sin(2x+π/3)(-π/6<x<π/6)的值域 (2)求函数y=2cos
(1)求函数y=2sin(2x+π/3)(-π/6<x<π/6)的值域 (2)求函数y=2cos∧2x+5sinx-4的值域
(1)求函数y=2sin(2x+π/3)(-π/6<x<π/6)的值域 (2)求函数y=2cos(1)求函数y=2sin(2x+π/3)(-π/6<x<π/6)的值域 (2)求函数y=2cos∧2x+5sinx-4的值域
(1)
∵ -π/6<x<π/6
∴-π/3<2x<π/3
∴0<2x+π/3<2π/3
当t∈(0,2π/3)时,y=sint的取值范围是(0,1]
∴y=2sint的取值范围是(0,2]
即y=2sin(2x+π/3)的值域是(0,2]
(2)
y=2cos²x+5sinx-4
=2(1-sin²x)+5sinx-4
=-2sin²x+5sinx-2
=-2(sin²x-5/2 sinx)-2
=-2(sinx-5/4)²+9/8
=-2(u-5/4)²+9/8
u=sinx的取值范围是[-1,1]
∴u=-1时,y最小=-9; u=1时,y最大=1
∴函数y=2cos∧2x+5sinx-4的值域[-1,9]
y=2sin(2x+π/3)
2kπ-π/2<2x+π/3<2kπ+π/2
kπ-5π/12
y=2cos^2x+5sinx-4=2-2sin^2x+5sinx+4=-2sin^2x+5sinx+6=-2(sinx-5/4)^2+73/8
值域[-1,9]