已知函数f(x)=2sin(2x+π⼀6)求1. 求函数的最小正周期 2. 求当x∈[0,π⼀2]时,函数f(x)的值域.(3)当

2025-05-13 12:03:50
推荐回答(1个)
回答(1):

1、最小正周期=2π/w=2π/2=π.

2、根据题意:
0<=x<=π/2
0<=2x<=π
π/6<=2x+π/6<=7π/6
所以:f(x)min=2sin(7π/6)=-1;
f(x)max=2sin(π/2)=2.

3.从-π到π,等同从0到2π。
根据题意:
2kπ+π/2<=2x+π/6<=2kπ+3π/2为递减区间
2kπ+π/3<=2x<=2kπ+4π/3
kπ+π/6<=x<=kπ+2π/3.
所以当k等于0时,有区间【π/6,2π/3];
当k等于1时有区间[7π/6,5π/3].