求助高一函数!!!:求函数y=3sin(2x+π⼀4),x∈〔0,π〕的单调递减区间。

2024-12-22 22:15:13
推荐回答(4个)
回答1:

2x+π/4=π/2+2kπ x=π/8+kπ
2x+π/4=3π/2+2kπ x=7π/8+kπ

函数y=3sin(2x+π/4),x∈〔0,π〕的单调递减区间
[π/8+kπ,7π/8+kπ],k为整数

回答2:

0<=x<=π
0<=2x<=2π
π/4<=2x+π/4<=9π/4

sinx的减区间是(2kπ+π/2,2kπ+3π/2)
即第23象限
则次数是π/2<2x+π/4<3π/2
π/4<2x<5π/4
π/8所以减区间(π/8,5π/8)

回答3:

求此函数的递减区间 就是求sin函数的递减区间
2x+π/4∈〔π/2+2kπ,3π/2+2kπ〕
求的x的范围 再与0,π〕求交集
所得的最终范围(π/8,5π/8〕

回答4:

2x+π/4=π/2+2kπ x=π/8+kπ
2x+π/4=3π/2+2kπ x=5π/8+kπ