函数f(x)=sinX+cosX的单调减区间为?百度搜到f(x)=sinX+cosX=根号2(sinXcosπ/4+cosXsinπ/4)=根号2 sin(X+π/4)2kπ+π/2 ≤ X+π/4 ≤ 2kπ+3π/2 ,即2kπ+π/4 ≤ X ≤ 2kπ+5π/4(k∈Z)时单调减.我想问 :2kπ+π/2 ≤ X+π

来源:学生作业帮助网 编辑:作业帮 时间:2024/05/06 22:54:21
函数f(x)=sinX+cosX的单调减区间为?百度搜到f(x)=sinX+cosX=根号2(sinXcosπ/4+cosXsinπ/4)=根号2 sin(X+π/4)2kπ+π/2 ≤ X+π/4 ≤ 2kπ+3π/2 ,即2kπ+π/4 ≤ X ≤ 2kπ+5π/4(k∈Z)时单调减.我想问 :2kπ+π/2 ≤ X+π

函数f(x)=sinX+cosX的单调减区间为?百度搜到f(x)=sinX+cosX=根号2(sinXcosπ/4+cosXsinπ/4)=根号2 sin(X+π/4)2kπ+π/2 ≤ X+π/4 ≤ 2kπ+3π/2 ,即2kπ+π/4 ≤ X ≤ 2kπ+5π/4(k∈Z)时单调减.我想问 :2kπ+π/2 ≤ X+π
函数f(x)=sinX+cosX的单调减区间为?
百度搜到
f(x)=sinX+cosX=根号2(sinXcosπ/4+cosXsinπ/4)=根号2 sin(X+π/4)
2kπ+π/2 ≤ X+π/4 ≤ 2kπ+3π/2 ,即2kπ+π/4 ≤ X ≤ 2kπ+5π/4(k∈Z)时单调减
.
我想问 :2kπ+π/2 ≤ X+π/4 ≤ 2kπ+3π/2 .2kπ+π/2 与2kπ+3π/2 怎么得来的呢?

函数f(x)=sinX+cosX的单调减区间为?百度搜到f(x)=sinX+cosX=根号2(sinXcosπ/4+cosXsinπ/4)=根号2 sin(X+π/4)2kπ+π/2 ≤ X+π/4 ≤ 2kπ+3π/2 ,即2kπ+π/4 ≤ X ≤ 2kπ+5π/4(k∈Z)时单调减.我想问 :2kπ+π/2 ≤ X+π
f(x)=sinx+cosx=(根号2)sin(x+π/4)
sinx的单调地减区间为[π/2+2πk,3π/2+2πk]
所以f(x)=(根号2)sin(x+π/4)的递减区间为
π/2+2πk