设函数f(x)=sin(2x+派/4)+cos(2x+派/4), 求函数对称轴和增减性. 要详细解答过程
来源:学生作业帮 编辑:作业帮 分类:数学作业 时间:2024/09/30 09:45:22
设函数f(x)=sin(2x+派/4)+cos(2x+派/4), 求函数对称轴和增减性. 要详细解答过程
f(x)=sin(2x+派/4)+cos(2x+派/4)
=sin2xcos(π/4)+cos2xsin(π/4)+cos2xcos(π/4)-sin2xsin(π/4)
=√2cos(2x)
(1)2x=kπ
对称轴:x=kπ/2
(2)增区间
2kπ-π≤2x≤2kπ
kπ-π/2≤x≤kπ
增区间[kπ-π/2,kπ],k∈Z
减区间
2kπ≤2x≤2kπ+π
kπ≤x≤kπ+π/2
增区间[kπ,kπ+π/2],k∈Z
再问: =sin2xcos(π/4)+cos2xsin(π/4)+cos2xcos(π/4)-sin2xsin(π/4) =√2cos(2x) 这个……是怎么整理的……
再答: =sin2xcos(π/4)+cos2xsin(π/4)+cos2xcos(π/4)-sin2xsin(π/4) =(√2/2)sin2x+(√2/2)cos2x+(√2/2)cos2x-(√2/2)sin2x =√2cos2x
=sin2xcos(π/4)+cos2xsin(π/4)+cos2xcos(π/4)-sin2xsin(π/4)
=√2cos(2x)
(1)2x=kπ
对称轴:x=kπ/2
(2)增区间
2kπ-π≤2x≤2kπ
kπ-π/2≤x≤kπ
增区间[kπ-π/2,kπ],k∈Z
减区间
2kπ≤2x≤2kπ+π
kπ≤x≤kπ+π/2
增区间[kπ,kπ+π/2],k∈Z
再问: =sin2xcos(π/4)+cos2xsin(π/4)+cos2xcos(π/4)-sin2xsin(π/4) =√2cos(2x) 这个……是怎么整理的……
再答: =sin2xcos(π/4)+cos2xsin(π/4)+cos2xcos(π/4)-sin2xsin(π/4) =(√2/2)sin2x+(√2/2)cos2x+(√2/2)cos2x-(√2/2)sin2x =√2cos2x
设函数f(x)=sin(2x+派/4)+cos(2x+派/4), 求函数对称轴和增减性. 要详细解答过程
一道高中数学题:设函数f(x)=sin(2x+4分之派)+cos(2x+4分之派),求函数的增区间和减区间.请写出详细过
函数f(x)=sin(2x+派/4)+cos(2x+派/4)
已知函数f(x)=2根号3sin(x/2+派/4)cos(x/2+派/4)-sin(x+派).求f(x)的最小正周期
设函数f(x)=sin(派/2x+派/6)-2sin^派/4x,求函数f(x)的最小正周期
已知函数f(x)=2根3sin(x-派/4)cos(x-派/4)-sin(2x-派)求单调递增区间
设函数f(x)=sin(2x+4分之派)求函数的增区间
函数f(x)=sin(x+ 7派/4)+cos(x- 3派/4)求详细化简过程
设函数f(x)=sin(派x/3-派/6)-2cos平方(派x/6)求f(x)最小正周期,单调增
设函数f(x)=sin(派x/3-派/6)-2cos平方派x/6.(1)求f(x)的最小正周期及单调
已知函数f(x)=cos(2x-3/派)+2sin(x-4/派)sin(x+4/派)1.求f(x)的最小正周期和图像对称
(1/2)高三数学函数.f(x)=cos(2x-派/3)+2sin(x-派/4)sin(x+派/4).求函数最小正周期和