已知函数f(x)=cos(2x-π/3)+2sin(x-π/4)sin(x+π/4)⑴求函数f(x)的最小正周期和图像的对称轴方程 ⑵求函数f(x)在区间[-π/12,π/2]上的值域

来源:学生作业帮助网 编辑:作业帮 时间:2024/05/07 07:14:48

已知函数f(x)=cos(2x-π/3)+2sin(x-π/4)sin(x+π/4)⑴求函数f(x)的最小正周期和图像的对称轴方程 ⑵求函数f(x)在区间[-π/12,π/2]上的值域
已知函数f(x)=cos(2x-π/3)+2sin(x-π/4)sin(x+π/4)
⑴求函数f(x)的最小正周期和图像的对称轴方程
⑵求函数f(x)在区间[-π/12,π/2]上的值域

已知函数f(x)=cos(2x-π/3)+2sin(x-π/4)sin(x+π/4)⑴求函数f(x)的最小正周期和图像的对称轴方程 ⑵求函数f(x)在区间[-π/12,π/2]上的值域
2sin(x-π/4)sin(x+π/4)
=2sin(x-π/4)cos[π/2-(x-π/4)]
=2sin(x-π/4) cos(π/4-x)
=2sin(x-π/4) cos(x-π/4)
=sin(2x-π/2)
=-sin(π/2-2x)
=-cos2x
∴ f(x)=cos2xcosπ/3+sin2xsinπ/3-cos2x
=-(cos2xcosπ/3-sin2xsinπ/3)
=-cos(2x+π/3)
T=2π/2=π
对称轴2x+π/3=kπ
x=(kπ-π/3)/2
做到这一步,相信下面的你会做了,不懂再问我.
建议楼主多给点分,还有你的三角函数要好好的学习,高考肯定是免不了的

2sin(x-π/4)sin(x+π/4)
=2sin(x-π/4)cos[π/2-(x-π/4)]
=2sin(x-π/4) cos(π/4-x)
=2sin(x-π/4) cos(x-π/4)
=sin(2x-π/2)
=-sin(π/2-2x)
=-cos2x
∴ f(x)=cos2xcosπ/3+sin2xsinπ/3-cos2x
=-(cos2xcosπ/3-sin2xsinπ/3)
=-cos(2x+π/3)
T=2π/2=π

f(x)=cos(2x-π/3)+2sin(x-π/4)sin(x+π/4)
=cos2xcosπ/3+sin2xsinπ/3+2(sinxcosπ/4-cosxsinπ/4)(sinxcosπ/4+cosxsinπ/4)
可以这样打开,不用记太多公式,但计算复杂。

已知函数f(x)=cos(2x-π/3)+2sin^2 x (2)设函数g(x)=[f(x)]^2+f(x),求g(x)的值域已知函数f(x)=cos(2x-π/3)+2sin^2 x(2)设函数g(x)=[f(x)]^2+f(x),求g(x)的值域 已知函数f(x)=(cosx)^2 +cos(3π/2 +x) +3 (0 已知函数f(x)=2cos(2x—(3π/4))求f(x的对称轴) 已知函数f(x )=sin ^2x +2√3sin x cos x +3cos^x 、求函数f (x )的单调增区间 已知a=2(cosωx,cosωx),b=(cosωx,√3sinωx),函数f(x)=a×b,若直线x=π/3是函数f(x)的一条对称轴 已知函数f(x)=cos(2x-π/3)+sin(^2)x+cos(^2)x.求化简~ 已知函数f(x)=cos (x/4) cos (π/2 -x/4) cos(π - x/2),将函数f(x)在(0,∞)的所有极值点从小到大排...已知函数f(x)=cos (x/4) cos (π/2 -x/4) cos(π - x/2),将函数f(x)在(0,∞)的所有极值点从小到大排成一数列, 已知函数f(x)=cos^2x+sinxcosx,x∈Rf(π/6) 已知函数f(x)=√2cos(x-π/12),x∈R 【高一数学】已知函数fx=2cos^2x+cos(2x+π/3)已知函数fx=2cos²x+cos(2x+π/3)(1)f(α)=√3/3+1,0 已知函数f(x)=2cos方x+2sinxcosx.记函数g(x)=f(x)*f(x+π/4) 求g(x)值域 已知函数f(x)=cos(2x-π/3)+2sin^2x-2求函数f(x)的最小正周期及图像对称轴方程 已知函数f(x)=asinωx·cosωx-(根号3)a(cosωx)^2+(根号3)(a+b)/2 (a>0)已知函数f(x)=asinωx·cosωx-(根号3)a(cosωx)^2+(根号3)(a+b)/2 (a>0)(1)当a=ω=1时,写出函数f(x)的单调递减区间(2)若函数f(x)满足f(x+π)=f(x), 已知函数 f(x)=sin2x+√2cos(x-π/4) 求f(x) 值域 已知函数f(x)=cos(π/3+x)*cos(π/3-x),g(x)=1/2sin2x-1/4,求f(x)的最小正周期 已知函数f(x)=cos(2x-3分之2π)-cos2x 已知函数f x=3cos(2X+π/4),求单调递减区间 已知函数f=cos(2x-π/3)-cos2x1求函数f(x)的最小正周期