已知函数f(x)=cos^4+2√3sinxcosx-sin^4
来源:学生作业帮 编辑:百度作业网作业帮 分类:数学作业 时间:2024/07/18 07:28:17
已知函数f(x)=cos^4+2√3sinxcosx-sin^4
1) 求f(x)的最小正周期
2)若x∈[0,π/2] 求f(x)的最大值、最小值
1) 求f(x)的最小正周期
2)若x∈[0,π/2] 求f(x)的最大值、最小值
![已知函数f(x)=cos^4+2√3sinxcosx-sin^4](/uploads/image/z/19234725-69-5.jpg?t=%E5%B7%B2%E7%9F%A5%E5%87%BD%E6%95%B0f%28x%29%3Dcos%5E4%2B2%E2%88%9A3sinxcosx-sin%5E4)
f(x)=(cosx)^4+2√3sinxcosx-(sinx)^4
=(cosx)^4-(sinx)^4+√3sin2x
=[(cosx)^2-(sinx)^2][(cosx)^2+(sinx)^2]+√3sin2x
=cos2x+√3sin2x
=2sin(2x+π/3)
1)f(x)的最小正周期:2π/2=π
2)x∈[0,π/2]
2x+π/3∈[π/3,4π/3]
f(x)最大值为2
最小值为-√3
=(cosx)^4-(sinx)^4+√3sin2x
=[(cosx)^2-(sinx)^2][(cosx)^2+(sinx)^2]+√3sin2x
=cos2x+√3sin2x
=2sin(2x+π/3)
1)f(x)的最小正周期:2π/2=π
2)x∈[0,π/2]
2x+π/3∈[π/3,4π/3]
f(x)最大值为2
最小值为-√3
已知函数f(x)=cos^4x+2√3sinxcosx-sin^4x
已知函数f(x)=cos^4(x)+(2根号3)sinxcosx-sin^4(x)
已知函数f(x)=sin^4-2根号3sinxcosx-cos^4x+1
已知函数f(x)=cos^4x-2sinxcosx-sin^4x
已知函数f(x)=cos^4x-2sinxcosx-sin^4x
已知函数f(x)=cos 4 x-2sinxcosx-sin 4 x
已知函数f(x)=sin^x+根号3sinxcosx+2cos^x,x属于R
已知f(x)=cos^4x-2根号3sinxcosx-sin^4x 化简
已知函数f(x)=cos^2x-sin^2x+2根号3sinxcosx+1
已知函数f(x)=根号3(sin^2x-cos^2x)-2sinxcosx
已知函数f(x)=sin^2x-2sinxcosx+3cos^2x
已知函数f(x)=sin^2x+2sinxcosx+3cos^2x