百度作业网函数f(x)=2cosxsin(x+π/3)-根号3sin^2x+sinxcosx的最小值为多少?此时x等于多少
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：2024/06/13 21:47:17
函数f(x)=2cosxsin(x+π/3)-根号3sin^2x+sinxcosx的最小值为多少?此时x等于多少
f(x)=2cosxsin(x+π/3)-√3sin^2x+sinxcosx
=2cosx(√3/2sinx+1/2cosx)-√3sin^2x+1/2sin2x
=√3/2sin2x+cos^2x-√3sin^2x+1/2sin2x
=(√3+1)/2sin2x+cos^2x-√3sin^2x
=(√3+1)/2sin2x+(cos2x+1)/2+√3/2(cos2x-1)
=(√3+1)/2(sin2x+cos2x)+(√3-1)/2
=(√6+√2)/2sin(2x+π/4)+(√3-1)/2
2x+π/4=2kπ-π/2 , x=kπ-3π/8 , k∈Z
最小值f(kπ-3π/8)=-(√6+√2)/2+(√3-1)/2
=2cosx(√3/2sinx+1/2cosx)-√3sin^2x+1/2sin2x
=√3/2sin2x+cos^2x-√3sin^2x+1/2sin2x
=(√3+1)/2sin2x+cos^2x-√3sin^2x
=(√3+1)/2sin2x+(cos2x+1)/2+√3/2(cos2x-1)
=(√3+1)/2(sin2x+cos2x)+(√3-1)/2
=(√6+√2)/2sin(2x+π/4)+(√3-1)/2
2x+π/4=2kπ-π/2 , x=kπ-3π/8 , k∈Z
最小值f(kπ-3π/8)=-(√6+√2)/2+(√3-1)/2
函数f(x)=2cosxsin(x+π/3)-根号3sin^2x+sinxcosx的最小值为多少?此时x等于多少
函数f(x)=2cosxsin(x+π/3)-根号3sin²x+sinxcosx
已知函数f(x)=2cosxsin(x+60°)-根号3sin^2x+sinxcosx
已知函数f(x)=2cosxsin(x+π/3)-根号3sin^2x+sinxcosx+2(x∈R),
求函数f(x)=2cosxsin(x+60度)-根号3乘sin的平方x+sinxcosx的值域
设函数f(x)=2cosxsin(x+π/3)-根号3sin^2x+sinxcosx,x属于[0,π/2],求f(x)的
已知函数f(x)=2cosxsin(x+π/3)-根号3sin^2x+sinxcosx,求方程f（x）=x/50π的个数
已知函数f(x)=2cosxsin(x+π/3)-根号3sin^2x+sinxcosx,求函数F(X)的对称轴对称中心
已知函数f(x)=2cosxsin(x+π/3)-根号3sin^2x+sinxcosx+1 （1）求函数f(x)的最大之
已知函数y=2cosxsin(x+π/3)-根号3 *(sin^2) x +sinxcosx
已知函数f(x)=2cosxsin(x+π/3)-根号3sin^2x+sinxcosx 当x∈[0,π/4]时,f(x)
已知函数f【x】=2cosxsin【x+60】-根号3sin平方x+sinxcosx,求最小正周期