- 高数已知函数f(x)=2cosxsin(x+π/3)
- 已知f(x)=2cosxsin(x+π/3)-根号3sin平方x+sinxcosx
1.求f(x)的最小周期;2.求f(x)的最小值及取得最小值时相应的x的值
- 已知函数f(x)=2cosxsin(x+π/3)-√3sin²x+sinxcosx
1.求f(x)的最小周期;2.求f(x)的最小值及取得最小值时相应的x的值
f(x)= 2cosxsin(x+π/3)-√3sin²x+sinxcosx
= 2cosxsin(x+π/3)-2sinx[(√3/2)sinx-(1/2)cosx]
= 2cosxsin(x+π/3)-2sinx[sin(π/3)sinx-cos(π/3)cosx]
= 2cosxsin(x+π/3)+2sinxcos(x+π/3)
= 2sin(2x+π/3)
最小正周期 T=2π/2=π
f(x)的最小值 = 2,此时,2x+π/3=2kπ+π/2--->x=kπ+π/12,k∈Z