(2010•内江二模)已知函数f(x)=2cosxsin(x+π3)−3sin2x+sinxcosx.
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(2010•内江二模)已知函数f(x)=2cosxsin(x+
)−
sin
π |
3 |
3 |
![(2010•内江二模)已知函数f(x)=2cosxsin(x+π3)−3sin2x+sinxcosx.](/uploads/image/z/18545732-44-2.jpg?t=%EF%BC%882010%E2%80%A2%E5%86%85%E6%B1%9F%E4%BA%8C%E6%A8%A1%EF%BC%89%E5%B7%B2%E7%9F%A5%E5%87%BD%E6%95%B0f%28x%29%EF%BC%9D2cosxsin%28x%2B%CF%803%29%E2%88%923sin2x%2Bsinxcosx%EF%BC%8E)
(1)函数f(x)=2cosxsin(x+
π
3)−
3sin2x+sinxcosx.
=2cosx(sinxcos
π
3+cosxsin
π
3)-
3sin2x+sinxcosx
=2sinxcosx+
3cos2x=2sin(2x+
π
3)
∴f(x)的最小正周期T=π.
f(x)的单调增区间为:[kπ-
5π
12,kπ+
π
12],k∈Z
(2)当2x=
π
3=2kπ-
π
2,k∈Z
即:x=kπ-
5π
12 k∈Z时,f(x)取最小值-2.
π
3)−
3sin2x+sinxcosx.
=2cosx(sinxcos
π
3+cosxsin
π
3)-
3sin2x+sinxcosx
=2sinxcosx+
3cos2x=2sin(2x+
π
3)
∴f(x)的最小正周期T=π.
f(x)的单调增区间为:[kπ-
5π
12,kπ+
π
12],k∈Z
(2)当2x=
π
3=2kπ-
π
2,k∈Z
即:x=kπ-
5π
12 k∈Z时,f(x)取最小值-2.
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