(2014•嘉兴模拟)已知函数f(x)=2sin(x+π3)cosx.
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(2014•嘉兴模拟)已知函数f(x)=2sin(x+
π |
3 |
![(2014•嘉兴模拟)已知函数f(x)=2sin(x+π3)cosx.](/uploads/image/z/15655880-56-0.jpg?t=%EF%BC%882014%E2%80%A2%E5%98%89%E5%85%B4%E6%A8%A1%E6%8B%9F%EF%BC%89%E5%B7%B2%E7%9F%A5%E5%87%BD%E6%95%B0f%EF%BC%88x%EF%BC%89%3D2sin%EF%BC%88x%2B%CF%803%EF%BC%89cosx%EF%BC%8E)
(1)∵f(x)=(sinx+
3cosx)cosx
=sinxcosx+
3cos2x
=
1
2sin2x+
3
2cos2x+
3
2
=sin(2x+
π
3)+
3
2,
∵-1≤sin(2x+
π
3)≤1,
∴函数f(x)的值域是[
3−2
2,
3cosx)cosx
=sinxcosx+
3cos2x
=
1
2sin2x+
3
2cos2x+
3
2
=sin(2x+
π
3)+
3
2,
∵-1≤sin(2x+
π
3)≤1,
∴函数f(x)的值域是[
3−2
2,
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