已知函数f（x）=2√3sinxcosx-2sin²x+1
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解决时间 2021-04-03 10:22
- 提问者网友：辞取
- 2021-04-02 22:42
已知函数f（x）=2√3sinxcosx-2sin²x+1
最佳答案
- 五星知识达人网友：狂恋
- 2021-04-02 23:48
f（x）=2√3sinxcosx-2sin²x+1
=√3sin2x+cos2x
=2sin(2x+π/6)
(2) 2kπ-π/2<=2x+π/6<=2kπ+π/2
kπ-π/3<=x<=kπ+π/6
增区间 【kπ-π/3，kπ+π/6】 k∈Z
（2）x∈【0，π/2】
2x+π/6∈【π/6，7π/6】
x=π/2 fmin=-1
(3) f（x0）=6/5
sin(2x0+π/6)=3/5 x0∈[π/4，π/2]，2x0+π/6∈[2π/3，7π/6]，
cos(2x0+π/6)=-4/5
sin2x0=sin[(2x0+π/6)-π/6]
=sin(2x0+π/6)cosπ/6-cos(2x0+π/6)sinπ/6
=3/5*√3/2+4/5*1/2
=(3√3+4)/10
=√3sin2x+cos2x
=2sin(2x+π/6)
(2) 2kπ-π/2<=2x+π/6<=2kπ+π/2
kπ-π/3<=x<=kπ+π/6
增区间 【kπ-π/3，kπ+π/6】 k∈Z
（2）x∈【0，π/2】
2x+π/6∈【π/6，7π/6】
x=π/2 fmin=-1
(3) f（x0）=6/5
sin(2x0+π/6)=3/5 x0∈[π/4，π/2]，2x0+π/6∈[2π/3，7π/6]，
cos(2x0+π/6)=-4/5
sin2x0=sin[(2x0+π/6)-π/6]
=sin(2x0+π/6)cosπ/6-cos(2x0+π/6)sinπ/6
=3/5*√3/2+4/5*1/2
=(3√3+4)/10
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