(2013•浙江模拟)已知函数f(x)=23sinxcosx+2cos2x-t.
来源:学生作业帮 编辑:神马作文网作业帮 分类:综合作业 时间:2024/09/24 04:15:24
(2013•浙江模拟)已知函数f(x)=2
3 |
(I)∵sinxcosx=
1
2sin2x,cos2x=
1
2(1+cos2x)
∴f(x)=2
3sinxcosx+2cos2x-t=
3sin2x+cos2x+1-t
=2(sin2xcos
π
6+cos2xsin
π
6)+1-t=2sin(2x+
π
6)+1-t
当x∈[0,
π
2]时,2x+
π
6∈[
π
6,
7π
6],可得-
1
2≤sin(2x+
π
6)≤1
∴方程f(x)=0有解,即
−1+1−t≤0
2+1−t≥0,解之得0≤t≤3;
(II)∵t=3,
∴f(x)=2sin(2x+
π
6)+1-t=2sin(2x+
π
6)-2
可得f(A)=2sin(2A+
π
6)-2=-1,sin(2A+
π
6)=
1
2sin2x,cos2x=
1
2(1+cos2x)
∴f(x)=2
3sinxcosx+2cos2x-t=
3sin2x+cos2x+1-t
=2(sin2xcos
π
6+cos2xsin
π
6)+1-t=2sin(2x+
π
6)+1-t
当x∈[0,
π
2]时,2x+
π
6∈[
π
6,
7π
6],可得-
1
2≤sin(2x+
π
6)≤1
∴方程f(x)=0有解,即
−1+1−t≤0
2+1−t≥0,解之得0≤t≤3;
(II)∵t=3,
∴f(x)=2sin(2x+
π
6)+1-t=2sin(2x+
π
6)-2
可得f(A)=2sin(2A+
π
6)-2=-1,sin(2A+
π
6)=
(2013•浙江模拟)已知函数f(x)=23sinxcosx+2cos2x-t.
(2005•浙江)已知函数f(x)=2sinxcosx+cos2x
(2011•重庆模拟)已知函数f(x)=23cos2x+2sinxcosx+m(x∈R).
(2013•河北区一模)已知函数f(x)=2cos2x+23sinxcosx
(2013•天津模拟)已知函数f(x)=sin2x+23sinxcosx+3cos2x,x∈R.求:
(2012•南昌模拟)已知函数f(x)=3sin2x+23sinxcosx+5cos2x. &nb
(2014•安徽模拟)已知f(x)=3sinxcosx-cos2x+12.
(2013•东莞二模)已知函数f(x)=23sinxcosx−2cos2x+1.
(2013•房山区一模)已知函数f(x)=2cos2x+23sinxcosx−1.
(2013•红桥区二模)已知函数f(x)=sin2x+2sinxcosx+3cos2x.
(2014•安徽模拟)设函数f(x)=2cos2x+23sinxcosx-1(x∈R).
(2014•大港区二模)已知函数f(x)=sinxcosx+3cos2x.