内容正文:
书书书
!" ω=
kπ
2
-π
6
,k∈Z,#0<ω<π2
,
$% ω=π3
.
(2)
&
(1)
'
,f(x)=2sin π
3
x+π( )3 ,
()
AB∥x*,+ B,-./)槡3,
(01
f(x)=槡3,2 sin
π
3
x+π( )3 =槡
3
2
,
!"
π
3
x+π
3
=2kπ+π33
π
3
x+π
3
=2kπ+
2π
3
,k∈Z,
$%
x=6k
3
x=6k+1,k∈Z,&456'B(1,槡3).
$%
→CA=(-2,槡3),
→CB=(-1,槡3),
$%
→|CA|=槡7,
→|CB|=2,
$%
cos∠ACB=
→CA·→CB
→ →|CA||CB|
= 5
槡27
= 槡57
14
.
21.(1)
!"
:
&789:;槡2a(槡2cosC-1)=
(c4sin2A2- )1 ,
"槡2sinA(槡2cosC-1)=sin (C 4sin2A2- )1 ,
$%槡2sinA(槡2cosC-1)=sinC(1-2cosA),
2
2sinAcosC-槡2sinA=sinC-2sinCcosA,
$%
2(sinAcosC+sinCcosA)=sinC+槡2sinA,
2
2sin(A+C)=sinC+槡2sinA.
()
sin(A+C)=sin(π-B)=sinB,
$%
2sinB=sinC+槡2sinA,
<=789:6"
2b=c+槡2a,
2槡2a,b,c>?@AB.
(2)
#
:
&
(1)
6'
,b=槡2a+c
2
.
C △ABCD,&E89:"
cosB=a
2+c2-b2
2ac
=
a2+c2 (- 槡2a+c)2
2
2ac
=
2a2+3c2- 槡22ac
8ac ≥
槡26ac- 槡22ac
8ac
=槡6-槡2
4
(
!"
#!
2a2 =3c2
$
,
%&'(
),
$%
sinB= 1-cos2槡 B≤ 1 (- 槡6-槡2)4槡
2
=槡6+槡2
4
,
F
BC
GH,I
h=c·sinB≤4×槡
6+槡2
4
=槡6+槡2,
$%
BC
GH,I,JKLMN
(0,槡6+槡2].
22.
#
:(1)f(x)=a·b
=(cos2ωx-sin2ωx,sinωx)·(槡3,2cosωx)
=槡3(cos
2ωx-sin2ωx)+2sinωxcosωx
=槡3cos2ωx+sin2ωx=2sin2ωx+
π( )3 .
&OP
x=π
2NQA
f(x)
5R,STUV*
,
6"
2sinπω+π( )3 =±2,
$% πω+π3
=kπ+π2
(k∈Z),
2 ω=k+
1
6
(k∈Z).
W ω∈(0,1),k∈Z,$% ω=
1
6
,
$%
f(x)=2sin 1
3
x+π( )3 .
(2)
X
y=f(x)
5RHYZ,[./\)]^,
1
6
,
_X$"5R`abc
π
3def
,
-./g\
,
"
h
y=2sin2x-π( )3 ,5R.
$%
h(x)=2sin2x-π( )3 .
1
2x-π
3
=t,
()
0≤x≤ π2
,
$%
-π
3≤
t≤
2
3π
.
iNjk
h(x)+k=0
Clm 0,π[ ]2 Hnopn
SdqA!
,
2jk
2sint+k=0
C
t∈ -π
3
,
2π[ ]3 H
n o p n S d q A !
,
r 2
y = 2sint,t∈
-π
3
,
2π[ ]3 s y=-k,5RnopnSdtZ,iN
uv5R
,
wx6'
-槡3≤-k<槡33-k=2.
+
-槡3<k≤槡33 k=-2.
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