BÀI TẬP LƯỢNG GIÁC
Bạn đang xem bản rút gọn của tài liệu. Xem và tải ngay bản đầy đủ của tài liệu tại đây (137.33 KB, 13 trang )
! " #
$%&''(!)*
+
# ,+
-
, .!
+
# ,+
"
∈
&!
# "
!&!
$/&''0!)*
+ +
# , , .!
1 "
∈
"
"
" "# 2 !
$&''0!)*
+
#& ,+
-
, .!
+ +
# ,
2 (
∈
2
" 3&" &#'
$%&''0!)*
+ +
# ,
1 "
, .!
+ +
#& ,
-
∈
3
2 2
2 ! "2#
)*
+ +
#& ,
, .!
+ +
# ,
2
∈
-
4 #&4
5678497:;
+ +
<& = >
)*
& 4 "≤ ≤
(
(& "(#&
?9@4
+ -+
= !
3 (
∈
)*
3"+ "3+ 30+
# = =
12 12 12
1
"
""& " 0#2 "
)*
+ +
# ,
1 0
, .!
(+ +
# ,
32 0
∈
0
9A&& & !#'
)*
#'
'
"
1#
)*
+
"#
"
÷
0- &" #1
)*
#
#&2
)*
#
"
& #( &2
)*
#
2
& #" &
)*
# = &#'
3
+
" ! # & !
-
)*
+
& !#&
-
-
"
#'
)*
#=9A#&
(
&
9#
)*
+
#'= !#&
2
1
2 2
2 ! "2#
)*
+ +
2& !#
" "
0
" "
# 2
)*
+
!#&
2
'
9A&" 9#2 " !
)*
9A#& "
+
& !#
"
" "
#&
)*
#'
2 2
+
!#
2 2
)*
+
& !#&
2
"
" "
2 "2 "" " 2#"
)*
+ +
2 !#
" -
2
& & #4
?9@44A 7 B7CD69E@756784F)*
' '
4
− +
≤ ≤
3
"+
32 &!
-9AG
#
9AG
?9@4αHIB7CD69E@756784
G#'
)J?")K
" "
& " # & "
$&''0!)*
9A#& "
9A#
9A#&
9A!#" &!"
)*
9A#&
9A #"
"
"
+
1 !# "
"
)*
9A#'
"
9A#
"
9A# "
2
"
&2 #'
)*
9A#
3
4&! &4! #4
?9@44HIB7CD69E@7LM56784
)*
& 4
≤ ≤
-
4 &2 4&#'
?9@44HIB7CD69E@7LM5678497:;
+
'= !
2
)*
1
N4N
"
(
& "#
)*
9A#'=9A#& "
1
" "
&2 &" #'
)*
"
9A#&=9A#O
"
0
2 2
" &2 #'
)*
9A#O=9A#O "
'
9A#"
)*
9A#
"
"#-
)*
9A#=9A#O "
9&# &
9A
$/&''"!)*
9A#
"
" " #'
)*
9A#&=9A#O "
2
"
32
-& #
)*
9A#
3
"
&2 #'
)*
9A#
-
9A & #" !
)*
9A#&=9A#O "
(
"
2&-4! "4&!4&! &24&"! #'
A PB7CD69E@7,74#
Q @44HIB7CD69E@7567845R:M7S94;967849ET
+
<'= >
2
")KU
! !#
$/&''(!)*
#
" "
"
#
)*
#&
"
9A#
)*
# = #&
2
& 2#
)*
#'
3
" "
& #4
?9@44HIB7CD69E@756784)*
& 4
≤ ≤
-
"
#'
)*
+ +
# , = # &, .!
2 "
ϕ ϕ
± ∈
(
" "
"
&#
)*
+
+
# & 4+
# ,+
2
9#* , .!=9# "&* 4 .
"+
#,+
# & 4+
2
ϕ
ϕ
∈ ∈
1
!#9A 9
)*
+
# ,+ , .!
2
∈
0
" 9& !&39A&!#
)*
+
#G& ,+
"
2
, .!=#V7+9A# !7 .
"+
3
# &G,+
2
∈ ∈
'
"!+
"9A &9A #1 & !
2
)*
+ &
9A # = !#
" 2
" "
&# &
)*
9A#= #'= #&
" 2 " 2
#
)*
9A#= #&
"
" "
9A & ! &#'
)*
#=9A#= #'
2
"
! &"&"#'
)*
+ +
& !#'= & !#
2 2
3
9#
)*
3&
# =& #
-
3#& !& !
)*
+
& !#
2
(
" "
#
)*
9A#&=& #&
1
"9A 29A2 9" 9 #'
)*
+
#& ,+
2
0
" "
9A9A 9A 9 9 9 #-
)*
#
'
9A 39A3 92#'
)*
#&
4 !#
9@44HIB7CD69E@75678497:;H W
+
<'= >
)*
4 &!
≤ ≤
" "
#4
?9@44HIB7CD69E@756784)*
4
∀ ∈
"
4 ! 9A 9 !#'
?9@44HIB7CD69E@75
67849ET
+
'= !
)*
4 ≤ −
2
#4 !
?9@44HIB7CD69E@75X9
7S94;967849ET
+
<'= >
)*
4 ≤
3
9 49A 9!#'
?9@44HIB7CD69E@756784)*
4 ≥
2YZ[\%]^_)`a`)b
YZ[
!#
$%&''1! )*
#& =#
(&#
$&''(! )*
2#'="#
"
- -
!&
#'
&
$/&''-! )*
3+
# ,+, .!
2
∈
2
" & #'
$/&''3! )*
2#
3
+
& !9A & #'
2
$%&''"! )*
#=#=9A#
-
&9A!!#9A
)*
9A#'=9A#&
(
"&2 !#
)*
+
-# &!
1
2 "9A &2 " "9A2#'
)*
"
#
9A#&
"
0
1 2 & "#'
)*
2#&
"#
'
" "
"
" " !# "
"2
)*
2 '
#
" O
≠
≠
!
2 2
& #
& 2! #-"
"
" "
&
#
2
"& & #
3
" " ! + − = +
-
3
3+
9A 9 # !
2
(
"
&#'
2
1
2 -# "
0
& "& "& 2#'
'
2 & & 2#
9A9A" #'
"
" & #'
!!"##$%!
3YZ[U/c
3 & #'
)*
'
#
≤
" " " "
9 9A#
)*
'
#
≥
"
+
1 #" !
2
)*
+
" ! '
2
#
≥
2
&
#2
)*
" "
# =#&
≥
3
" " #
)*
+
!#
"
-
" 9A !#3" !
)*
9A#"
(
& ! # 2
)*
+
,+
2
= ±
1
" "
9! 9A!#
)*
'
+ ≥
=
0
#
)*
9A#&= #
-%d/e[
X7f65gA∆/h:
"
!/! /!#
)*
+
/##
-
X7f65gA∆/h:
3
/ " ! #'
)*
'
/#"' =#
" 7i647∆/5#'
'
h:
/
/& #
2 X7f65gA∆/Qh9jH "659W 97L7SBj;6kL
" "
/#
3 X7f65gA∆/h:
Q A
/#
≤
)*
' '
/#0' =##23
- 7 ∆/,7l69m97nA4oHp:,8
/ #"
?9X7QA
65gA∆/)*
' '
/#0' =##23
( 7i647Eq6∆/5X97S94;965Qq6-'
'
,7kL7r,7
/
# "
/
1 7i647∆/k:l6,7
A
9 #
Q
0 7i647h:∆/k:l69W/h:
Q A
#
'7i647∆/k:l6h:
/ /
& #
7i647∆/k:l69W/h:
" !2 !#3
7i647∆/5
/#2/
97@sL∆k:l6
"7i647h:∆/5
9A/9A# 9
97@∆t
27i647∆/th:
" "
/ /
#
37i647h:∆/th:
/
# 9 / 9 !
/
-7i647∆/th:
AQ#9A A9A/Q9A!
(7 ∆/97nA4o
A &Q /#A/&Q
?7i647∆/k:l6
7AMtF
1∆/sL∆6@h:
( )
A Q /&!#A &Q !/!
(PHƯƠNG TRÌNH LƯỢNG GIÁC TRONG ĐỀ THI ĐẠI HỌC
TỪ NĂM 2002 ĐẾN 2013
Bài 1 (ĐH A2002) @4678497:;,7 P6'=
π
!gAB7CD69E@7*
" "
3 "
+
+ = +
÷
+
ĐS :
3
=
" "
π π
= =
Bài 2 (ĐH B2002) PB7CD69E@7*
" 2 3 - − = −
ĐS :
=
0
π π
= =
&∈
!
Bài 3 (ĐH D2002)@497:;H W
[ ]
'=2
6784Hu6gAB7CD69E@7*
" 2 " 2 '
− + − =
ĐS :
" 3 (
= = =
π π π π
= = = =
Bài 4 (ĐH A2003) PQS9B7CD69E@7*
9
9A
− = + −
+
ĐS :
2
π
π
= +
&∈
!
Bài 5 (ĐH B2003) PQS9B7CD69E@7*
9 9A 2
− + =
ĐS :
"
π
π
= ± +
&∈
!
Bài 6 (ĐH D2003) PB7CD69E@7*
9A 9 '
2
π
− − =
÷
ĐS :
=
2
π
π π π
= + = − +
&∈
!
Bài 7 (ĐH A2004) 7 9A46f/,7l69m?97nA4oHp:,8*
"' ( ) *
+ + =
X7QA65gA9A46f/ĐS :
' '
0' = 23( ) *= = =
Bài 8 (ĐH B2004) PB7CD69E@7*
3 " ! 9A
− = −
ĐS :
3
=
- -
π π
π π
= + = +
&∈
!
Bài 9 (ĐH D2004) PB7CD69E@7*
! !
− + = −
ĐS :
=
" 2
π π
π π
= ± + = − +
&∈
!
Bài 10 (ĐH A2005) PB7CD69E@7*
" '' '
− =
ĐS :
π
=
&
∈
!
Bài 11 (ĐH B2005) PB7CD69E@7*
' '
+ + + + =
ĐS :
=
" 2
π π
π π
= ± + = − +
&∈
!
Bài 12 (ĐH D2005) PB7CD69E@7*
2 2
"
" '
2 2
' '
π π
+ + − − − =
÷ ÷
ĐS :
2
π
π
= +
&∈
!
Bài 13 (ĐH A2006) PB7CD69E@7*
- -
!
'
'
+ −
=
−
ĐS :
3
2
π
π
= +
&
∈
!
Bài 14 (ĐH B2006) PB7CD69E@7*
9 9A 9A 2
+ + =
÷
ĐS :
3
=
π π
π π
= + = +
&∈
!
Bài 15 (ĐH D2006) PB7CD69E@7*
" '' '
+ − − =
ĐS :
=
"
π
π π
= = ± +
&
∈
!
Bài 16 (ĐH A2007) P78B7CD69E@7*
( ) ( )
+ + + = +
ĐS :
= =
2
π π
π π π
= = + = − +
&
∈
!
Bài 17 (ĐH B2007) P78B7CD69E@7
( + − =
ĐS :
3
= =
1 2 1 " 1 "
π π π π π π
= + = + = +
&
∈
!
Bài 18 (ĐH D2007) P78B7CD69E@7*
"
+ + =
÷
ĐS :
=
-
π π
π π
= + = − +
&∈
!
Bài 19 (ĐH A2008) P78B7CD69E@7*
(
2 !
"
2
!
π
π
+ = −
−
ĐS :
3
= =
2 1 1
π π π
π π π
= − + = − + = +
&∈
!
Bài 20 (ĐH B2008) P78B7CD69E@7*
" "
" " ' − = −
ĐS :
=
2 "
π π π
π
= + = − +
&∈
!
Bài 21 (ĐH D2008) P78B7CD69E@7*
( )
+ + = +
ĐS :
=
" 2
π π
π π
= ± + = +
&∈
!
Bài 22 (ĐH A2009) PB7CD69E@7*
( )
( ) ( )
"
−
=
+ −
ĐS :
1 "
π π
= − +
&
∈
!
Bài 23 (ĐH B2009)PB7CD69E@7*
( )
"
" " 2 + + = +
ĐS :
=
- 2 (
π π π
π
= − + = +
&∈
!
Bài 24 (ĐH D2009) PB7CD69E@7*
" 3 " '− − =
ĐS :
=
1 " -
π π π π
= + = − +
&∈
!
Bài 25 (ĐH A2010) PB7CD69E@7*
! !
2
9 A
π
+ + +
=
+
ĐS :
(
=
- -
π π
π π
= − + = +
&
∈
!
Bài 26 (ĐH B2010) PB7CD69E@7*
! #' ' ' + + −
ĐS :
2
π π
= +
&∈
!
Bài 27 (ĐH D2010) PB7CD69E@7*
" ' − + − − =
ĐS :
3
=
- -
π π
π π
= + = +
&
∈
!
Bài 28 (ĐH A2011) PB7CD69E@7*
9
'
+ +
=
+
ĐS :
=
2
π π
π π
= + = +
&
∈
!
Bài 29 (ĐH B2011) PB7CD69E@7*
# +
ĐS :
=
" "
π π π
π
= + = +
&
∈
!
Bài 30 (ĐH D2011) PB7CD69E@7*
'
" 9 A
+ − −
=
+
ĐS :
"
π
π
= +
&∈
!
Bài 31 (ĐH A2012) PB7CD69E@7*
" # &
ĐS :
= =
"
π π
π π π
= + = = +
&
∈
!
Bài 32 (ĐH B2012) PB7CD69E@7*
" ! "
+ = − +
ĐS :
=
" "
π π
π
= + =
&∈
!
Bài 33 (ĐH D2012) PB7CD69E@7*
" "v #
ĐS :
(
= =
2
π π π π
π π
= + = + = − +
&∈
!
Bài 34 (ĐH A2013) PB7CD69E@7*
9A
2
π
+ = +
÷
ĐS :
=
2 "
π π
π π
= − + = ± +
&∈
!
Bài 35 (ĐH B2013) PB7CD69E@7*
3 + =
ĐS :
=
- " 2 (
π π π π
= − + = − +
&
∈
!
Bài 36 (ĐH D2013) PB7CD69E@7
" '
+ − =
ĐS :
(
= =
2 - -
π π π π
π π
= + = − + = +
&
∈
!
