I/. GOC - CUNG LệễẽNG GIAC
Bi 1: i ra n v radian cỏc gúc (cung) cú s o:
a/ 15
o
b/ 12
o
30 c/ -200
o
Bi 2: i ra n v ( phỳt, giõy) cỏc gúc (cung) cú s o:
5 3
a / b / c /
6 7 5
p p p
-
Bi 3: Cho
( )
( )
Ou,Ov k2 k Z
8
p
p
= + ẻ
uur uur
a/ Tỡm k
( )
63
Ou, Ov
8
p
=-
uur uur
b/ Giỏ tr
65
8
p
-
cú phi l 1 s o ca
( )
Ou, Ov
uur uur
khụng ? ti
sao?
Bi 4: Tỡm im ngn ca cỏc cung sau:
ẳ
ằ
ằ
k2
a / AM k b / AN k. c / AP
3 2 3 3
p p p p
p
= = + =- +
II/. GIA TRề LệễẽNG GIAC
Bi 1: Cho
sin 0,8 < < .Tớnh cos ,tan ,cot .
2
p
a a p a a a
ổ ử
ữ
ỗ
=
ữ
ỗ
ữ
ỗ
ố ứ
Bi 2: Cho 5cosa + 4 = 0
( )
o o
180 < a < 270
.Tớnh sina , tana, cota.
Bi 3: Cho
o o o o
tan15 2 3. Tớnh sin15 ,cos15 ,cot15 .= -
Bi 4: Tớnh
tan x cot x
A
tan x cot x
+
=
-
bit
1
sinx = .
3
Bi 5: Tớnh
2sin x 3cos x
B
3sin x 2cos x
+
=
-
bit tanx = -2
Bi 6: Tớnh
2 2
2
sin x 3sin x cosx 2cos x
C
1 4sin x
+ -
=
+
bit cotx = -3
Bi 7: n gin biu thc:
( ) ( )
2
2 2
2
2cos x 1 sin x tan x cos x.tan x
A ; C sin x 1 cot x cos x 1 tan x ; B sin x.cot x; D cot x.cos x
sin x cos x tan x
sin x
- +
= = + + + = - = -
+
Bi 8: Chng minh:
4 4 2 2 6 6 2 2
a/sin x+cos x=1-2sin xcos x; b/sin x+cos x=1-3sin xcos x
(s dng nh 1 cụng thc)
2 2 2 2 2 2
c/tan x = sin x+sin x.tan x; d/sin x.tanx + cos x.cotx + 2sinx.cosx = tanx + cotx
Bi 9: Chng minh:
2 2
2 2 2
2 2 2
1-2cos x 1+sin x cosx 1
a/ = tan x-cot x; b/ = 1+2tan x; c/ +tanx =
1+sinx cosx
sin x.cos x 1-sin x
sinx 1+cosx 2 1-sinx cosx sinx+cosx-1 cosx
d/ + = ; e/ = ; f/ =
1+cosx sinx sinx cosx 1+sinx sinx-cosx+1 1+sinx
1+cosx
g/
( )
( )
2 2
2 2 2 2
2
2 2 2 2
1-cosx 4cotx sin x cos x
- = ; h/1- - = sinx.cosx;
1-cosx 1+cosx sinx 1+cotx 1+tanx
1 tan x-tan y sin x-sin y
i/ 1-cosx 1+cot x = ; j/ =
1+cosx
tan x.tan y sin x.sin y
Bi 10: Chng minh cỏc biu thc sau c lp i vi x:
( ) ( ) ( ) ( )
( ) ( ) ( ) ( )
6 6 4 4 4 2 4 2
2
4 4 2 2 8 8 8 8 6 6 4
6 6
4 2 4 2
4 4
A=2 sin x+cos x -3 sin x+cos x ; B=cos x 2cos x-3 +sin x 2sin x-3
C=2 sin x+cos x+sin xcos x - sin x+cos x ; D=3 sin x-cos x +4 cos x-2sin x +6sin x
sin x+cos x-1
E= sin x+4cos x + cos x+4sin x; F= ;
sin x+cos x-1
4 4
6 6 4
2 2
sin x+3cos x-1
G=
sin x+cos x+3cos x-1
H=cosx 1-sinx 1-cosx 1-sin x +sinx 1-cosx 1-sinx 1-cos x ;(x 0; )
2
p
ộ ự
ờ ỳ
ẻ
ờ ỳ
ở ỷ