ĐƯNG TRN LƯNG GIC
!"
OP
!"#$%&'(
)*+,)#-./0123"45
362$78+2+9'(:-#;
:<9)2=>?@(,*.6'(#;
AB@C
D72E,!FGHIJKLFMN9)âm(,dương
#$%&
'
OP
(
OP
>
<
) )
'
P
(
P
)
tg
α
α
OQ
OM
'
AHAH
OA
OQ
α
AH
'
OQ
=
OP
PM
OM
'
OP
'
BK
OP
OM
BK
OB
g
α
BK
*+" !, "-&
/0 !,12"1&
/0 !,34"3&
= = =
= = =
=
=
=
=
= =
tg
α
=
PM
OP
OQ
OP
α
α
g
α
OP
PM
OP
OQ
α
α
=
=
tg
α
= =
=
g
α
/0 !, "-&
OP
OQ
>
)
M thuc ptư I:
)
)
)
)
α
>
)tg
α
>
)cotg
α
>
AH
BK
>
)
α
>
>
>
)
(
π
α
< <
.5678
»
AB
)
M thuc ptư II:
)
)
)
)
α
>
>
'
P
'
Q
)
α
<
'
OP
'
OQ
<
(
π
α π
< <
'
AH
'
BK
)tg
α
<
)cotg
α
<
<
<
'
H
'
K
.5678
»
BA
′
>
)
M thuc ptư III:
)
)
)
)tg
α
>
)cotg
α
>
>
)
α
<
<
(
H
(
K
(
P
(
Q
)
α
<
(
AH
(
BK
(
OP
(
OQ
9
(
π
π α
< <
.5678
¼
A B
′ ′
<
.5678
)
M thuc ptư IV:
)
)
)
>
)
α
>
<
)tg
α
<
)cotg
α
<
)
α
<
9
H
9
K
9
Q
9
P
9
OP
9
OQ
9
AH
9
BK
9
(
(
π
α π
< <
»
B A
′
<
<
'
O
O
O
0 1
O
0 1
O
/0 !, "-&
=
.:;<=>&
?@%- A &
O
O
=
=
'
OQ
2
O
=
'
0P1
(O28'(>0P1
O
QR
(
(
α
α
+
(
(
α
α
=
(
'
α
(
(
'
'
tg
α
α
+ =
(O28'(>0P1
O
QR
(
(
α
α
(
(
α
α
(
'
α
(
(
'
'
cotg
α
α
+ =
+
=
Btg cotg
α α
=
α
α
α
α
=
u ư ă
9 (
9
'
x x
tg x tg x tgx
x
+
= + + +
ả
VT
=
x x
x
+
(
'
x
C' Dtgx+
(
C' Dtg x+
9 (
'tg x tg x tgx+ + +
VP
x x
x x
+
÷
=
=
(
C' Dtg x+
=
=
C!D
*E&!=6 :+"FG
H>&
E
=
I
9 x
( I
( x x−
I J
9 (x x+ −
I I
9C Dx x+
−
J J
(C Dx x+
( ( ( ( ( 9 ( 9
9KC D C D L (KC D C D Lx x x x= + − +
( ( ( ( (
9KC D ( Lx x x x= + −
( ( I I ( (
(KC DC DLx x x x x x− + + −
( ( (
9C' ( Dx x= −
( ( ( ( ( ( (
(B'BKC D ( Lx x x x x x− + − −
( ( ( ( (
9 J (C' 9 Dx x x x= − − −
( ( ( (
9 J ( J 'x x x x= − − + =
I ( I (
C9 ( D C9 ( DE x x x x= − + −
=
*+5M:+"FG
*E&NEGAGAGB1&
N7>O&
9
C ( D
(
x
π
π
< <
( (
'x x+ =
( (
' x x= −
(
'
'
P
= − −
÷
IQ
IR
=
)x >
IQ IQ I 9
IR P P
x = = =
x
tgx
x
=
'
P
I 9
P
−
=
' P
P
I 9
= −
÷
'
I 9
= −
'
cotgx
tgx
=
'
'
I 9
=
−
I 9
'
'
= −
÷
÷
I 9= −
N &
(
x
'
'
IR
= −
D7
9
(
(
x
π
π
< <
'
P
x = −
)
)
)
J
π
9
π
I
π
(
π
)
9)
)
IS
)
J)
)
R)
α
α
α
tg
α
cotg
α
)
'
(
9
I
I
9
(
'
)
)
9
9
'
9
9
'
9
9
)
MS!
T9JU V
9JU VW=
)
α
=
'
α
=
)tg
α
=
cotg
α
= +∞
")T3U4*+,)#-./
#V:.W"
M A≡
{
X&
)
o
α
=
)C Drad
α
=
) B( B(k k
α π π
= + =
C Dk ∈¢
23A6!.Y 58!
Z"[\Z$<
]!67^"Z3A_
7@&
4 5&
5
) B9J) B9J)
o o o
k k
α
= + =
·
)
o
AOM =
'
α
= −
cotg
α
= −∞
M A
′
≡
{
)
α
=
)tg
α
=
23`A6!.Y 58!
Z"[\Z$<
]!67^"Z3`A_
7@&
X&
·
'Q)
o
AOA
′
=
)
'Q)
α
=
C Drad
α π
=
4 5&
5
) )
'Q) B9J)k
α
= +
(k
α π π
= +
C Dk ∈¢
'
α
=
)
α
=
tg
α
= +∞
)cotg
α
=
M B≡
{
X&
4 5&
5
21A6!.Y 58!
Z"[\Z$<
]!67^"Z1A_
7@&
·
R)
o
AOB =
(
π
α
=
)
R)
α
=
(
(
k
π
α π
= +
) )
R) B9J)k
α
= +
C Dk ∈¢
X&
4 5&
5
21`A6!.Y 58!
Z"[\Z$<
]!67^"Z1`A_
7@&
C Dk ∈¢
'
α
= −
tg
α
= −∞
M B
′
≡
{
)
α
=
)cotg
α
=
·
R)
o
AOB
′
= −
)
R)
α
= −
C D
(
rad
π
α
= −
) )
R) B9J)k
α
= − +
(
(
k
π
α π
= − +
'
α
=
)
α
=
'
α
= −
'
α
=
)
α
=
'
α
= −
)tg
α
=
tg
α
= +∞
tg
α
= −∞
)cotg
α
=
cotg
α
= +∞
cotg
α
= −∞
M A≡
M B≡
M A
′
≡
M B
′
≡
{
{
{
)
α
=
)tg
α
=
{
)
α
=
)cotg
α
=
C ( Dk
α π
=
C ( Dk
α π π
= +
C ( D
(
k
π
α π
= +
C ( D
(
k
π
α π
= − +
k
α π
=
(
k
π
α π
= +
C Dk ∈¢
Cc cung liên kt
C_a(bDc_
C_a(bDc_
C_a(bDc_
C_a(bDc_
1.Cung sai km k2π:
Nh :
ngha l :
=d
=d
=d
=d
T X=d
C_a(bD
_
C_a(bD
.
.`
`
e
e`
N
#f5.`6!;Gg .Y $O
f,Ng h7G,5&
X
,
i iC DOPM OQ M g c g∆ = ∆ − −
¼
i
(
đ AM
π
α
= −
#+;7j57 "
8&
iOP OQ=
PM Q M
′ ′
=
OQ OP
′
=
(
π
α α
= −
÷
{
{
iOP OQ=
{
(
π
α α
= −
÷
¼
Ađ AM
α
=
¼
¼
đ AM đ M B
′
=
(B&
N "Z"F&
(
π
α
−
÷
c_
c_
c_
c_
(
π
α
−
÷
(
π
α
−
÷
(
π
α
−
÷
(
π
α
−
÷
Nh :
k &
=d
=d
=d
=d
-X0
(
π
α
−
÷
α
X
,
.
.`
e
e`
-
9B;&Cl_D
¼
¼
AM AM
′
=
¼
¼
đ AM đ AM
′
= −
#f5.`6!;G
g .Y 7&
OPM OPM
′
∆ = ∆
OP OP=
{
{
{
{
OP OP=
C D
α α
= −
C D
α α
= − −
C D
α α
− =
C D
α α
− = −
{
C Dtg tg
α α
− = −
C Dcotg cotg
α α
− = −
PM PM
′
= −
OQ OQ
′
= −