Trigonometry
,Amistad
"
REDUCTIONRULESTHEt80.RU
→
then
If an angle involves a
multiple of 180 and some acute
to the same ratio of the acute
angle
,
it is numerically equal
angle
s.gl?EEnam-ple..s
.
To determine its sign ,
use the CAST
diagram .
"
±
¥¥Tt
- -
.
¥¥
-
.
.
.
it ii) 246
costs
finsin (180+60)
-
-
-
-
=
COS (180-30)
=
o =
Sind
-
-
NBZB.ir)
-
-
-
"
iii. tan 315
tan (360-45) =
cos570
Cos (540+30) a#
549-0
=
-tan45_ = -
Cogeco
D= sin 1110
Sin (1080+30) f÷
sin30-NEGATIVEANGLESCUSINal80.ru#
=
→ ADD 360°
i ) tan C 60 ) -
360)
taf¥ff
soo
I
ii ) sin f-225)
= Sin (-2251-360)
= sin 135
= Sin (180-45)
=
sin45
, THE 90 RULE
⑧
→
If an angle involves 90 or 210 and some acute
angleTothen
,
it
determine
is
numerically equal to the co ratio of
-
the acute
angle .
its reference to the ratio
sign the
,
use CAST
diagram with
original .
i) Ii) sin 110
'
cos 10 I I
=
Cos (90-80) tho -
O
=
Sin (180-70) 180¥
ing sin 70
-
-
=
=
sin (90-20)
=
Costco
GENERALITIES
→ Read the angles L -
R
(O 180)
#
i) wink:Fiftifuad
Sin
.i
-
because sin is tore
= -
Sin @ .
.
#
ii ) cost x )
Addofi
)
-
=
cos I -
at360
+ soo
in
=
Cosa
Naka Add 360 to negative anglesZ in your
general solution too :
0=-43
°
t k 360
. K E
O = -
430 t 360 t k 360 .
=
317 t k 360.
-
, COMPOUND ANGLES
⑧
Formed by
suN_orDtFFof2or@angles.a taking
→ the
)
n
" "
.
am zoo Main
28+0
a +
-
SUM of
-
2 Angles
Soul of
2 Angles
IsBB.DE#t0NS
① Costain Accepted without proof
② cos Cat B) shot 9:#Iat
= cos C- BD ,
EA -
to a so
=
cos A. cost B) t sin A. sin C- B) -
=
COSA cos B t sin At sin B)
.
sina.sinB.i.COSCATBI-coSA.cosb-sinA.si#T
= COSA .
Cos B -
③ Sinha B) -
④ sinfatb )
= Cos [90 -
CA -
BD = Sin LA EB)] -
=
Cos Cao -
Atb ) =
sin A. cost B ) - -
COSA sine B )
.
-
= Cos Gao -
A) EB) ]-
=
Sin A. cos B -
COSA C-sin B)
-
= COSMO -
A) -
cost B) t Sinko A) sin C-B)
-
= sin A. cos B t cos A. sink
sinCATBJ-sinA.cosbtcoSA.sn#--sinA.oosB
Bt sin A. cos COSA C-sin B) :
=
. .
B -
COSA Sin.
sinta-BI-sinA.cosB-cosA.sn#DoubleAngles-
i
.
⑤ sin 2A →
From ④ ⑥ cos 2A →
From ②
=
sin # +A) = COSCA + A)
=
sina.cosatcoSA.sn A =
COSA Cosa sin A. sin A
-
-
= 25in A. cos A = Costa Sinha -
: . sin2A-2sinA.co# : . cos2A=Cos2A-Sin#
but sin2Atcos2A= I
}
'
Sinha = I -
cos 2A
D. O T S
.
.
COSTA I Sinan
- -
= -
,Amistad
"
REDUCTIONRULESTHEt80.RU
→
then
If an angle involves a
multiple of 180 and some acute
to the same ratio of the acute
angle
,
it is numerically equal
angle
s.gl?EEnam-ple..s
.
To determine its sign ,
use the CAST
diagram .
"
±
¥¥Tt
- -
.
¥¥
-
.
.
.
it ii) 246
costs
finsin (180+60)
-
-
-
-
=
COS (180-30)
=
o =
Sind
-
-
NBZB.ir)
-
-
-
"
iii. tan 315
tan (360-45) =
cos570
Cos (540+30) a#
549-0
=
-tan45_ = -
Cogeco
D= sin 1110
Sin (1080+30) f÷
sin30-NEGATIVEANGLESCUSINal80.ru#
=
→ ADD 360°
i ) tan C 60 ) -
360)
taf¥ff
soo
I
ii ) sin f-225)
= Sin (-2251-360)
= sin 135
= Sin (180-45)
=
sin45
, THE 90 RULE
⑧
→
If an angle involves 90 or 210 and some acute
angleTothen
,
it
determine
is
numerically equal to the co ratio of
-
the acute
angle .
its reference to the ratio
sign the
,
use CAST
diagram with
original .
i) Ii) sin 110
'
cos 10 I I
=
Cos (90-80) tho -
O
=
Sin (180-70) 180¥
ing sin 70
-
-
=
=
sin (90-20)
=
Costco
GENERALITIES
→ Read the angles L -
R
(O 180)
#
i) wink:Fiftifuad
Sin
.i
-
because sin is tore
= -
Sin @ .
.
#
ii ) cost x )
Addofi
)
-
=
cos I -
at360
+ soo
in
=
Cosa
Naka Add 360 to negative anglesZ in your
general solution too :
0=-43
°
t k 360
. K E
O = -
430 t 360 t k 360 .
=
317 t k 360.
-
, COMPOUND ANGLES
⑧
Formed by
suN_orDtFFof2or@angles.a taking
→ the
)
n
" "
.
am zoo Main
28+0
a +
-
SUM of
-
2 Angles
Soul of
2 Angles
IsBB.DE#t0NS
① Costain Accepted without proof
② cos Cat B) shot 9:#Iat
= cos C- BD ,
EA -
to a so
=
cos A. cost B) t sin A. sin C- B) -
=
COSA cos B t sin At sin B)
.
sina.sinB.i.COSCATBI-coSA.cosb-sinA.si#T
= COSA .
Cos B -
③ Sinha B) -
④ sinfatb )
= Cos [90 -
CA -
BD = Sin LA EB)] -
=
Cos Cao -
Atb ) =
sin A. cost B ) - -
COSA sine B )
.
-
= Cos Gao -
A) EB) ]-
=
Sin A. cos B -
COSA C-sin B)
-
= COSMO -
A) -
cost B) t Sinko A) sin C-B)
-
= sin A. cos B t cos A. sink
sinCATBJ-sinA.cosbtcoSA.sn#--sinA.oosB
Bt sin A. cos COSA C-sin B) :
=
. .
B -
COSA Sin.
sinta-BI-sinA.cosB-cosA.sn#DoubleAngles-
i
.
⑤ sin 2A →
From ④ ⑥ cos 2A →
From ②
=
sin # +A) = COSCA + A)
=
sina.cosatcoSA.sn A =
COSA Cosa sin A. sin A
-
-
= 25in A. cos A = Costa Sinha -
: . sin2A-2sinA.co# : . cos2A=Cos2A-Sin#
but sin2Atcos2A= I
}
'
Sinha = I -
cos 2A
D. O T S
.
.
COSTA I Sinan
- -
= -
