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BAHAN AJAR
Mata Pelajaran : Matematika
Kelas, Semester : XI , 1
SK./KD. : 2. / 2.1
Tujuan Pembelajaran : Ss!a "a#at men$$una%an rumus %&snus jumla'/sels' "ua su"ut(ater Pembelajaran :
A. R)()S TRI*+N+(TRI )NT)K J)(-AH D)A S)D)T DAN S-ISIH D)A S)D)T
1. Rumus &s α 0 β
Per'at%an $ambar ln$%aran satuan " ba!a' n
Ber"asar%an rumus jara% "ua tt% ma%a :
AB2 3 4&s α0 4&s β2 5 sn α0 sn β2 3 &s2 α 6 2.4&s α.4&s β5 &s2 β 5 Sn2α 6 2 sn α.sn β5 Sn2 β
3 &s2 α 5 Sn2 α 5 &s2 β 5 Sn2 β −2.4&s α.4&s β − 2. sn α.sn β 3 &s2α 5 Sn2α 5 &s2 β 5 Sn2 β 6 2 &sα &s β 5 Snα Sn β
3 1 5 10 2&s
α
&s
β
5 Sn
α
Sn
β
3 2 – 2 ( Cosα Cos β + Sinα Sin β ) 7777777 1
Per'at%an se$t$a A+B :
+A 3 +B 3 1 satuan "an besar su"ut A+B 3 α 0 β
Den$an men$$una%an aturan %&snus "#er&le' :
AB2 3 +A2 5 +B2 6 2. +A.+B. 4&s ∠ A+B 3 12 5 12 6 2.1.1.&s α 0 β
3 2 – 2.Cos(α - β ) 7777777777..2
Dar 1 "an 2 "#er&le' :
2 6 2.&sα 0 β 3 2 6 2 &sα &s β 5 Snα Sn β atau :
6 2.&sα 0 β 3 6 2 &sα &s β 5 Snα Sn β
⇔ &sα - β 3 &sα &s β 5 Snα Sn β
Ja" : Cos (α - β ) = Cosα Cos β + Sinα Sin β
2. Rumus &s α 5 β
&s α 5 β 3 &s α 00 β
3 &s α.&s 0β 5 Snα
.Sn 0β %arena : &s0 β 3 &s β "anSn0 β 3 0 Sn β
3 &s α .&s β 0 Snα .Sn β
Ja" : Cos (α + β ) = Cos α .Cos β - Sinα .Sin β
Contoh :
Den$an men$$una%an rumus &s α5β atau &s α−β jabar%an bentu% ber%ut :
1
8
X+
α
A4&s α, sn α
βB4&s β, sn β
Jar0jar ln$%aran r 31 satuan. Besar su"ut X+A3 α "an besar su"ut X+B3 β.K&&r"nat %utub tt% Ar, α tt% Br, β
K&&r"nat artesus tt% A r.4&s α, r.sn α3 4&s α, sn α "an tt% B 4&s β, sn β.
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1. 4&s 95 ;. 4&s P−. 4&s ;A−?B
"an se"er'ana%an
?. &s 1?@ 3 4&s @0>?@ . &s
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3 ?
;
!atihan "ji #om$etensi %
1. Jabar%an se4ara lan$sun$ :
a. 4&s 90 ". 4&s F EA02B $. 4&s 295
b. 4&s ;#0G e. 4&s F (0>N '. 4&s ?#5;G
4. 4&s >(0N . 4&s 95 . &s (52N
2. Nata%an ta# bentu% ber%ut "alam bentu% %&snus jumla' atau sels' "ua su"ut
%emu"an se"er'ana%anla' :
a. 4&s (. 4&s N 5 sn (. sn N . 4&s β.4&s β 5 sn β. Sn β b. 4&s ;a.4&s b 0 sn ;a. sn b $. 4&s
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>. Den$an men$$una%an rumus 4&s α+β "an 4&sα−β, tunju%%an ba'!a :a. &s 5α 3 0 Sn α 4. &s 2
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BAHAN AJAR
Mata Pelajaran : MatematikaKelas, Semester : XI , 1
SK./KD. : 2. / 2.1
Tujuan Pembelajaran : Ss!a "a#at men$$una%an rumus snus jumla'/sels' "ua su"ut.
(ater Pembelajaran : &. 'ms Sin (α + β )
Su"a' %ta %eta'u ba'!a Sn α & 3 &s 6 α & "an Sn 0α & 3&s α &
se'n$$a :
Snα 5 β & 3 &s 6α 5 β &
3 &s 6 α 0 β &
3 &s 6 α
0β
&
3 &s 0α & .4&s β& 5 Sn0α & sn β& 3 sn α&.&s β & 5 4&s α& .Sn β &
Ja" : Sn α 5 β & 3 Snα &.&s β & 5 &s α & .Sn β &
J%a men$$una%an satuan ra"an ma%a
Sin (α + β ) = Sinα .Cos β + Cos α .Sin β
. 'ms Sin (α − β )Su"a' %ta %eta'u ba'!a &s − β 3 &s β "an Sn− β 3 − Sn β se'n$$a :
Sn α 0 β 3 Sn α 5 − β 3 Sn α .4&s − β 5 &s α . Sn− β
3 Sn α .4&s β 5 &s α . −Sn β 3 Sn α .4&s β − &s α . Sn β
Ja" Sn α − β 3 Sn α . &s β − &s α . Sn β
Contoh :
Den$an men$$una%an rumus sn α5β atau sn α−β jabar%an bentu% ber%ut :1. sn (5N ;. sn A−>B2. sn ;95 >. sn B 3 sn A. 4&s >B 6 4&s A .sn >B>. sn
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Contoh :
D%eta'u ?
;Asn =
"an 1;
12Bsn =
"en$an A su"ut lan4# "an B su"ut " %ua"ra %e"ua..
Htun$la' sn A−B.
Jawa :
?
;Asn =
C 1;
12Bsn =
Sn A− B 3 Sn A. &s B − &s A. Sn B)ntu% menentu%an 4&s A "an 4&s B %ta "a#at men$$una%an "enttas : sn2 9 5 4&s2 9 3 1
• sn2 A 5 4&s2 A 3 1 ⇔ 2?D
1A4&s2 −=
Karena A su"ut lan4# ma%a
⇔1A4&s
?
; 22
=+
⇔ 2?1
A4&s2 =
?
>A4&s =
⇔ 1A4&s2?D 2
=+ ⇔ ?>
A4&s ±=
• sn2 B 5 4&s2 B 3 1 ⇔ 1D1>>
1B4&s2 −=Karena B su"ut " %ua"ran
%e"ua ma%a
⇔1B4&s
1;
12 22
=+
⇔ 1D2?
B4&s2 =
1;
?B4&s −=
⇔ 1B4&s
1D
1>> 2 =+⇔ 1;
?B4&s ±=
Sn A− B 3 Sn A. &s B − &s A. Sn B
3 1;
12.
?
>
1;
?./
?
; −−Ja" sn A−B 3 ?
;−
3 ?
>E1? −−
3 ?
;−
!atihan "ji #om$etensi 2
1. Jabar%an se4ara lan$sun$ :
a. sn 95 b. sn P0= 4. sn ;95? ". sn 2(0N
2. Nata%an ta# bentu% ber%ut "alam bentu% snus jumla' atau sels' "ua su"ut %emu"an
se"er'ana%anla' :
a. sn A 4&s B 5 4&s A. sn B ". sn
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;. Nata%an ta# bentu% ber%ut "alam bentu% snus jumla' atau sels' "ua su"ut %emu"an
'tun$la' tan#a tabel atau %al%ulat&r:
a. Sn 2&.&s 1 5 &s 2&.Sn 1 e. Sn 0 &s
b. Sn 2E&.&s 1
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Jawa :
1.
tanyx.tan1
tany-tanx
y)-tan(x +=
;.
B;
B;
B;
tanA.2
1
tan1
tanA2
1tan
)A2
1tan(
−
+
=+
2.
tan2L7K.tan1
tan2L-tan7K 2L)-tan(7K
+
=
Contoh :
Den$an menata%an
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;. Nata%an ta# bentu% ber%ut "alam bentu% tan$en jumla' atau sels' "ua su"ut
%emu"an se"er'ana%anla' :
a. αα−α+α2tan.?tan1
2tan?tan
4.
1>tan.;tan1
1>tan;tan
−
+
b. ββ−
β+β
tan.tan1
tantan
".
2tan.tan.Etan1
>tanEtan
−
+
4.
Dtan.21tan1
Dtan21tan
−
+
b.
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. Tentu%an nla tan β+α "an tan α−β j%a "%eta'u :
a. tan α 3 >1
, tan β 3 ?
;
"en$an α "an β su"ut lan4#
b. Sn α 3 ?;
, Sn β 3 1;
?
"en$an α su"ut lan4# "anβ su"ut " %ua"ran II
11
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BAHAN AJAR
Mata Pelajaran : Matematika
Kelas, Semester : XI , 1
SK./KD. : 2. / 2.1
Tujuan Pembelajaran : Ss!a "a#at men$$una%an rumus tr$&n&metr untu% su"ut ran$%a#.
(ater Pembelajaran : C. '"M"S ,'/0/M1,' S"", 'A0#AP
%. 'ms Sin 2α
sn 2α 3 sn α 5α 3 sn α . 4&s α 5 4&s α . sn α 3 sn α . 4&s α 5 sn α . 4&s α 3 2 snα . 4&s α
Ja" Sn 2α 3 2 Snα .&sα
2. 'ms Cos 2α
&s 2α 3 4&sα 5 α 3 4&s α . 4&s α 6 sn α . sn α
3 4&s 2α 6 sn2α
Ja" : 4&s 2α 3 4&s2α 6 sn2α
Rumus lan "ar 4&s 2α :
Tela' %ta %eta'u ba'!a Sn2
α 5 &s2
α 3 1 ⇔ &s2
α 3 1 6 Sn2
α ⇔ sn2α 3 1 6 4&s2α• 4&s 2α 3 &s2α 6 Sn2α 3 16 Sn2α 6 Sn2α
3 1 6 2.Sn2αJa" 4&s 2α 3 1 6 2.Sn2α
• 4&s 2α 3 &s2α 6 Sn2α 3 &s2α 6 1 6 4&s2α 3 &s2α 6 1 5 &s2α 3 2.&s2α 6 1
Ja" 4&s 2α 3 2.4&s2α 0 1
&. 'ms tan 2α
tan 2α 3 tan α 5α
3 αα−α+α
tan.tan1
tantan
Ja" : α−
α=α
2tan1
tan22tan
12
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3 α−
α2
tan1
tan.2
Contoh :
D%eta'u E,sn =α "an α su"ut lan4#. Tentu%an nla 4&s α ,tan α, sn 2α , 4&s 2α"an tan 2α
Jawa :
(sal%an "en$an bantuan se$t$a s%u0s%u AB :
?
>
1
EE,
AB
Bsn ====α
, B 3 > , AB 3 ?
Ber"asar%an te&rema #t'a$&ras
;D12?BABA 22 ==−=−=
4&sα 3 ?;
AB
A=
C ;
>
A
Btan ==α
sn 2 α 3 2.snα .4&sα 3 2?2>
?
;.
?
>.2 =
4&s 2α 3 1 6 2.sn2α
3 2?
<
2?
;21
2?
1/21
?
>./21
2 −=−=−=−
<
2>
21
1
;
>/2
tan1
tan.2
2tan 22 −=−=−=−=−=
−
=α−
α=α
Contoh :
Htun$la' nla "ar :
1. 2 sn 1?& .4&s 1?& 2. 10 2. sn 2 22,?& ;.&2
&
?,22tan1
?,22tan.
−
Jawa :
1. 2 sn 1?& .4&s 1?& 3 sn 2.1?& 3 sn ;& 3 2
1
2. 10 2. sn 2 9 "alam 29
. 4&s >9 "alam sn 29 l. tan ( "alam F (
1;
α
B
A
α
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2. Htun$la' ber%ut n tan#a tabel atau %al%ulat&r :a. 2. sn 22,?&. 4&s 22,?& e. 2. 4&s2 1? & 5 12
b. 2. 4&s2 . D%eta'u tan A 3 2
1−
, "en$an A su"ut tum#ul. Htun$la' sn 2A, 4&s 2A, "an tan 2A.
1>
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?. D%eta'u tan P3 2
1
, tan =3 >
1
. Htum$la' tan 2P, tan 2=, tan 2P5=, "an tan P52=.
. D%eta'u sn 93 t . Tentu%an sn 29 "an 4&s 29.
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BAHAN AJAR
Mata Pelajaran : Matematika
Kelas, Semester : XI , 1SK./KD. : 2. / 2.2
Tujuan Pembelajaran : Ss!a "a#at men$una%an rumus #er%alan snus "an %&snus
(ater Pembelajaran : D. R)()S PRKA-IAN SIN)S DAN K+SIN)S
%. 'ms Perkalian Sins 3an #osins
Den$an menjumla'%an rumus sn β+α "an sn β−α
Sn β+α 3 Sn α&sβ 5 &sα SnβSn α 0 β 3 Sn α&sβ 0 &sα Snβ
Sn β+α 5 sn β−α 3 2.Sn α . 4&s β ⇔ 2. Sn α &s β 3 sn β+α 5 sn β−α
Ja" : 2.Sn α&s β 3 Sn β+α 5 Sn α 0 β
Sn β+α 3 Sn α&sβ 5 &sα SnβSn α 0 β 3 Sn α&sβ 0 &sα Snβ
sn β+α 0 sn β−α 3 2.&sα .sn β ⇔ 2.&sα . Snβ 3 Sn β+α 0 sn β−α
Ja" : 2. &sα .Snβ 3 Sn β+α 0 Sn α 0 β
Contoh :
Nata%an bentu% ber%ut seba$a jumla' atau sels' snus
1. 2.&s ;2 Sn E
2. 2. sn >&. 4&s 2&
;. . sn & 6 sn 2>&
2. 2. sn >&. 4&s 2& 3 sn >52& 5 sn >02& 3 sn & 5 sn 2&
;. . sn
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". E.sn ?α &s α '. Sn ;
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>. Tunju%%an ba'!a :
a. x x x 2sn;2
1
;
4&s/.
;
sn/.2 +=−+ π π
b. 92sn19;
4&s/.9>
sn/.2 +=−π
+π
4.&&&
92sn;2
1;9sn/.;94&s/.2 +=−+
". >.sn ° 4&s 12° sn 1E° 3 1 5 sn °0 4&s 12°.e. >.sn 12° 4&s 2>° sn ;° 3 1 5 ; sn 12°0 4&s 2>°.
BAHAN AJAR
Mata Pelajaran : Matematika
Kelas, Semester : XI , 1
SK./KD. : 2. / 2.2
Tujuan Pembelajaran : Ss!a "a#at men$$una%an rumus #er%alan %&snus/#er%alan snus.
(ater Pembelajaran : 2. 'ms Perkalian #osins 3an 'ms Perkalian Sins
&sα 5β 3 &sα&s β 0 Snα Sn β&sα 0β 3 &sα&s β 5 Snα Sn β
4&sα 5β 5 4&sα 0β 3 2 &sα&s β ⇔ 2 &sα&s β 3 &sα 5β 5 &sα 0β
Ja" : 2.&sα&s β 3 &sα 5β 5&sα 0β
&sα 5β 3 &sα&s β 0 Snα Sn β&sα 0β 3 &sα&s β 5 Snα Sn β
&sα 5β − &sα −β 3 − 2 Snα Sn β ⇔ −2 Snα Sn β 3 &sα 5β − &sα −β
Ja" : −2.Snα Sn β 3 &s α 5β − &s α −β
Contoh :
Nata%an bentu% ber%ut "alam bentu% #enjumla'an
1. 2 &s E &s ? ;. E.&s ?9 &s ;92. 2. sn ?&. sn 1?& >. sn 9 sn 29
Jawa :
1. 2.4&s E 4&s ?3 4&s E5?& 6 4&s E−?& 3 4&s 1;& − 4&s ;&
2. 2. sn ?&. sn 1?&3 −4&s ?51? 6 4&s ?−1? 3 −4&s
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>. sn 9 sn 29 3 −F 4&s 9529 6 4&s 9−293 −F 4&s E9 − 4&s >9 3 −F.4&s E9 5 F. 4&s >9
!atihan "ji #om$etensi
1. Nata%an bentu% ber%ut "alam bentu% #enjumla'ana. 2 4&s 9. 4&s . E. sn 95. sn 90 b. 2. sn 9. sn $. 1. 4&s ;#5G. 4&s ;#0G4. 2. 4&s & '. 4&s m5n. 4&s m0n". 2. sn ?&. sn E& . Sn ;&. sn E&
e. . sn (. sn N j. 4&s >&. 4&s 1;&
2. Htun$la' nla "ar :
a.2&s
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?. D%eta'u se$t$a AB s%u0s%u " B. J%a1
;sn.Asn = "an
#2
?Asn/ =− . Htun$la' nla #.
BAHAN AJAR
Mata Pelajaran : Matematika
Kelas, Semester : XI , 1
SK./KD. : 2. / 2.2
Tujuan Pembelajaran : Ss!a "a#at men$$una%an rumus #enjumla'an/#en$uran$an snus /
%&snus.(ater Pembelajaran :
1. '"M"S P10J"M!A4A05 P10"'A0A0 S0"S A0 #/S0"S
Rumus0rumus #er%alan snus "an %&snus an$ tela' "ba'as sebelumna atu :
2. sn α 4&s β 3 sn β+α 5 sn α 0 β 2. 4&s α sn β 3 sn β+α − sn α 0 β 2. 4&s α&s β 3 4&s β+α 5 4&s α 0 β −2. sn α sn β 3 4&s β+α − 4&s α 0 β atau
2. sn α sn β 3 4&s β α − − 4&s α 5 β
"a#at %ta men$uba'na menja" rumus #enjumla'an/#en$uran$an snus atau 4&snus
"en$an 4ara seba$a ber%ut :
(sal%an β+α 3 977.1α − β3 77.2
se'n$$a α "an β "a#at "nata%an "alam 9 "an atu :J%a #ersamaan 1 "tamba' "en$an #ersamaan 2 ma%a "#er&le' :
β+α3 9α − β3
α 3 21
95
J%a #ersamaan 1 "%uran$ "en$an #ersamaan 2 ma%a "#er&le' :β+α 3 9
α 0 β3
2
5
−
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L 3 2
1
9−
se'n$$a rumus0rumus :
2. sn α 4&s β 3 sn β+α 5 sn α 0 β 2. 4&s α sn β 3 sn β+α − sn α 0 β 2. 4&s α&s β 3 4&s β+α 5 4&s α 0 β −2. sn α sn β 3 4&s β+α − 4&s α 0 β
"a#at "nata%an seba$a :
sn 9 5 sn 3 2. sn 2
1
95 4&s 2
1
90
sn 9 − sn 3 2. 4&s 21
95 sn 2
1
90
4&s 9 5 4&s 3 2. 4&s 2
1
95 &s 2
1
90
4&s 9 − 4&s 3 −2. sn 21
95 sn 2
1
90
Contoh :
Nata%an ber%ut n %e "alam bentu% #er%alan, %emu"an se"er'ana%an :
1. sn ??° 5 sn ;?°2.sn 1° − sn 2°
;.4&s ;a 5 4&s a>.4&s 9 − 4&s 29Jawa :
1. sn ??& 5 sn ;?& 3 2. sn 2
1
??5;?&. &s 2
1
??−;?& 3 2. sn >?&.4&s 1&
3 2. 2
1
√2.4&s 1&
3 √2 . 4&s 1 &.
2. sn 1& − sn 2& 3 2.4&s 21
152&. sn 2
1
1−2& 3 24&s &.sn >& 3 2. 21
.4&s
?&
3 4&s ? &.
;. 4&s ;a 5 4&s a 3 2. 4&s 2
1
;a5a. 4&s 2
1
;a0a 3 2. 4&s 2a. 4&s a
>. 4&s 9 − 4&s 29 3 − 2. sn 21
9529. sn 2
1
9−29 3 −2. sn >9. sn 29
!atihan "ji #om$etensi 6
1. Nata%an %e "alam bentu% #er%alan :
1. 4&s ( 5 4&s N . Sn 5 sn 2;. sn A 5 sn B 11. sn 952' − sn 9
>. sn K − sn - l2. sn 21
π5A − sn 21
π−A?. 4&s 95 5 4&s >9−
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E. 4&s E?& − 4&s ;?&
2. Tan#a table atau %al%ulat&r 'tun$la' nla "ar :
a. Sn
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BAHAN AJAR Mata Pelajaran : Matematika
Kelas, Semester : XI , 1
SK./KD. : 2. / 2.;
Tujuan Pembelajaran : Ss!a "a#at membu%t%an "enttas tr$&n&metr.
(ater Pembelajaran : . IDNTITAS TRI*+N+(TRI
I"enttas meru#a%an suatu #ersamaan an$ selalu benar untu% %&nstanta an$ mana#un ju$a.
)ntu% membu%t%an suatu #ersamaan meru#a%an "enttas "a#at "$una%an rumus0rumus an$su"a' ""ens%an atau "bu%t%an sebelumna.
ara membu%t%an "enttas tr$&n&metr a"a "ua 4ara atu :
1. (en$uba' sala' satu ruas se'n$$a "#er&le' bentu% an$ sama "en$an ruas an$ lan.
2. (en$uba' %e"ua ruas se'n$$a "#er&le' bentu% an$ sama "%e"ua ruas.
ara %e"ua "la%u%an j%a 4ara #ertama men$alam %esultan.
Contoh :
Bu%t%an "enttas0"enttas ber%ut :
1. 4&s 29 − sn 29. sn >9 3 4&s 29. 4&s >9
2.
9tan
9>4&s9E4&s
9>sn9Esn=
+
+
;. sn 295 sn 95sn E9 3 >. sn >9 .4&s ;9.4&s 9
Bkti : sala' satu alternat
1. 4&s 29 − sn 29. sn >9 3 4&s 29. 4&s >9Ruas %r 3 4&s 29 − sn 29. sn >9
3 4&s 29 − sn 29. 2.sn 29.4&s 293 4&s 29 − 2.sn2 29.4&s 293 4&s 29 1 − 2.sn2 293 4&s 29. 4&s >9.
3 Ruas %anan terbu%t
2.9tan
9>4&s9E4&s
9>sn9Esn=
++
Ruas %r 3 9>4&s9E4&s
9>sn9Esn
++
39>9E/
2
14&s9>9E/
2
14&s2
9>9E/2
14&s9>9E/
2
1sn.2
−+
−+
3 924&s.94&s.2
924&s.9sn.2
3 94&s
9sn
3 tan 9
3 Ruas %anan terbu%t
;. sn 295 sn 95sn E9 3 >. sn >9 .4&s ;9.4&s 9
Ruas %r 3 sn 295 sn 95sn E9
2;
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3 sn 9 5 sn 29 5 sn E9
3 2. sn2
19529.4&s
2
19−29 5 2. sn >9.4&s >9
3 2. sn >9. 4&s.29 5 2 sn >9. 4&s >9
3 2. sn >9 4&s 29 5 4&s >9
3 2. sn >9 4&s >9 5 4&s 29
3 2. sn >9 2.4&s2
1>9529.4&s
2
1>9029
3 >. sn >9 .4&s ;9.4&s 9
!atihan "ji #om$etensi 7
Bu%t%an "enttas0"enttas ber%ut :
1.a2tan
a;4&sa4&s
a;snasn=
++
E. :tan.9tan1
:tan9tan
:94&s/
:9sn/
++
=−+
2.atan
a?sna;sn
a?4&sa;4&s=
+−
. 9sn94&s
9sn94&s
9sn94&s
9sn94&s9tan.2
+−
−−+
=
;.a2sn.2
a;snasn
a;4&sa?4&s=
−−
1. tan 29 6 sn 29 3 tan 29.sn 29.tan 9
2>
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>.a4&s.2
asn21
a4&sa;4&s
2 =
−
+
11. sn 295 sn >95sn 9 3 >.4&s 9.4&s 29.sn ;9
?.
92tan19sn.2/9sn.2
9;4&s94&s
2 =−
−
12. 2. sn 9 5 sn ;9 − sn ?9 3 1. sn;9.4&s29.
.9tan
92sn
924&s1=
−
1;.9>tan
94&s9>4&s924&s
9sn9>sn92sn=
+−+−
2?
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.4&s2 29 3 2 5 2.4&s >9 1>.9tan
9;sn94&s9Dsn
9D4&s9sn9;4&s=
−−−−
2
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"!A0A0 4A'A0
1. D%eta'u 4&s 93 ?
1
"an sn 3 ?
;
"en$an 9, su"ut0su"ut lan4#. Tentu%an :
a. 4&s 9− 4. sn 9− e. tan 9− b. 4&s 95 ". sn 95 . tan 95
2. D%eta'u tan a 3 2
1
"an tan b3 ;
1
. Tentu%an :
a. tan a− b 4. tan 2a e. tana52b
b. tan a5b ". tan 2b . tan
2a− b
;. Nata%an ber%ut n "alam snus, 4&snus, "an tan$en an$ tun$$al :
a. 2. sn #.4&s# 4. 1−2sn2 & ". sn F π5α− sn F π−α
. Se3erhanakan tan$a tael5kalklator :
a. sin %&;o + sin *;o . 2.os 6;o.os *;o 2.sin %;;o. sin 7;o
. os %*o os 6*o 3. sin %;;o. os 7;o + os %&;o. sin %%;o
6. Bktikan ahwa :
a.9tan
9;4&s9?4&s
9;sn9?sn =+−
b.a?tan
aE4&sa24&s
aEsna2sn=
++
4. sn 9 5 sn ;9 5 sn ?9 5 sn . 4&s 9. 4&s 29. sn >9
". 4&s 9 − 4&s ;9 −4&s ?9 5 4&s . sn 9. sn 29. 4&s >9.
2
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T)*AS HARI INI (N*RJAKAN S+A- DI BAOAH
SBA*AI NI-AI T)*AS TRI*+N+(TRI
1. D%eta'u 4&s 93 ?
1
"an sn 3 ?
;
"en$an 9, su"ut0su"ut lan4#. Tentu%an :
a. 4&s 9− 4. sn 9− e. tan 9− b. 4&s 95 ". sn 95 . tan 95
2. D%eta'u tan a 3 2
1
"an tan b3 ;
1
. Tentu%an :
a. tan a− b 4. tan 2a e. tan a52b b. tan a5b ". tan 2b . tan 2a− b
;. Nata%an ber%ut "alam bentu% #enjumla'an/#en$uran$an :
a. 2.4&s 19.4&s