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III .SequencesandTrigonometry
: I T R A
P Sequences s d r o
W Pronunciation Indonesian
e c n e u q e
S /'s:ikwən s/ Barisan
n o i s s e r g o r
P /'prə'gre∫ n/ Barisan
c i t e m h t i r
A sequence /ə'rɪθmətɪk 's:ikwən s/ Barisan Aritmatika c
i r t e m o e
G /dƷɪə'mətrɪk 's:ikwən s/ Barisan Geometri e
c n e r e ff i
D /'dɪfrən s/ Beda
o i t a
R /'reɪ∫ɪəʊ/ Rasio
s e i r e
S /'sɪər :iz/ Deret
e t i n i
F /f'aɪnaɪt / Berhingga
e t i n if n
I /'ɪnfɪnət / TakBerhingga
m r e
T /tɜ:m/ Suku
m r e T t s r i
F /fɜ: tst ɜ:m/ SukuPertama
e l d d i
M Term /'mɪd tl ɜ:m/ SukuTengah
s m r e T e v i t u c e s n o
C /kən'sekjʊtɪv tɜ: z/ m SukuBerurutan
l a i t r a
P msu /'pɑ: l∫ sΛm/ J(suumkula)h sebagian
Example:
• An arithmetic sequenceisasequenceo fthe f orma ,a+d ,a+2d ,….
• Thenumber ais thefirstterm ,and disthedifferenceo fthesequence.
• The formula f or n-thterm o fthe arithmeticsequence isa +( n- d1 )
• a1 ,a2 ,a3 arethefirst threeterms.
• a(n+1)/2 iscalled middle term.
• anand an+1aretwo consecutive terms.
• For arithmetic sequence a ,a+d ,a+2d ,… ,the formula for n-th partia l m
u
s Sn is (n/2 ()2a +(n − )1 d)
• Ageometric sequence is sequence in the form of a ,ar ,ar2 ,… where r is e
h
t ratio.
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e c i t c a r P
. s r e w s n a t r o h s e v i g r o s e c n e t n e s e h t e t e l p m o C
.
1 The ifrst 6 termso fthearithmetic sequence13,7,1,. ..are ______________. .
2 I fthe10thtermo fan arithmeticsequencei s 55 and the 2nd termi s 7 , s
t i n e h
t 1st term is___. .
3 The sumo fthe ifrst 40 termso fthearithmeticsequence 3,7,11,15 ..,i s _
_ _ _
_ .
.
4 I fthethird termo fa geometricsequencei s20 and thesixth termi s2.5 , o
i t a r n o m m o c s t i e h t n e h
t is______.
.
5 The ___________________o fageometricsequencewhose ifrst term i s2 e
r a e v if s i _ _ _ _ _ _ _ _ _ _ _ _ d n
a 2, 10, 50 ,250 ,and 1250.
.
6 The ____________________ o fsequence 1,2,4,8 ., .. i s256. .
7 I fthe3rd termo fa geometricsequence i s63/4 ,and the6th termi s 2
3 / 1 0 7
1 ,then the 4th termis_________. .
8 The sumo f1 ,0.5 ,0.25 ,0.125 ,.. i s ______________.
t e b a h p l A k e e r G : I I T R A P
s r e t t e L g i
B Smal lLetters Words Pronunciation
Α α alpha /'æflə/
Β β beta /'b:itə/
Γ γ gamma /'gæmə/
Δ δ delta /'deltə/
Ε ε epslion /'epsliən /
Ζ ζ zeta /'ziːtə/
Η η e ta /i'ːtə/
Θ θ theta /'θiːtə/
Ι ι iota /aɪ'əʊtə/
Κ κ kappa /'kæpə/
Λ λ lamda /l'æmdə/
Μ μ m u /'mjuː/
Ν ν n u /'njuː/
Ξ ξ x i /'ksaɪ/
Ο ο omicron '/əʊmɪkrən /
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Ρ ρ r ho /'rəʊ/
Σ σ sigma /'sɪgmə/
Τ τ t au /t'ɑʊ/
Υ υ upslion /j'ʊpsɪlən /
Φ φ p hi /f'aɪ/
Χ χ c hi /'kaɪ/
Ψ ψ p si /'psaɪ/
Ω ω omega /'əʊmɪgə/
I T R A
P I :I Trigonometry s
d r o
W Pronunciation Indonesian
y r t e m o n o g i r
T /trɪgə'nɒmətrɪ/ Trigonometri
t n e c a j d
A side /ə'dƷeɪs ants ɪd/ Sis isamping
e s u n e t o p y
H /haɪ'pɒtənyu:z/ Sis imiring
e t i s o p p
O side /ɒpəzɪt as ɪd/ Sis idepan
e l g n
A /'æŋg l/ Sudut
s e e r g e
D /dɪ'gr :iz/ Derajat
d o i r e
P /'pɪərɪəd / Periode
t n a r d a u
Q /'kwɒdrən t/ Kuadran
n a i d a
R /'rəɪdɪən / Radian
l a c o r p i c e
R /rɪ'siprək l/ Kebailkan
n o i t c n u F c i r t e m o n o g i r T
n i
s sine /saɪn /
o
c s c so ;cosine /kɒz/;/kɒzaɪn / n
a
t tan ;tangent /tæn/;/tændƷən t/ e
s c s ce ; /sek/
s
c c cosec ; /'kəʊsek/
t o
c cotangent /'kəʊtændƷənt /
Examples:
¬ Trigonometry isthestudy o fanglemeasurement.
¬ The hypotenuse wli lalways be the longest side ,and opposite from the t
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¬ The opposite side is the side directly across from the angle you are .
g n i r e d i s n o c
¬ The adjacentsideisthesidenext toangleyouareconsidering.
¬ All f unctionshave positivevalues f oranglesi n Quadrant ,I but only s ein
a
h s positivevalues f or angles i nQuadrant II .
¬ The sineand cosinefunctionshavetheperiod 2π ( 3600).
e c i t c a r P
0 ( n i s s a h c u s , n o i t a u q e e h t y a s d n a w o l e b e l b a t e h t l li
F 0)=….
s e e r g e
D Radians S in C os T an
0 0
0
3 π /6
5
4 π /4
0
6 π /3
0
9 π /2
e c i t c a r P
. s n o i s s e r p x e g n i w o ll o f e h t d a e R
.
1 (Formulasf or Additionand Subtraction) sin(A+ B )=sin AcosB+ cosAsinB
A ( s o
c - B )= cosAcos B+sin AsinB A
( n a
t + B )= tan A+ tan B/( 1 - tanAtan B)
.
2 (PhytagoreanI dentities) sin2θ +cos2θ =1 θ
θ+ = 2
2 1 sec
n a t
.
3 (Formula forDouble Angle) sin 2A= 2 sinAcos A
.
4 (Formula f orhal fangle) cos θ = ± 1+cos θ
2 2
.
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e s i c r e x E
. s r e w s n a t r o h s e v i g r o s e c n e t n e s e h t e t e l p m o C
.
1 Tangenthas positivevaluesf or anglesi n_______________ ,and _
_ _ _ _ _ _ _ _ _ _ _ _
_ h sa positive valuesf or anglesi n Quadrant I V. .
2 Thetangentand cotangent f unctionshavetheperiod __________ .
3 I fsinα = 0.8 ,then the valueo fsin ( 180- )α is_________ and thevalue α
n a t f
o is ______________ .
4 Without using calculator, f ind cos(150.) .
5 Find thevalueso fxf or which sin3x =0.5 fi i t i sgiven that 0< <x 09 0. .
6 What i s theequa lvaluei n degrees f orx radians? .
7 Say anythingabouttrigonometry o fthepicturebelow
e l p m a x e r o
F :
. C / A s i a n i s
A
C
a
b
