1
RANGKUMAN
RUMUS
3
Sin(a + b) = sin a . cos b + cos a . Sin b
Sin(a - b) = sin a . cos b – cos a . Sin b
Rumus
jumlah dan selisih dua sudut...
4
tan(α + β) =
tan(α - β) =
βα
βα
tan.tan1
tantan
−
+
βα
βα
tan.tan1
tantan
+
−
5
Rumus Sudut Rangkap
Sin 2a = 2 sin a . Cos a
Cos 2a =
asinacos 22
−
asinacos 22
−
Cos 2a = 1acos2 2
−
Cos 2a = asin21 2
...
Rumus Sudut Setengahan
sin a = 2
acos1−
±A
B
C
tan a =
2
1
cos a =2
1
2
acos1+
±
2
1
acos1
asin
asin
acos1
acos1
acos1
+
=...
7
Rumus
jumlah dan selisih sin dan cos
)ba(
2
1
sin).ba(
2
1
sin2bsinasin −+=+
)ba(
2
1
sin).ba(
2
1
cos2bsinasin −+=−
)ba...
8
Rumus
perkalian sin dan cos
2 sin a . cos b = sin (a + b) + sin (a – b)
2 cos a . sin b = sin (a + b) – sin (a – b)
2 co...
S + S
S – S
C + C
C - C
Menghafal Rumus
2 S C
2 C S
2 C C
– 2 S S
+
2
1
−
2
1
+ –
)ba(
2
1
cos).ba(
2
1
sin2bsinasinSC2SS ...
10
1. Sin 75o
= ….
Answer :
sin750
= sin(450
+ 300
)
= sin450
cos300
+ cos450
sin300
= ½√2.½√3 + ½√2.½
= ¼√6 + ¼√2
= ¼√2(√...
11
2. Diketahui sin A = cos B =
A dan B adalah sudut-sudut lancip
sin(A – B) =….
Bahasan:
sin(A – B)= sin A cos B – cos A ...
12
sin(A – B) = sin A cos B – cos A sin B
= x - x
=
=
5
3
25
7
5
4
25
24
125
96
125
21
−
5
3
125
75
−=−
13
Solve:
cos α cos β + sin α sin β = cos (α - β)
=
=
=
....sinsincoscos 28
13
7
5
28
13
7
5
=+ ππππ
=+ 28
13
7
5
28
13
7
...
14
1. tan 105° = ….
Solve :
tan105° = tan(60° + 45°)
oo
oo
45tan.60tan1
45tan60tan
−
+
=
1.31
13
−
+
=
x
31
31
−
+
=
31
31...
15
tan 105° = x
=
=
=
= -2 - √3
31
31
−
+
31
31
+
+
31
)31( 2
−
+
31
3321
−
++
2
324
−
+
SELAMAT BELAJAR
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Trigonometry

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Trigonometry

  1. 1. 1
  2. 2. RANGKUMAN RUMUS
  3. 3. 3 Sin(a + b) = sin a . cos b + cos a . Sin b Sin(a - b) = sin a . cos b – cos a . Sin b Rumus jumlah dan selisih dua sudut Cos(a + b) = cos a . cos b – sin a . Sin b Cos(a - b) = cos a . cos b + sin a . Sin b
  4. 4. 4 tan(α + β) = tan(α - β) = βα βα tan.tan1 tantan − + βα βα tan.tan1 tantan + −
  5. 5. 5 Rumus Sudut Rangkap Sin 2a = 2 sin a . Cos a Cos 2a = asinacos 22 − asinacos 22 − Cos 2a = 1acos2 2 − Cos 2a = asin21 2 − A B C tan 2a = atan1 atan2 2 −
  6. 6. Rumus Sudut Setengahan sin a = 2 acos1− ±A B C tan a = 2 1 cos a =2 1 2 acos1+ ± 2 1 acos1 asin asin acos1 acos1 acos1 + = − = + − ±
  7. 7. 7 Rumus jumlah dan selisih sin dan cos )ba( 2 1 sin).ba( 2 1 sin2bsinasin −+=+ )ba( 2 1 sin).ba( 2 1 cos2bsinasin −+=− )ba( 2 1 cos).ba( 2 1 cos2bcosacos −+=+ )ba( 2 1 sin).ba( 2 1 sin2bcosacos −+−=−
  8. 8. 8 Rumus perkalian sin dan cos 2 sin a . cos b = sin (a + b) + sin (a – b) 2 cos a . sin b = sin (a + b) – sin (a – b) 2 cos a . cos b = cos (a + b) + cos (a – b) – 2 sin a . sin b = cos (a + b) – cos (a – b)
  9. 9. S + S S – S C + C C - C Menghafal Rumus 2 S C 2 C S 2 C C – 2 S S + 2 1 − 2 1 + – )ba( 2 1 cos).ba( 2 1 sin2bsinasinSC2SS −+=+→=+ )ba(sin)ba(sinbcos.asin2SSCS2 −++=→+=
  10. 10. 10 1. Sin 75o = …. Answer : sin750 = sin(450 + 300 ) = sin450 cos300 + cos450 sin300 = ½√2.½√3 + ½√2.½ = ¼√6 + ¼√2 = ¼√2(√3 + 1) Example : Remember : sin(α + β) = sinα.cosβ + cosα.sinβ
  11. 11. 11 2. Diketahui sin A = cos B = A dan B adalah sudut-sudut lancip sin(A – B) =…. Bahasan: sin(A – B)= sin A cos B – cos A sin B sin A = cosA = 5 3 25 7 ? ? 5 3 A 3 5 4 5 4 B cos B = sin B = 25 7 7 25 24 25 24
  12. 12. 12 sin(A – B) = sin A cos B – cos A sin B = x - x = = 5 3 25 7 5 4 25 24 125 96 125 21 − 5 3 125 75 −=−
  13. 13. 13 Solve: cos α cos β + sin α sin β = cos (α - β) = = = ....sinsincoscos 28 13 7 5 28 13 7 5 =+ ππππ =+ 28 13 7 5 28 13 7 5 sinsincoscos ππππ )cos( 28 13 7 5 ππ − )(cos 28 7π )(cos 4 π 2 2 1
  14. 14. 14 1. tan 105° = …. Solve : tan105° = tan(60° + 45°) oo oo 45tan.60tan1 45tan60tan − + = 1.31 13 − + = x 31 31 − + = 31 31 + +
  15. 15. 15 tan 105° = x = = = = -2 - √3 31 31 − + 31 31 + + 31 )31( 2 − + 31 3321 − ++ 2 324 − +
  16. 16. SELAMAT BELAJAR

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