This document provides information about trigonometry including: 1) Conversions between degrees and radians, definitions of sine, cosine, and tangent, and trigonometric ratios. 2) Values of trigonometric functions for special angles like 0°, 30°, 45°, 60°, 90°. 3) Relations between trigonometric functions of complementary, coterminal, and reference angles. 4) Formulas for sum and difference of trigonometric functions. 5) Graphs of sine, cosine, and tangent functions.

1. TRIGONOMETRI
KELOMPOK 1

3. x rad =
𝑥
𝜋
. 360°
x° =
𝑥
180
. 𝜋 𝑟𝑎𝑑
Konversi
Radian = Sudut

4. 𝑺𝒊𝒏 𝜶 =
𝑫𝒆𝒑𝒂𝒏
𝑴𝒊𝒓𝒊𝒏𝒈
=
𝒒
𝒓
𝑪𝒐𝒔 𝜶 =
𝑺𝒂𝒎𝒑𝒊𝒏𝒈
𝑴𝒊𝒓𝒊𝒏𝒈
=
𝒑
𝒓
𝑻𝒂𝒏 𝜶 =
𝑫𝒆𝒑𝒂𝒏
𝑺𝒂𝒎𝒑𝒊𝒏𝒈
=
𝒒
𝒑
𝑪𝒔𝒄 𝜶 =
𝟏
𝑺𝒊𝒏 𝜶
=
𝟏
𝒒
𝒓
=
𝑴𝒊𝒓𝒊𝒏𝒈
𝑫𝒆𝒑𝒂𝒏
𝑺𝒆𝒄 𝜶 =
𝟏
𝑪𝒐𝒔 𝜶
=
𝟏
𝒑
𝒓
=
𝑴𝒊𝒓𝒊𝒏𝒈
𝑺𝒂𝒎𝒑𝒊𝒏𝒈
𝑪𝒐𝒕 𝜶 =
𝟏
𝑻𝒂𝒏 𝜶
=
𝟏
𝒒
𝒑
=
𝑺𝒂𝒎𝒑𝒊𝒏𝒈
𝑫𝒆𝒑𝒂𝒏
Perbandingan Trignometri
Terhadap Sudut α
A
B C
𝜶
q
p
r

5. 0˚ 30˚ 45˚ 60˚ 90˚
sin 0
1
2
1
2
2
1
2
3 1
cos 1
1
2
3
1
2
2
1
2
0
tan 0
1
3
3 1 3 ∞
Sudut – Sudut Istimewa

6. Sudut - Sudut Berelasi
180°/360° 90°/270°
sin sin cos
cos cos sin
tan tan cot
sec sec csc
csc csc sec
cot cot tan
α = [+] berlawanan
α = [–] searah
0°/360°
90°
180°
270°
Kuadran I
semua (+)
Kuadran II
sin (+)
Kuadran III
tan (+)
Kuadran IV
cos (+)
sin 210° = sin (180° + 30°)
= - sin 30°
= -
1
2
= cos (270° – 60°)
= - cos 60°
= -
1
2
- cos 135° = cos (180° – 45°)
= - cos 45°
= -
1
2
2
= sin (90° + 45°)
= - sin 45°
= -
1
2
2
Contoh

7. Jumlah & Selisih Dua
Sudut
 𝑆𝑖𝑛 𝛼 ± 𝛽 = 𝑆𝑖𝑛 𝛼 𝐶𝑜𝑠 𝛽 ± 𝐶𝑜𝑠 𝛼 𝑆𝑖𝑛 𝛽
 Cos (𝛼 ± 𝛽) = 𝐶𝑜𝑠 𝛼 𝐶𝑜𝑠 𝛽 ± 𝑆𝑖𝑛 𝛼 𝑆𝑖𝑛 𝛽
 𝑇𝑎𝑛 𝛼 ± 𝛽 =
𝑇𝑎𝑛 𝛼±𝑇𝑎𝑛 𝛽
1 ± 𝑇𝑎𝑛 𝛼 𝑇𝑎𝑛 𝛽
Perkalian Sinus
& Kosinus
 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)

8. Penjumlahan & Pengurangan
Sin, Cos
 Cos α + Cos β = 2 Cos ½ (α+β) Cos ½ (α-β)
 Cos α – Cos β = -2 Sin ½ (α+β) Sin ½ (α-β)
 Sin α + Sin β = 2 Sin ½ (α+β) Cos ½ (α-β)
 Sin α – Sin β = 2 Cos ½ (α+β) Sin ½ (α-β)
Sudut
Rangkap
 Sin 2α = 2 Sin α Cos α
 Cos 2α = Cos 2α – Sin 2α
 t𝑎𝑛2𝛼 =
2 𝑡𝑎𝑛𝛼
1−𝑡𝑎𝑛2 𝛼
 sin 3𝛼 = 3 𝑠𝑖𝑛 𝛼 − 4 𝑠𝑖𝑛3 𝛼

10. y = sin x
Keteran gan
0 = 0° atau 180° atau 360°
1
2 = 30° atau 150°
1
2 2 = 45° atau 135°
1
2 3 = 60° atau 120°
1 = 90°
- 1
2 = 210° atau 150°
- 1
2 2 = 225° atau 315°
- 1
2 3 = 240° atau 300°
- 1 = 270°

11. y = cos x
Keteran gan
0 = 90° atau 270°
1
2 = 60° atau 120°
1
2 2 = 45° atau 135°
1
2 3 = 30° atau 150°
1 = 0° atau 360°
- 1
2 = 240° atau 300°
- 1
2 2 = 225° atau 315°
- 1
2 3 = 210° atau 150°
- 1 = 180°

12. y = tan x
Keteran gan
0 = 0° atau 180° atau 360°
1
3 3 = 30° atau 210°
1 = 45° atau 225°
3 = 60° atau 240°
∞ = 90°
- 1
3 3 = 150° atau 330°
- 1 = 135° atau 315°
- 3 = 120° atau 300°
∞ = 270°

13. Ukuran Derajat Ukuran Radian
 sin x° = sin a°
𝑥 = 𝑎 + 𝑘 . 360
𝑎𝑡𝑎𝑢 𝑥 = 180 − 𝑎 + 𝑘 .360′
 cos 𝑥° = cos 𝑎°
𝑥 = 𝑎 + 𝑘 . 360
𝑎𝑡𝑎𝑢 𝑥 = −𝑎 + 𝑘 .360
 tan 𝑥° = tan 𝑎°
𝑥 = 𝑎 + 𝑘 . 180
 sin 𝑥 = sin 𝑎
𝑥 = 𝑎 + 𝑘 . 2𝜋
𝑎𝑡𝑎𝑢 𝑥 = 𝜋 − 𝑎 + 𝑘 . 2𝜋
 cos 𝑥 = cos 𝑎
𝑥 = 𝑎 + 𝑘 . 2𝜋
𝑎𝑡𝑎𝑢 𝑥 = −𝑎 + 𝑘 . 2𝜋
 tan 𝑥 = tan 𝑎
𝑥 = 𝑎+ . 𝜋
PERSAMAANTRIGONOMETRI

14. QUIZ
QUIZ

15. 5
6
πrad=…
QUIZ
QUIZ Close
Penyelesaian
5
6
𝜋 𝑟𝑎𝑑 =
5
6
× 180°
= 150°

16. Nilaidarisin10
15°adalah
QUIZ
QUIZ Close
Penyelesaian
= 2 𝑐𝑜𝑠 (45° − 30°) = 2 𝑐𝑜𝑠 15°
= 𝑐𝑜𝑠 15° + 𝑐𝑜𝑠 15°𝑠𝑖𝑛 105° + 𝑐𝑜𝑠 15°
= 𝑠𝑖𝑛 (90° + 15°) + 𝑐𝑜𝑠 15°
= ½ (√6 + √2) = ½√6 + ½√2
= 2 (½√2. ½√3 + ½√2 . ½)𝑠𝑖𝑛 105° + 𝑐𝑜𝑠 15°
= 2 (𝑐𝑜𝑠 45° 𝑐𝑜𝑠 30° + 𝑠𝑖𝑛 45° 𝑠𝑖𝑛 30°)

17. melintangpadasebuahja
sudut30°.Jikapanjang
adalah8meter,tentukan
tersebut!
QUIZ
QUIZ Close
Penyelesaian
𝐿𝑒𝑏𝑎𝑟 𝑗𝑎𝑙𝑎𝑛 = 𝐵𝐶 = 4 𝑚𝑒𝑡𝑒𝑟𝐵𝐶
= 1/2 × 𝐴𝐶 = 1/2 × 8
= 4 𝑚𝑒𝑡𝑒𝑟𝐵𝐶/𝐴𝐶 = 1/2𝑠𝑖𝑛 30°
= 𝐵𝐶/𝐴𝐶𝑠𝑖𝑛 30° = 1/2

18. Tan75°=
QUIZ
QUIZ Close
Penyelesaian
tan 75° = tan 45° + 30°
=
tan 𝐴 + 𝑡𝑎𝑛𝐵
1 − 𝑡𝑎𝑛𝐴 × 𝑡𝑎𝑛𝐵
=
tan 45° + 𝑡𝑎𝑛30°
1 − 𝑡𝑎𝑛45° × 𝑡𝑎𝑛30°
=
1 + (1
3) 3
1 − [1 × 1
3 3]
=
(3 + 3)
3
(3 − 3)
3
=
(3 + 3)
3
(3 − 3)
3
×
(3 + 3)
3
(3 + 3)
3
=
(9 + 6 3 + 3)
9
(9 − 3)
9
=
(12 + 6 3)
9
6
9
=
12 + 6 3
6

19. panjangAC=AB=6c
sebesar120°.Tentu
segitigaABC!
QUIZ
QUIZ Close
Penyelesaian
𝑇𝐶
𝐴𝐶
= cos 60 °
𝑇𝐶 = 𝐴𝐶 cos 60°
= 6 ×
1
2
= 3 𝑐𝑚
𝐴𝑇
𝐴𝐶
= 𝑠𝑖𝑛 60 °
𝑇𝐶 = 𝐴𝐶 𝑠𝑖𝑛 60°
= 6 ×
1
2
3
= 3 3 𝑐𝑚
𝐴𝐵 = 2𝐴𝑇 = 6 3
𝐿𝑢𝑎𝑠 =
𝐴𝐵 × 𝑇𝐶
2
=
6 3 × 3
2
= 9 3 𝑐𝑚2
A B
C
T
60° 6 cm6 cm

21. KELOMPOK

22. AFIFAH PINAKARATNA [3]
JULIUS DANES NUGROHO [17]
VENI INGRID [36]
ANANDWI ARRETO [6]
HANIF ABDURRAHMAN [15]
AJENG VIOLA [4]
TIARA MARTHA [35]

23. THANK YOU