This document provides information about trigonometry including definitions of trigonometric ratios, quadrant values, trigonometric identities, and example problems. It begins with definitions of sine, cosine, and tangent ratios. It then covers key topics like trigonometric ratios in each quadrant, trigonometric identities, addition and subtraction formulas, multiplication formulas, and example problems with solutions. The document is a lesson plan on trigonometry concepts and formulas for a high school math class.

1. MATEMATIKA
TRIGONOMETRI
Disusun oleh :
DINI H NUPUS
.
Kelas :
X IIS 3
MATERI PELAJARAN
TENTANG

2. TRIGONOMETRI
Konsep Umum : PHYTAGORAS
Sin ∝ =
𝑑𝑒𝑝𝑎𝑛
𝑚𝑖𝑟𝑖𝑛𝑔
=
3
5
Cos ∝ =
𝑠𝑎𝑚𝑝𝑖𝑛𝑔
𝑚𝑖𝑟𝑖𝑛𝑔
=
4
5
Tan ∝ =
𝑑𝑒𝑝𝑎𝑛
𝑠𝑎𝑚𝑝𝑖𝑛𝑔
=
3
4
Sec ∝ =
1
𝐶𝑜𝑠 ∝
=
1
4
5
=
5
4
Cosec ∝ =
1
𝑆𝑖𝑛 ∝
=
1
3
5
=
5
3
Cot ∝ =
1
𝑇𝑎𝑛 ∝
=
1
3
4
=
4
3

3. KUNCI SUKSES MATERI
TRIGONOMETRI
WAJIB
DI HAFALKAN !!!

4. NILAI PERBANDINGAN
TRIGONOMETRI
RUMUS IDENTITAS
TRIGONOMETRI
RUMUS 1
PENJUMLAHAN
SUDUT (sinus/cosinus)
RUMUS 2
JUMLAH & SELISIH
SUDUT (sinus/cosinus)
RUMUS 3
PERKALIAN SUDUT
(sinus/cosinus)
RUMUS 4
TRIGONOMETRI

5. NILAI PERBANDINGAN
TRIGONOMETRI
Kuadran II
(180°− ∝)
90° < 𝐱 < 180°
Sin +
Kuadran I
(90°− ∝)
< 90°
All +
Kuadran III
(180°+ ∝)
180° < 𝐱 < 360°
Tan +
Kuadran IV
(360°− ∝)
Cos +

6. Contoh Soal
A.Sin 140° = … B.Cos 240° = …
Penyelesaian:
B. Cos 240° = Kuadran III
Cos (18𝟎°+ ∝) = 240°
Cos (1𝟖𝟎° + 𝟔𝟎°) = 240°
∝ = 6𝟎°
Cos 60° =
Penyelesaian:
A. Sin 135° = Kuadran II
Sin (180°− ∝) = 135°
Sin (180° − 𝟒𝟓°) = 135°
∝ = 𝟒𝟎°
Sin 𝟒𝟓° =

7. RUMUS IDENTITAS
TRIGONOMETRI
1. 𝑺𝒊𝒏 𝟐
𝑨 + 𝑪𝒐𝒔 𝟐
𝑨 = 𝟏
2. 1 + 𝑻𝒂𝒏 𝟐
𝑨 =
𝟏
𝑪𝒐𝒔 𝟐 𝑨
= 𝑺𝒆𝒄 𝟐
𝑨
3. 1 + 𝑪𝒐𝒕 𝟐
𝑨 =
𝟏
𝑺𝒆𝒄 𝟐 𝑨
= 𝑪𝒐𝒔𝒆𝒄 𝟐
𝑨
Tidak ada contoh soal

8. RUMUS 1
PENJUMLAHAN SUDUT
(SINUS/COSINUS)
SINUS
1. 𝐒𝐢𝐧 𝐀 + 𝐁 = 𝐒𝐢𝐧𝐀. 𝐂𝐨𝐬𝐁 + 𝐂𝐨𝐬𝐀. 𝐒𝐢𝐧𝐁
2. 𝐒𝐢𝐧 𝐀 − 𝐁 = 𝐒𝐢𝐧𝐀. 𝐂𝐨𝐬𝐁 − 𝐂𝐨𝐬𝐀. 𝐒𝐢𝐧𝐁
COSINUS
1. Cos 𝐀 + 𝐁 = 𝐂𝐨𝐬𝐀. 𝐂𝐨𝐬𝐁 − 𝐒𝐢𝐧𝐀. 𝐒𝐢𝐧𝐁
2. Cos 𝐀 − 𝐁 = 𝐂𝐨𝐬𝐀. 𝐂𝐨𝐬𝐁 + 𝐒𝐢𝐧𝐀. 𝐒𝐢𝐧𝐁

9. Contoh Soal
Penyelesaian:
A. Sin (45° + 60°)
= Sin 45°. Cos 60° + Cos 45°. Sin 60°
= 1
2 2. 1
2+1
2 2.1
2 3
= 1
4 2+1
4 6
B. Sin 36°. Cos 24° + Cos 36°. Sin 24°
= Sin (36° + 24°)
= Sin 60°
= 1
2 3
Tentukan Nilai dari:
A.Sin (45° + 𝟔𝟎°) !
B.Sin 36°. 𝐂𝐨𝐬 𝟐𝟒° + 𝐂𝐨𝐬 𝟑𝟔°. 𝐒𝐢𝐧 𝟐𝟒° !

10. RUMUS 2
JUMLAH & SELISIH SUDUT
(SINUS/COSINUS)
SINUS
1. 𝐒𝐢𝐧𝐀 + 𝐒𝐢𝐧𝐁 = 𝟐. 𝐒𝐢𝐧 𝟏
𝟐 𝐀 + 𝐁 . 𝐂𝐨𝐬 𝟏
𝟐 𝐀 − 𝐁
2. 𝐒𝐢𝐧𝐀 − 𝐒𝐢𝐧𝐁 = −𝟐. 𝐒𝐢𝐧 𝟏
𝟐 𝐀 + 𝐁 . 𝐂𝐨𝐬 𝟏
𝟐 𝐀 − 𝐁
COSINUS
1. Cos𝐀 + 𝐂𝐨𝐬𝐁 = 𝟐. 𝐂𝐨𝐬 𝟏
𝟐 𝐀 + 𝐁 . 𝐂𝐨𝐬 𝟏
𝟐 𝐀 − 𝐁
2. 𝐂𝐨𝐬𝐀 − 𝐂𝐨𝐬𝐁 = −𝟐. 𝐒𝐢𝐧 𝟏
𝟐 𝐀 + 𝐁 . 𝐒𝐢𝐧 𝟏
𝟐 𝐀 − 𝐁

11. Contoh Soal
Penyelesaian:
Cos 90° + 𝐶𝑜𝑠 30°
= 2. 𝐶𝑜𝑠 1
2 𝐴 + 𝐵 . 𝐶𝑜𝑠 1
2 𝐴 − 𝐵
= 2. 𝐶𝑜𝑠 1
2 90° + 30° . 𝐶𝑜𝑠 1
2 90° − 30°
= 2. 𝐶𝑜𝑠 1
2 . 120° . 𝐶𝑜𝑠 1
2 . 60°
= 2. 𝐶𝑜𝑠 60° . 𝐶𝑜𝑠 30°
= 2. 1
2 . 1
2 3
= 1 . 1
2 3
Tentukan Nilai dari :
Cos 90° + 𝐂𝐨𝐬 𝟑𝟎° !

12. RUMUS 3
PERKALIAN SUDUT
(SINUS/COSINUS)
1. 𝟐. 𝐒𝐢𝐧𝐀. 𝐂𝐨𝐬𝐁 = 𝐒𝐢𝐧 𝐀 + 𝐁 + 𝐒𝐢𝐧 𝐀 − 𝐁
2. 𝟐. 𝐂𝐨𝐬𝐀. 𝐒𝐢𝐧𝐁 = 𝐒𝐢𝐧 𝐀 + 𝐁 − 𝐒𝐢𝐧 𝐀 − 𝐁
3. 2.Cos𝐀. 𝐂𝐨𝐬𝐁 = 𝐂𝐨𝐬 𝐀 + 𝐁 + 𝐂𝐨𝐬 𝐀 − 𝐁
4. −𝟐. 𝐂𝐨𝐬𝐀. 𝐂𝐨𝐬𝐁 = 𝐂𝐨𝐬 𝐀 + 𝐁 − 𝐒𝐢𝐧 𝐀 − 𝐁

13. Contoh Soal
Penyelesaian:
2. Cos 60°. Sin 60°
= 2. Sin 60° + 30° − Sin 60° − 30°
= 2. Sin 90° − Sin 30°
= 2. 1 - 1
2
= 2 - 1
2
𝐓𝐞𝐧𝐭𝐮𝐤𝐚𝐧 𝐍𝐢𝐥𝐚𝐢 𝐝𝐚𝐫𝐢 ∶
𝟐. 𝐂𝐨𝐬 𝟔𝟎°. 𝐒𝐢𝐧 𝟑𝟎°

14. RUMUS 4
TRIGONOMETRI
1. 𝑺𝒊𝒏 𝟐
∝ = 𝟐. 𝑺𝒊𝒏 ∝. 𝑪𝒐𝒔 ∝
2. 𝑪𝒐𝒔 𝟐
∝ = 𝑪𝒐𝒔 𝟐
∝ −𝑺𝒊𝒏 𝟐
∝
=2. 𝑪𝒐𝒔 𝟐
∝ −1
3. 𝑻𝒂𝒏 𝟐
∝ =
𝟐.𝑻𝒂𝒏 ∝
𝟏−𝑻𝒂𝒏 𝟐∝

15. Contoh Soal
Penyelesaian:
𝑆𝑖𝑛230° = 𝑆𝑖𝑛 30° 2
= 1
2
2
= 1
4
Bentuk sederhana dari :
𝑺𝒊𝒏 𝟐
𝟑𝟎° !

16. LATIHAN
SOAL
1. Cos (270°)
2. Sin (204°)
3. Tan (60°)
4. Sec (167°)
5. Sin260°+Cos260°
6. 2. 𝐶𝑜𝑠260°+2. 𝑆𝑖𝑛245+3. 𝑇𝑎𝑛245°
7. Sin 135°
8. Cos(90°-30°)
9. Cos 60°-Cos 30°
10.Jika f(x) = (Cos x + Sin x) . Tentukan nilai f(x),
jika x = 45°

17. PEMBAHASAN
SOAL
1. Cos (270°) = K III
Cos (180°+∝) = 270°
Cos (180°+𝟗𝟎°) = 270°
∝ = 𝟗𝟎°
Cos 𝟗𝟎° = 𝟎
2. Sin (204°) = K III
Sin (180°+∝) = 204°
Sin (180°+𝟐𝟒°) = 204°
∝ = 𝟐𝟒° (−)
3. Tan (60°) = K I
Tan (90°− ∝) = 60°
Tan (90° − 𝟑𝟎°) = 60°
∝ = 𝟑𝟎°
Tan 3𝟎° = 𝟏
𝟑 𝟑
4. Sec (167°) = K II
Sec (180° −∝) = 167°
Sin (180° − 𝟏𝟑°) = 167°
∝ = 𝟏𝟑° (+)

18. 5. 𝐒𝐢𝐧 𝟐60°+𝐂𝐨𝐬 𝟐60°
= (Sin 60°) 𝟐+(Cos 60°) 𝟐
= ( 𝟏
𝟐 𝟑) 𝟐
+( 𝟏
𝟐) 𝟐
= 𝟏
𝟒 . 𝟑 + 𝟏
𝟒
= 𝟑
𝟒 + 𝟏
𝟒
= 𝟒
𝟒
= 1
6. 2. 𝐂𝐨𝐬 𝟐60°+2. 𝐒𝐢𝐧 𝟐45+3. 𝐓𝐚𝐧 𝟐45°
= 2(Cos 60°) 𝟐
+ 2(Sin 60°) 𝟐
+3(Tan 𝟒𝟓°) 𝟐
= 2( 𝟏
𝟐) 𝟐 + 𝟐( 𝟏
𝟐 𝟐) 𝟐+𝟑(𝟏) 𝟐
= 2( 𝟏
𝟒) +2( 𝟏
𝟒.2)+3.1
= 𝟐
𝟒+ 𝟐
𝟒.4+3
= 𝟐
𝟒+2+3
= 𝟐
𝟒 + 𝟓

19. 7. Sin 135° = (Sin 90+45)
= 𝐒𝐢𝐧 𝐀 + 𝐁 = 𝐒𝐢𝐧𝐀. 𝐂𝐨𝐬𝐁 + 𝐂𝐨𝐬𝐀. 𝐒𝐢𝐧𝐁
= Sin 90°.Cos 45°+Cos 90°.Sin 45°
= 1. 𝟏
𝟐 𝟐+0. 𝟏
𝟐 𝟐
= 𝟏
𝟐 𝟐
8. Cos(90°-30°)
= Cos 𝐀 − 𝐁 = 𝐂𝐨𝐬𝐀. 𝐂𝐨𝐬𝐁 + 𝐒𝐢𝐧𝐀. 𝐒𝐢𝐧𝐁
= Cos 90°.Cos 45°+Sin 90°.Sin 45°
= 𝟏
𝟐 𝟐.0+ 𝟏
𝟐 𝟑. 𝟏
= 𝟏
𝟐 𝟑

20. 9. Cos 60°-Cos 30°
= 𝐂𝐨𝐬𝐀 − 𝐂𝐨𝐬𝐁 = −𝟐. 𝐒𝐢𝐧 𝟏
𝟐 𝐀 + 𝐁 . 𝐒𝐢𝐧 𝟏
𝟐 𝐀 − 𝐁
= −𝟐. 𝐒𝐢𝐧 𝟏
𝟐 𝟔𝟎° + 𝟑𝟎° . 𝐒𝐢𝐧 𝟏
𝟐 𝟔𝟎° − 𝟑𝟎°
= −𝟐. 𝐒𝐢𝐧 𝟏
𝟐 𝟗𝟎° . 𝐒𝐢𝐧 𝟏
𝟐 𝟑𝟎°
= −𝟐. 𝐒𝐢𝐧 𝟒𝟓°. 𝐒𝐢𝐧 𝟑𝟎°
= −𝟐. 𝟏
𝟐 𝟐. 𝐒𝐢𝐧 𝟏𝟓°
= − 𝟐
𝟐 . −𝟐. 𝐒𝐢𝐧 𝟏𝟓°
= −𝟏. −𝟐. 𝐒𝐢𝐧 𝟏𝟓°
= 𝟐. 𝐒𝐢𝐧 𝟏𝟓°

21. 10. Jika f(x) = (Cos x + Sin x) . Tentukan nilai f(x),
jika x = 45°
F (x) = (Cos x + Sin x) ( Cos x + Sin x)
= 𝑪𝒐𝒔 𝟐 𝒙 + 𝑺𝒊𝒏 𝒙. 𝐂𝐨𝐬 𝒙+ 𝑺𝒊𝒏 𝒙. 𝐂𝐨𝐬 𝒙+ 𝑺𝒊𝒏 𝟐 𝒙
= 𝑪𝒐𝒔 𝟐 𝒙 + 𝑺𝒊𝒏 𝟐 𝒙 + 𝑺𝒊𝒏 𝒙. 𝐂𝐨𝐬 𝒙+ 𝑺𝒊𝒏 𝒙. 𝐂𝐨𝐬 𝒙
= 1 + 𝑺𝒊𝒏 𝒙. 𝐂𝐨𝐬 𝒙+ 𝑺𝒊𝒏 𝒙. 𝐂𝐨𝐬 𝒙
= 1 + (Sin (A+B)+Sin (A-B))
= 1 + (Sin (45°+45°)+Sin (45°-45°))
= 1 + (Sin 90° +Sin90°)
= 1 + 1 + 0
= 2