1. 42
5
0011 0010 1010 1101 0001 0100 1011
1

2. INTEGRANTES
Brayan Choque Chura
Anthony Chambilla Chuquimia
42
5
‘’5to G’’
0011 0010 1010 1101 0001 0100 1011
1 Erick Gallegos Colana
Edwin Huamolle Mamani
Franklin Juárez Musaja

3. 42
5
0011 0010 1010 1101 0001 0100 1011
1

4. 42
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0011 0010 1010 1101 0001 0100 1011
1

5. 42
5
0011 0010 1010 1101 0001 0100 1011
1 2 Cos 3푥 + 3 = 0
Cos 3푥 = 푎푟푐 Cos −
3
2
3푥 = 휋 − 푎푟푐 Cos
3
2
3푥 = π −
휋
6
∴ 풙 =
ퟓ흅
ퟏퟖ

6. 42
5
0011 0010 1010 1101 0001 0100 1011
1 2Sen 푥 − 3 = 0
푥 = 푛휋 + −1 푛푎푟푐 Sen
3
2
휋
3
∴ 퐱 = 퐧흅 + −ퟏ 풏.
흅
ퟑ

7. 42
5
0011 0010 1010 1101 0001 0100 1011
1

8. 42
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0011 0010 1010 1101 0001 0100 1011
1 C o tg 3 푥 − ퟏ = ퟎ → C o t g 3 푥 − ퟏ
푥 =
푛휋 + 푎푟푐 Cotg 1
3
푥 =
푛휋 +
휋
4
3
푥 =
푛휋
3
+
휋
12 ∴ 풙 = ퟔퟎ°풏 + ퟏퟓ° ∴ 푪, 푺. = ퟏퟓ°; ퟕퟓ°; ퟏퟑퟓ°

9. 42
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0011 0010 1010 1101 0001 0100 1011
1 ퟒ 퐒퐞퐧 풙 퐂퐨퐬 풙 − ퟏ = ퟎ
2.2 Sen 푥 Cos 푥 − 1 = 0
2 Sen 2푥 − 1 = 0
Sen 2푥 =
1
2
2푥 = 30°; 150°; 390°; …
푥 = 15°; 75°; 195°; …
∴ 풙 = ퟏퟓ°
퐒퐞퐧 ퟐ풙 = ퟐ 퐒퐞퐧 풙 퐂퐨퐬 풙

10. 42
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0011 0010 1010 1101 0001 흅
0100 1011
1 풂풓풄 퐒퐞퐧 ퟐ풙 + ퟏ =
ퟔ
풂풓풄 퐒퐞퐧 풙 = 풚 → 퐒퐞퐧 풚 = 풙
푎푟푐 Sen 2푥 + 1 =
휋
6
Sen
휋
6
= 2푥 + 1
1
2
= 2푥 + 1 → 풙 = −
ퟏ
ퟐ

11. 42
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0011 0010 1010 1101 0001 0100 1011
1

12. 42
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T푔 2푥 = 1
2푥 = 푎푟푐 Tg 1
0011 0010 1010 1101 0001 0100 1011
1 2푥 = 푎푟푐 Tg 1
2푥 =
휋
4
∴=
흅
ퟖ
SOLUCION
PRINCIPAL

13. 42
5
Cos 2푥 =
0011 0010 1010 1101 0001 0100 1011
1 2
2
푥 =
2푛휋 ± 푎푟푐 Cos
2
2
2
푥 =
2푛휋 ±
휋
4
2
⇒ ∴ 풙 = 풏흅 ±
흅
ퟖ
SOLUCION
GENERAL

14. 2 = Sec 2푥 → Sec 2푥 = 2
42
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2푛휋 ± 푎푟푐 Cos 2
푥 =
0011 0010 1010 1101 2
0001 0100 1011
1 푥 =
2푛휋 ±
휋
3
2
푥 = 2푛 ±
휋
6
∴ 풙 = ퟏퟖퟎ°풏 ± ퟑퟎ°SOLUCION
GENERAL
푥 = 180° 0 − 30° = −30°
푥 = 180° 0 + 30° = 30°
푥 = 180° 1 − 30° = 150°
푥 = 180° 1 + 30° = 210°
푥 = 180° 2 − 30° = 330°
푥 = 180° 2 + 30° = 390°
NO!!
NO!!
∴ 푪. 푺 = ퟑퟎ°; ퟏퟓퟎ°; ퟐퟏퟎ°; ퟑퟑퟎ°

15. 퐒퐞퐧 ퟑ풙 + ퟑ 퐂퐨퐬 ퟑ풙 = ퟐ
42
5
Sen 훼 + 훽 = Sen 훼 Cos 훽 + Cos 훼 + Sen 훽
Sen 3푥 + 3 Cos 3푥 = 2
0011 0010 1010 1101 0001 0100 1011
1 1
2
Sen 3푥 +
3
2
Cos 3푥 = 1
Sen 3푥.
1
2
+ Cos 3푥.
3
2
= 1
Sen 3푥 . Cos 60° + Cos 3푥 . Sen 60° = 1
Sen 3푥 + 60° = Sen 90°
3푥 + 60° = 90°
∴ 풙 = ퟏퟎ° SOLUCION
PRINCIPAL

16. 42
5
Sec 푎푟푐 Sen 2푥 = Sec 60°
푎푟푐 Sen 2푥 = 60°
0011 0010 1010 1101 0001 0100 1011
Sen 60° = 2푥
1 3
2
= 2푥
∴ 풙 =
ퟑ
ퟒ

17. 42
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2Cos2 푥 − 5Cos 푥 + 2 = 0
Cos 푥
2Cos 푥
−2
−1
0011 Cos 0010 푥 1010 − 2 1101 2Cos 0001 푥 − 0100 1 = 1011
0
1 Cos 푥 − 2 = 0
Cos 푥 = 2
2Cos 푥 − 1 = 0
Cos 푥 =
1
2 ∴ 풙 = ퟔퟎ°

18. 42
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푆푒푛2푥 + Cos 푥 = 0
2Sen 푥 Cos 푥 + Cos 푥 = 0
0011 0010 1010 1101 0001 0100 1011
cos 푥 2Sen 푥 + 1 = 0
1 Cos 푥 = 0
풙 = ퟗퟎ°
Sen 푥 + 1 = 0
Sen 푥 = −
1
2
푥 = ퟐퟏퟎ°
∴ 풙 = ퟗퟎ°

19. 42
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푎푟푐 Sen 푥 + 1 = 훼 → Sen 훼 = 푥 + 1
푎푟푐 Cos 1 − 푥 = 훽 → Cos 훽 = 1 − 푥
휋
훼 + 훽 =
2
0011 0010 1010 1101 0001 0100 1011
1 Sen 훼 = Cos 훽
푥 + 1 = 1 − 푥
2푥 = 0
∴ 풙 = ퟎ

20. 42
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4cos 푥 − 3Sec 푥 = 2T푔 푥
4Cos 푥 − 3
1
Cos 푥
= 2
Sen 푥
Cos 푥
0011 0010 4Cos2 1010 푥 1101 − 3
0001 2Sen 0100 푥
1011
1 =
Cos 푥
Cos 푥
4Cos3 푥 − 3
Cos 3푥
=
2Sen 푥 Cos 푥
Sen 2푥
3푥 + 2푥 = 90° ∴ 풙 = ퟏퟖ°

21. 1 0011 42
5
0010 1010 1101 0001 0100 1011
Tg2 푥 + 2Tg 푥 − 1 = 0
2Tg 푥 = 1 − T푔2 푥
2Tg 푥
= 1
1 − Tg2 푥
Tg 2푥 = 1
푥 =
푛휋 + 푎푟푐 Tg 1
2
푥 =
푛휋 +
휋
4
2
→ 푥 =
푛휋
2
+
휋
8
∴ 풙 =
ퟒ풏 + ퟏ
ퟖ
흅