ListaTrigonometria

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LISTA TRIGONOMETRIA 
 
1. h² = a² + b² sin = �
√�	 cos = � .√�	
√�	 .√�	 
 h² = 3³ + 1² sin = �√�	

�	 .√�	 cos = 
√�	
�	 
 h² = 10 sin = �√�	
√�		 tan = �
� 
 h = √10 sin = �√�	
�	 tan = 3 
 
2. ACD = 30° tan 60° = ��
�� DC + BD 
 tan 30° = ��
�� tan 60° = ��
�� 1 + 3 = 4 
 tan 30° = ��
�� √3 = √�
�� 
 AC = 
√�
√�
�
 BD = 
√�
√� 
 AC = 3 BD = 1 
 
3. sin 30° = ��
� 
 
�
� = ��
�	 
 CO = 10 
 AD + KC 
 20 + 10 = 30cm 
 
4. sin 30° = �
� 
 
�
� = �
� 
 H = 2B 
 
5. sin 30° = 
�	 cos 30° = �
� 
 
�
� . 10 = ! 
√�
� . 10 = " 
 A = 5 B = 5√3 C = 10 
 
6. A = 3 . K A = 3.30 
 B = 4 . K A = 90° 
 C = 5 . K B = 4.30 
 A + B + C = 3K + 4K + 5K = 360° B = 120° 
 12K = 360° C = 150° 
 K = 30° 
 
 A) D = 
#	
� = 45° B) 
$
%&' ()° = 2R 
,
%&' -	° = 2R 
 E = 
��	
� = 60° X = 2 . 10 . 
√�
� Y = 2 . 10 . 
√�
� 
 F = 
�)	
� = 75° X = 10√2 Y = 10√3 
 
 Z² = 10² + 10² - 2 . 10 . 10 . cos 150° 
 Z² = 200 + 100√3 
Z² = 100 (2 + √3) 
 Z = /10002 + √32 
 Z = √100 . 
2 + √3 
 Z = 10 
2 + √3 
 
 
 
 
7. tan 18° = 4
5 tan 20° = 46)
5 
4
	,�� = 46)
	,�- 
 Y = 
4
89' �:° Y = 
46)
89' �	° 0,36X = 0,32(X+5) 
 Y = 
4
	,�� X+5 = 0,36Y 0,36X – 0,32X = 1,6 
Y = 
46)
	,�- 0,04X =1,6 
 X = 40m 
 
 
8. P = 4X =10 sin 15° = ��
;< 
 X = 10/4 DP = 2,5/0,26 
 X = 5/2 DP = 9,61cm 
 
9. 
 �
%&' ()° = �
%&' -	° 30 . 
�
√� . √�
� = AC tan 30° = �;
 � 
 
�	
√=
=
 . sin 60° = !> 
�	 .√�
√� . √2 = !> tan 30° = �;
�)√�√� 
 
�	
√=
=
 . √�
� = !> 
�	 .√�.√�
� = AC 
√�
� = �;
�)√�√� 
 AC = 15√3√2 CD = 15√2? 
 
10. 
� 
%&' )#° = ��
%&' -)° 
 
�	
	,:) = ��
	,#	 
 BC = 10 . 0,90 / 0,85 
 BC = 10,58 
 
11. 360° / 12 = 30° 
 ÂNGULO FORMADO PELOS PONTEIROS DO RELÓGIO É DE 45°. 
 
12. 1 HORA = 360° = VM = 360°/H = 360°/60 MINUTOS 
 1 HORA = 360° = VM = 30°/H = 30°/60 MINUTOS 
 VM = 6°/MIN 
 VM = 0,5°/MIN 
 ∝ = ∝ A + B . C 
6°/MIN . T = 270° + 0,5 MIN .T 
 5,5T = 270° 
 T = 
�D	°
),) T = 49,09 min 
13. X = 45, FIZ OLHANDO UM DESENHO QUE FIZ SÓ QUE FICOU NA FOLHA. 
 
14. cos ∝ = � 
� 
 Cos ∝ = (
) /1 
 Cos ∝ = (
) 
 
15. (sin ∝)² = 1/2 
 (sin ∝) = ±√1/2 
 (sin ∝) = �
√� . √�
√� 
 (sin ∝) = ±√2/2 
16. A) 2R B) C/D = K x = 94,20/1,884 
 R = 60/2 C = 3,14 . 60 x = 50 voltas 
 R = 30 C = 188,4cm 
 1,884m 
17. C = 2K. L P = 2K − 1 + 1 + 1 
 C = 2K. N? P = 2K + 1 
 S = ∝ . O 
 1.1 = 1cm 
 
18. A) 1640°/360° = 4, SOBROU 200 – 2° QUADRANTE 
 B) 2630°/360° = 7, SOBROU 110 – 2° QUADRANTE 
 C)248 K/4 = 62 K = 62K/2K = 31 – 4° QUADRANTE 
 
 
 
19. A) 1640°/360° = 5 VOLTAS -- 1° QUADRANTE 
 B) 25K/4 . 
)P
( = 2 VOLTAS – 1° QUADRANTE 
 C) 1200°/360° = 3 VOLTAS – 3° QUADRANTE 
D) 2350°/360° = 6 VOLTAS – 3° QUADRANTE 
E)31 K/6 . K/6 = 5 K . K/6 = 2 VOLTAS – 3° QUADRANTE 
F)
�-P
: . P
: = 2K . P
: = 1 VOLTA – 1° QUADRANTE 
 
20. F(x) = 100 + X/2 + 3sin(KQ/6) F(2) = 100 + 2/2 + 3 sin K/3 
 F(1) = 100 + ½ + 3/2 F(2) = 101 + 3 √3/2 
 F(1) = 204/2 F(2) = 103,59 
 F(1) = 102 
 
 F(3) = 100 + 3/2 + 3 sin 3K/6 
 F(3) = 203/2 + 3 sin 90° 
 F(3) = 101,5 +3 = 104,5 F(1) + F(2) + F(3) = 102 + 103,59 + 104,5 = 310,05 
 
22. tan 60° = ��
� 
 √3 = 4
�-	° 
 X = 160√3 
 
23. tan 60° = �
;S 
 √30 = �	
;S 
 Ds = 30/√3 . √3/√3 
 Ds = 10√3m