This document contains mathematical equations and calculations involving trigonometric functions such as sine, cosine, and tangent. Tables are presented showing the values of sine and cosine for various angle inputs. Calculations are shown to solve for unknown lengths and angles using trigonometric ratios and properties. Diagrams are included to illustrate applications of trigonometry to problems involving right triangles.

1. 𝑃𝑟𝑜𝑓𝑒𝑠𝑠𝑜𝑟 𝐸𝑑𝑔𝑎𝑟 𝑅. 𝑆. 𝑆𝑜𝑢𝑧𝑎

2. 180° = π 𝑟𝑎𝑑 →
5 ∙ 180
12
→
÷ 12
÷ 12
5 ∙ 15 = 75

3. 𝑐𝑚 rad
12 2𝜋
2 𝛼
𝛼 =
2 ∙ 2𝜋
12
=
4𝜋
12
=
𝜋
3
1
3

4. ≅
𝜋
2
𝑟𝑎𝑑
>
𝜋
2
𝑟𝑎𝑑= 2𝜋 rad
<
𝜋
2
𝑟𝑎𝑑
𝑜𝑏𝑠: 2𝜋 𝑟𝑎𝑑 ≅ 6,28 𝑟𝑎𝑑
𝑒𝑛𝑡ã𝑜
𝜋
2
𝑟𝑎𝑑 ≅ 1, 57 𝑟𝑎𝑑

6. 𝜋
4 5𝜋
4
9𝜋
4 13𝜋
4

7. 2
2
;
2
2
−
2
2
;
2
2
−
2
2
; −
2
2
2
2
; −
2
2

8. x 𝑠𝑒𝑛1𝑥 𝑦
0 𝑠𝑒𝑛1 ∙ 0 0
𝜋 2 𝑠𝑒𝑛1 ∙ 𝜋/2 1
𝜋 𝑠𝑒𝑛1 ∙ 𝜋 0
3𝜋/2 𝑠𝑒𝑛1 ∙ 3𝜋/2 −1
2𝜋 𝑠𝑒𝑛1 ∙ 2𝜋 0
𝑇𝐴𝐵 1
x 𝑠𝑒𝑛2 ∙ 𝑥 𝑦
0 𝑠𝑒𝑛 2 ∙ 0 0
𝜋 4 𝑠𝑒𝑛 2 ∙ 𝜋/4 1
𝜋/2 𝑠𝑒𝑛 2 ∙ 𝜋/2 0
3𝜋/4 𝑠𝑒𝑛 2 ∙ 3𝜋/4 −1
𝜋 𝑠𝑒𝑛 2 ∙ 𝜋 0
𝑇𝐴𝐵 2

9. 𝑘 = 2
2
𝑃 𝑡
2𝜋 1
4𝜋 𝑡
𝑡 =
1 ∙ 2𝜋
4𝜋
𝑡 =
1
2
Logo 𝑘 − 𝑡 = 2 −
1
2
=
4 − 1
2
=
3
2

10. 1
(0,2)
𝑓 0 = 1 − 1 = 0
𝑓 0 = 1 + 1 = 2
𝑓 0 = cos(0 − 1) = cos(−1)
𝑓 0 = cos(0 + 1) = 𝑐𝑜𝑠1

11. 𝐶(𝑥)
𝐿 𝑥 = 𝑉 𝑥 − 𝐶(𝑥)
V(x)
𝐿 𝑥 = 𝑉 𝑥 − 𝐶(𝑥) = 3 − 2 = 1 → 𝐿 𝑥 = 1000.000
1
2
4
1

12. (3,3)

13. 𝝅
𝟐

14. 𝑡𝑎𝑛𝑔𝑒𝑛𝑡𝑒!!!
𝑡𝑔𝛼 =
𝐶𝑂
𝐶𝐴
→ 𝑡𝑔50° =
𝑃𝑂𝑁𝑇𝐸
10
→ 1,19 =
𝑃𝑂𝑁𝑇𝐸
10
→ 𝑃𝑂𝑁𝑇𝐸 = 10 ∙ 1,19 → 𝑃𝑂𝑁𝑇𝐸 = 11,9 𝑚
𝐶𝑎𝑡𝑒𝑡𝑜 𝑜𝑝𝑜𝑠𝑡𝑜
𝐶𝑎𝑡𝑒𝑡𝑜 𝑎𝑑𝑗𝑎𝑠𝑐𝑒𝑛𝑡𝑒

16. 200𝑚
1,5𝑚
ℎ
𝐴𝑙𝑡 = ℎ + 1,5𝑚
𝑡𝑔𝛼 =
𝐶𝑂
𝐶𝐴
→ 𝑡𝑔 30° =
ℎ
200
→ 0,577 =
ℎ
200
→ ℎ = 200 ∙ 0,577
→ ℎ ≅ 115,4 𝑚 𝐴𝑙𝑡 = ℎ + 1,5𝑚→ 𝐴𝑙𝑡 = 115,4 + 1,5 → 𝐴𝑙𝑡 ≅ 116,9𝑚