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Understanding Trigonometric Functions and SOHCAHTOA Concepts

This document covers essential trigonometric values and concepts using the SOHCAHTOA framework. It explores the relationships between the sides of right triangles and angles, presenting examples including sine, cosine, tangent, cosecant, secant, and cotangent functions. Key problems demonstrate how to calculate heights and distances using trigonometric ratios. The examples range from basic definitions to real-world applications, highlighting the importance of right triangles in trigonometry. This resource is ideal for students seeking a solid understanding of trigonometric functions.

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Understanding Trigonometric Functions and SOHCAHTOA Concepts

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  1. Trig Values and SOHCAHTOA

  2. Question 1 - 10 SinΘ = 1/√2

  3. Answer 1 – 10 45⁰

  4. Question 1 - 20 Sin = opposite/?

  5. Answer 1 – 20 Hypotenuse

  6. Question 1 - 30 Csc30 =2/?

  7. Answer 1 – 30 1

  8. Question 1 - 40 ? = hypotenuse/opposite

  9. Answer 1 – 40 Cosecant

  10. Question 1 - 50 CscΘ = 2/√3

  11. Answer 1 – 50 60⁰

  12. Question 2 - 10 Cos = ?/hypotenuse

  13. Answer 2 – 10 Adjacent

  14. Question 2 - 20 SecΘ = 2

  15. Answer 2 – 20 60⁰

  16. Question 2 - 30 ? = hypotenuse/adjacent

  17. Answer 2 – 30 Secant

  18. Question 2 - 40 Cos30 = ?/2

  19. Answer 2 – 40 √3

  20. Question 2 - 50 Sec30 = ?/√3

  21. Answer 2 – 50 2

  22. Question 3 - 10 Tan = ?/adjacent

  23. Answer 3 – 10 Opposite

  24. Question 3 - 20 Tan45 = ?

  25. Answer 3 – 20 1

  26. Question 3 - 30 Cot30 = ?

  27. Answer 3 – 30 √3

  28. Question 3 - 40 TanΘ = 1/√3

  29. Answer 3 – 40 30

  30. Question 3 - 50 Cot45 = ?

  31. Answer 3 – 50 1

  32. Question 4 - 10

  33. Answer 4 – 10 1

  34. Question 4 - 20 A man is staring at a tree at a 30 degree angle, 43 yards from the tree. How tall is the tree?

  35. Answer 4 – 20 Tan30 = x/35 35tan30 = x X = 20.207 yards

  36. Question 4 - 30 A man in a car is staring up to the top of his work building at a 55 degree angle. He is 57 feet away from the building. What is the height of the office building?

  37. Answer 4 – 30 Tan55 = x/57 57tan55 = x X = 81.404 feet

  38. Question 4 - 40

  39. Answer 4 – 40

  40. Question 4 - 50 A fisherman was out on a fishing trip when he noticed a lighthouse 100 meters away. He was wondering how tall the lighthouse was. Looking up at a 60 degree angle, how tall was the lighthouse?

  41. Answer 4 – 50 Tan60 = x/100 100tan60 = x X = 173.205 meters tall

  42. Question 5 - 10 ? Is the opposite of Secant

  43. Answer 5 – 10 Cosine

  44. Question 5 - 20 True/False One can use SOHCAHTOA on any triangles

  45. Answer 5 – 20 False; only right triangles

  46. Question 5 - 30 How many special triangles are there with SOHCAHTOA?

  47. Answer 5 – 30 2; 30-60-90 triangles and 45-45-90 triangles

  48. Question 5 - 40 How many trig functions are there?

  49. Answer 5 – 40 6; sin, cos, tan, csc, sec, cot

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