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# Trig 1 lesson 4 sine

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Defining the Sine ratio in Trigonometry.

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### Trig 1 lesson 4 sine

1. 1. Defining the sine, cosine and tangent ratios for angles in right-angled trianglesPart 1 - Sine<br />
2. 2. The Sine Ratio<br />
3. 3. The Sine Ratio<br />πineπ=πππππ ππ‘ππ―π¦πππ‘πππ’π π<br />Β <br />
4. 4. The Sine Ratio<br />The sine of an angle is defined as the ratio between the Opposite and Hypotenuse:<br />πineπ=πππππ ππ‘ππ―π¦πππ‘πππ’π π<br />Β <br />
5. 5. The Sine Ratio<br />The sine of an angle is defined as the ratio between the Opposite and Hypotenuse:<br />πineπ=πππππ ππ‘ππ―π¦πππ‘πππ’π π<br />Β <br />
6. 6. The Sine Ratio<br />The sine of an angle is defined as the ratio between the Opposite and Hypotenuse:<br />πineπ=πππππ ππ‘ππ―π¦πππ‘πππ’π π<br />Β <br />
7. 7. The Sine Ratio<br />The sine of an angle is defined as the ratio between the Opposite and Hypotenuse:<br />πineπ=πππππ ππ‘ππ―π¦πππ‘πππ’π π<br />Β <br />
8. 8. The Sine Ratio<br />The sine of an angle is defined as the ratio between the Opposite and Hypotenuse:<br />πineπ=πππππ ππ‘ππ―π¦πππ‘πππ’π π<br />Β <br />
9. 9. The Sine Ratio<br />The sine of an angle is defined as the ratio between the Opposite and Hypotenuse:<br />πineπ=πππππ ππ‘ππ―π¦πππ‘πππ’π π<br />Β <br />
10. 10. The Sine Ratio<br />The sine of an angle is defined as the ratio between the Opposite and Hypotenuse:<br />πineπ=πππππ ππ‘ππ―π¦πππ‘πππ’π π<br />Β <br />Remember:<br />
11. 11. The Sine Ratio<br />The sine of an angle is defined as the ratio between the Opposite and Hypotenuse:<br />πineπ=πππππ ππ‘ππ―π¦πππ‘πππ’π π<br />Β <br />Remember:<br />
12. 12. The Sine Ratio<br />The sine of an angle is defined as the ratio between the Opposite and Hypotenuse:<br />πineπ=πππππ ππ‘ππ―π¦πππ‘πππ’π π<br />Β <br />S<br />Remember:<br />
13. 13. The Sine Ratio<br />The sine of an angle is defined as the ratio between the Opposite and Hypotenuse:<br />πineπ=πππππ ππ‘ππ―π¦πππ‘πππ’π π<br />Β <br />S<br />Remember:<br />
14. 14. The Sine Ratio<br />The sine of an angle is defined as the ratio between the Opposite and Hypotenuse:<br />πineπ=πππππ ππ‘ππ―π¦πππ‘πππ’π π<br />Β <br />SO<br />Remember:<br />
15. 15. The Sine Ratio<br />The sine of an angle is defined as the ratio between the Opposite and Hypotenuse:<br />πineπ=πππππ ππ‘ππ―π¦πππ‘πππ’π π<br />Β <br />SO<br />Remember:<br />
16. 16. The Sine Ratio<br />The sine of an angle is defined as the ratio between the Opposite and Hypotenuse:<br />πinππ=πππππ ππ‘ππ―π¦πππ‘πππ’π π<br />Β <br />SOH<br />Remember:<br />
17. 17. The Sine Ratio<br />Remember: SOH<br />
18. 18. The Sine Ratio<br />Remember: SOH<br />
19. 19. The Sine Ratio<br />Remember: SOH<br />sineofπisequalto πΆπππ―ππ=ππ=π.πππ.ππ<br />Β <br />
20. 20. The Sine Ratio<br />Remember: SOH<br />sineofπisequalto πΆπππ―ππ=ππ=π.πππ.ππ<br />Β <br />
21. 21. The Sine Ratio<br />Remember: SOH<br />sineofπisequalto πΆπππ―ππ=ππ=π.πππ.ππ<br />Β <br />
22. 22. The Sine Ratio<br />Remember: SOH<br />sineofπisequalto πΆπππ―ππ=ππ=π.πππ.ππ<br />Β <br />Opposite<br />
23. 23. The Sine Ratio<br />Remember: SOH<br />Remember: SOH<br />sineofπisequalto πΆπππ―ππ=ππ=π.πππ.ππ<br />Β <br />Opposite<br />
24. 24. The Sine Ratio<br />Remember: SOH<br />sineofπisequalto πΆπππ―ππ=ππ=π.πππ.ππ<br />Β <br />Hypotenuse<br />Opposite<br />
25. 25. The Sine Ratio<br />Remember: SOH<br />sineofπisequalto πΆπππ―ππ=ππ=π.πππ.ππ<br />Β <br />Hypotenuse<br />Opposite<br />
26. 26. The Sine Ratio<br />Remember: SOH<br />sineofπisequalto πΆπππ―ππ=ππ=π.πππ.ππ<br />Β <br />Hypotenuse<br />Opposite<br />
27. 27. The Sine Ratio<br />Remember: SOH<br />sineofπisequalto πΆπππ―ππ=ππ=π.πππ.ππ<br />Β <br />Hypotenuse<br />Opposite<br />
28. 28. The Sine Ratio<br />Remember: SOH<br />sineofπisequalto πΆπππ―ππ=ππ=π.πππ.ππ<br />Β <br />Hypotenuse<br />Opposite<br />
29. 29. The Sine Ratio<br />Remember: SOH<br />sineofπisequalto πΆπππ―ππ=ππ=π.πππ.ππ<br />Β <br />Hypotenuse<br />Opposite<br />
30. 30. The Sine Ratio<br />Remember: SOH<br />sineofπisequalto πΆπππ―ππ=ππ=π.πππ.ππ<br />Β <br />Hypotenuse<br />Opposite<br />
31. 31. The Sine Ratio<br />Remember: SOH<br />sineofπisequalto πΆπππ―ππ=ππ=π.πππ.ππ<br />Β <br />Hypotenuse<br />Opposite<br />
32. 32. The Sine Ratio<br />Remember: SOH<br />sineofπisequalto πΆπππ―ππ=ππ=π.πππ.ππ<br />Β <br />Hypotenuse<br />Opposite<br />
33. 33. The Sine Ratio<br />πineπ=πππππ ππ‘ππ―π¦πππ‘πππ’π π<br />Β <br />
34. 34. The Sine Ratio<br />ο±<br />πineπ=πππππ ππ‘ππ―π¦πππ‘πππ’π π<br />Β <br />
35. 35. The Sine Ratio<br />ο±<br />πineπ=πΆπ―<br />Β <br />πineπ=πππππ ππ‘ππ―π¦πππ‘πππ’π π<br />Β <br />
36. 36. The Sine Ratio<br />ο±<br />πineπ½=πΆπ―<br />Β <br />πineπ=πππππ ππ‘ππ―π¦πππ‘πππ’π π<br />Β <br />
37. 37. The Sine Ratio<br />ο±<br />πineπ=πΆπ―<br />Β <br />πineπ=πππππ ππ‘ππ―π¦πππ‘πππ’π π<br />Β <br />
38. 38. The Sine Ratio<br />ο±<br />πineπ=π.πππ―<br />Β <br />πineπ=πππππ ππ‘ππ―π¦πππ‘πππ’π π<br />Β <br />
39. 39. The Sine Ratio<br />ο±<br />πineπ=π.πππ―<br />Β <br />πineπ=πππππ ππ‘ππ―π¦πππ‘πππ’π π<br />Β <br />
40. 40. The Sine Ratio<br />ο±<br />πineπ=π.πππ.ππ<br />Β <br />πineπ=πππππ ππ‘ππ―π¦πππ‘πππ’π π<br />Β <br />
41. 41. The Sine Ratio<br />ο±<br />πineπ=π.πππ.ππ<br />Β <br />πineπ=πππππ ππ‘ππ―π¦πππ‘πππ’π π<br />Β <br />
42. 42. The Sine Ratio<br />ο±<br />πineπ=π.πππ.ππ<br />Β <br />ο‘<br />πineπ=πππππ ππ‘ππ―π¦πππ‘πππ’π π<br />Β <br />
43. 43. The Sine Ratio<br />ο±<br />πineπ=π.πππ.ππ<br />Β <br />πineο±=πΆπ―<br />Β <br />ο‘<br />πineπ=πππππ ππ‘ππ―π¦πππ‘πππ’π π<br />Β <br />
44. 44. The Sine Ratio<br />ο±<br />πineπ=π.πππ.ππ<br />Β <br />πineο‘=πΆπ―<br />Β <br />ο‘<br />πineπ=πππππ ππ‘ππ―π¦πππ‘πππ’π π<br />Β <br />
45. 45. The Sine Ratio<br />ο±<br />πineπ=π.πππ.ππ<br />Β <br />πineο‘=πΆπ―<br />Β <br />ο‘<br />πineπ=πππππ ππ‘ππ―π¦πππ‘πππ’π π<br />Β <br />
46. 46. The Sine Ratio<br />ο±<br />πineπ=π.πππ.ππ<br />Β <br />πineο‘=ππ―<br />Β <br />ο‘<br />πineπ=πππππ ππ‘ππ―π¦πππ‘πππ’π π<br />Β <br />
47. 47. The Sine Ratio<br />ο±<br />πineπ=π.πππ.ππ<br />Β <br />πineο‘=ππ―<br />Β <br />ο‘<br />πineπ=πππππ ππ‘ππ―π¦πππ‘πππ’π π<br />Β <br />
48. 48. The Sine Ratio<br />ο±<br />πineπ=π.πππ.ππ<br />Β <br />πineο‘=ππ<br />Β <br />ο‘<br />πineπ=πππππ ππ‘ππ―π¦πππ‘πππ’π π<br />Β <br />
49. 49. The Sine Ratio<br />ο±<br />πineπ=π.πππ.ππ<br />Β <br />πineο‘=ππ<br />Β <br />ο‘<br />πineπ=πππππ ππ‘ππ―π¦πππ‘πππ’π π<br />Β <br />
50. 50. The Sine Ratio<br />ο±<br />πineπ=π.πππ.ππ<br />Β <br />πineο‘=ππ<br />Β <br />ο‘<br />πineπ=πππππ ππ‘ππ―π¦πππ‘πππ’π π<br />Β <br />ο’<br />
51. 51. The Sine Ratio<br />ο±<br />πineπ=π.πππ.ππ<br />Β <br />πineο‘=ππ<br />Β <br />ο‘<br />πineπ=πππππ ππ‘ππ―π¦πππ‘πππ’π π<br />Β <br />πineο±=πΆπ―<br />Β <br />ο’<br />
52. 52. The Sine Ratio<br />ο±<br />πineπ=π.πππ.ππ<br />Β <br />πineο‘=ππ<br />Β <br />ο‘<br />πineπ=πππππ ππ‘ππ―π¦πππ‘πππ’π π<br />Β <br />πineο’=πΆπ―<br />Β <br />ο’<br />
53. 53. The Sine Ratio<br />ο±<br />πineπ=π.πππ.ππ<br />Β <br />πineο‘=ππ<br />Β <br />ο‘<br />πineπ=πππππ ππ‘ππ―π¦πππ‘πππ’π π<br />Β <br />πineο’=πΆπ―<br />Β <br />ο’<br />
54. 54. The Sine Ratio<br />ο±<br />πineπ=π.πππ.ππ<br />Β <br />πineο‘=ππ<br />Β <br />ο‘<br />πineπ=πππππ ππ‘ππ―π¦πππ‘πππ’π π<br />Β <br />πineο’=ππ―<br />Β <br />ο’<br />
55. 55. The Sine Ratio<br />ο±<br />πineπ=π.πππ.ππ<br />Β <br />πineο‘=ππ<br />Β <br />ο‘<br />πineπ=πππππ ππ‘ππ―π¦πππ‘πππ’π π<br />Β <br />πineο’=ππ―<br />Β <br />ο’<br />
56. 56. The Sine Ratio<br />ο±<br />πineπ=π.πππ.ππ<br />Β <br />πineο‘=ππ<br />Β <br />ο‘<br />πineπ=πππππ ππ‘ππ―π¦πππ‘πππ’π π<br />Β <br />πineο’=ππ.ππ<br />Β <br />ο’<br />
57. 57. The Sine Ratio<br />ο±<br />πineπ=π.πππ.ππ<br />Β <br />πineο‘=ππ<br />Β <br />ο‘<br />πineπ=πππππ ππ‘ππ―π¦πππ‘πππ’π π<br />Β <br />πineο’=ππ.ππ<br />Β <br />ο’<br />
58. 58. The Sine Ratio<br />ο±<br />πineπ=π.πππ.ππ<br />Β <br />πineο‘=ππ<br />Β <br />ο‘<br />πineπ=πππππ ππ‘ππ―π¦πππ‘πππ’π π<br />Β <br />ο¦<br />πineο’=ππ.ππ<br />Β <br />ο’<br />
59. 59. The Sine Ratio<br />ο±<br />πineπ=π.πππ.ππ<br />Β <br />πineο‘=ππ<br />Β <br />ο‘<br />πineπ=πππππ ππ‘ππ―π¦πππ‘πππ’π π<br />Β <br />ο¦<br />πineο±=πΆπ―<br />Β <br />πineο’=ππ.ππ<br />Β <br />ο’<br />
60. 60. The Sine Ratio<br />ο±<br />πineπ=π.πππ.ππ<br />Β <br />πineο‘=ππ<br />Β <br />ο‘<br />πineπ=πππππ ππ‘ππ―π¦πππ‘πππ’π π<br />Β <br />ο¦<br />πineο¦=πΆπ―<br />Β <br />πineο’=ππ.ππ<br />Β <br />ο’<br />
61. 61. The Sine Ratio<br />ο±<br />πineπ=π.πππ.ππ<br />Β <br />πineο‘=ππ<br />Β <br />ο‘<br />πineπ=πππππ ππ‘ππ―π¦πππ‘πππ’π π<br />Β <br />ο¦<br />πineο¦=πΆπ―<br />Β <br />πineο’=ππ.ππ<br />Β <br />ο’<br />
62. 62. The Sine Ratio<br />ο±<br />πineπ=π.πππ.ππ<br />Β <br />πineο‘=ππ<br />Β <br />ο‘<br />πineπ=πππππ ππ‘ππ―π¦πππ‘πππ’π π<br />Β <br />ο¦<br />πineο¦=π.πππ―<br />Β <br />πineο’=ππ.ππ<br />Β <br />ο’<br />
63. 63. The Sine Ratio<br />ο±<br />πineπ=π.πππ.ππ<br />Β <br />πineο‘=ππ<br />Β <br />ο‘<br />πineπ=πππππ ππ‘ππ―π¦πππ‘πππ’π π<br />Β <br />ο¦<br />πineο¦=π.πππ―<br />Β <br />πineο’=ππ.ππ<br />Β <br />ο’<br />
64. 64. The Sine Ratio<br />ο±<br />πineπ=π.πππ.ππ<br />Β <br />πineο‘=ππ<br />Β <br />ο‘<br />πineπ=πππππ ππ‘ππ―π¦πππ‘πππ’π π<br />Β <br />ο¦<br />πineο¦=π.πππ<br />Β <br />πineο’=ππ.ππ<br />Β <br />ο’<br />
65. 65. The Sine Ratio<br />ο±<br />πineπ=π.πππ.ππ<br />Β <br />πineο‘=ππ<br />Β <br />ο‘<br />πineπ=πππππ ππ‘ππ―π¦πππ‘πππ’π π<br />Β <br />ο¦<br />πineο¦=π.πππ<br />Β <br />πineο’=ππ.ππ<br />Β <br />ο’<br />
66. 66. The Sine Ratio<br />Remember:<br />πΊππππ=πΆππππ ππ‘ππ―π¦πππ‘πππ’π π ->SOH<br />Β <br />
67. 67. The Sine Ratio<br />Remember:<br />πΊππππ=πΆππππ ππ‘ππ―π¦πππ‘πππ’π π ->SOH<br />Β <br />
68. 68. The Sine Ratio<br />Remember:<br />πΊππππ=πΆππππ ππ‘ππ―π¦πππ‘πππ’π π->SOH<br />Β <br />
69. 69. The Sine Ratio<br />Remember:<br />πΊππππ=πΆππππ ππ‘ππ―π¦πππ‘πππ’π π ->SOH<br />Β <br />
70. 70. The Sine Ratio<br />Remember:<br />πΊππππ=πΆππππ ππ‘ππ―π¦πππ‘πππ’π π ->SOH<br />Β <br />
71. 71. The Sine Ratio<br />Remember:<br />πΊππππ=πΆππππ ππ‘ππ―π¦πππ‘πππ’π π ->SOH<br />Β <br />
72. 72. The Sine Ratio<br />Remember:<br />πΊππππ=πΆππππ ππ‘ππ―π¦πππ‘πππ’π π ->SOH<br />Β <br />