Successfully reported this slideshow.
Upcoming SlideShare
×

# Trig 1 lesson 4 cosine

630 views

Published on

Defining the Cosine ratio in Trigonometry.

Small changes between slides so can be clicked through quickly.

Published in: Education, Technology, Design
• Full Name
Comment goes here.

Are you sure you want to Yes No
• Be the first to comment

• Be the first to like this

### Trig 1 lesson 4 cosine

1. 1. Defining the sine, cosine and tangent ratios for angles in right-angled trianglesPart 2 - Cosine<br />
2. 2. The Cosine Ratio<br />
3. 3. The Cosine Ratio<br />
4. 4. The Cosine Ratio<br />The Cosine of an angle is defined as the ratio between the Adjacent and the Hypotenuse<br />
5. 5. The Cosine Ratio<br />The Cosine of an angle is defined as the ratio between the Adjacent and the Hypotenuse<br />πosineπ=π¨πππππππ‘π―π¦πππ‘πππ’π π<br />Β <br />
6. 6. The Cosine Ratio<br />The Cosine of an angle is defined as the ratio between the Adjacent and the Hypotenuse<br />πosineπ=π¨πππππππ‘π―π¦πππ‘πππ’π π<br />Β <br />
7. 7. The Cosine Ratio<br />The Cosine of an angle is defined as the ratio between the Adjacent and the Hypotenuse<br />πosineπ=π¨πππππππ‘π―π¦πππ‘πππ’π π<br />Β <br />
8. 8. The Cosine Ratio<br />The Cosine of an angle is defined as the ratio between the Adjacent and the Hypotenuse<br />πosineπ=π¨πππππππ‘π―π¦πππ‘πππ’π π<br />Β <br />
9. 9. The Cosine Ratio<br />The Cosine of an angle is defined as the ratio between the Adjacent and the Hypotenuse<br />πosineπ=π¨πππππππ‘π―π¦πππ‘πππ’π π<br />Β <br />
10. 10. The Cosine Ratio<br />The Cosine of an angle is defined as the ratio between the Adjacent and the Hypotenuse<br />πosineπ=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 Cosine Ratio<br />The Cosine of an angle is defined as the ratio between the Adjacent and the Hypotenuse<br />πosineπ=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 Cosine Ratio<br />The Cosine of an angle is defined as the ratio between the Adjacent and the Hypotenuse<br />πosineπ=π¨πππππππ‘π―π¦πππ‘πππ’π π<br />Β <br />C<br />Remember:<br />
13. 13. The Cosine Ratio<br />The Cosine of an angle is defined as the ratio between the Adjacent and the Hypotenuse<br />πosineπ=π¨πππππππ‘π―π¦πππ‘πππ’π π<br />Β <br />C<br />Remember:<br />
14. 14. The Cosine Ratio<br />The Cosine of an angle is defined as the ratio between the Adjacent and the Hypotenuse<br />πosineπ=π¨πππππππ‘π―π¦πππ‘πππ’π π<br />Β <br />CA<br />Remember:<br />
15. 15. The Cosine Ratio<br />The Cosine of an angle is defined as the ratio between the Adjacent and the Hypotenuse<br />πosineπ=π¨πππππππ‘π―π¦πππ‘πππ’π π<br />Β <br />CA<br />Remember:<br />
16. 16. The Cosine Ratio<br />The Cosine of an angle is defined as the ratio between the Adjacent and the Hypotenuse<br />πosineπ=π¨πππππππ‘π―π¦πππ‘πππ’π π<br />Β <br />CAH<br />Remember:<br />
17. 17. The Cosine Ratio<br />Remember: CAH<br />
18. 18. The Cosine Ratio<br />Remember: CAH<br />
19. 19. The Cosine Ratio<br />Remember: CAH<br />cosine of π is equal to πππhπ¦π=πͺπ«=7.038.21<br />Β <br />
20. 20. The Cosine Ratio<br />Remember: CAH<br />cosine of π is equal to πππhπ¦π=πͺπ«=7.038.21<br />Β <br />
21. 21. The Cosine Ratio<br />Remember: CAH<br />cosine of πis equal toπππhπ¦π=πͺπ«=7.038.21<br />Β <br />
22. 22. The Cosine Ratio<br />Remember: CAH<br />cosine of πis equal toπππhπ¦π=πͺπ«=7.038.21<br />Β <br />Adjacent<br />
23. 23. The Cosine Ratio<br />Remember: CAH<br />cosine of πis equal toπππhπ¦π=πͺπ«=7.038.21<br />Β <br />Adjacent<br />
24. 24. The Cosine Ratio<br />Remember: CAH<br />cosine of πis equal toπππhπ¦π=πͺπ«=7.038.21<br />Β <br />Adjacent<br />
25. 25. The Cosine Ratio<br />Remember: CAH<br />cosine of πis equal toππππππ=πͺπ«=7.038.21<br />Β <br />Adjacent<br />
26. 26. The Cosine Ratio<br />Remember: CAH<br />cosine of πis equal toππππππ=πͺπ«=7.038.21<br />Β <br />Hypotenuse<br />Adjacent<br />
27. 27. The Cosine Ratio<br />Remember: CAH<br />cosine of πis equal toππππππ=πͺπ«=7.038.21<br />Β <br />Hypotenuse<br />Adjacent<br />
28. 28. The Cosine Ratio<br />Remember: CAH<br />cosine of πis equal toππππππ=πͺπ«=7.038.21<br />Β <br />Hypotenuse<br />Adjacent<br />
29. 29. The Cosine Ratio<br />Remember: CAH<br />cosine of πis equal toππππππ=πͺπ«=7.038.21<br />Β <br />Hypotenuse<br />Adjacent<br />
30. 30. The Cosine Ratio<br />Remember: CAH<br />cosine of πis equal toππππππ=πͺπ«=ππ.π8.21<br />Β <br />Hypotenuse<br />Adjacent<br />
31. 31. The Cosine Ratio<br />Remember: CAH<br />cosine of πis equal toππππππ=πͺπ«=ππ.πππ.π<br />Β <br />Hypotenuse<br />Adjacent<br />
32. 32. The Cosine Ratio<br />Remember: CAH<br />cosine of πis equal toππππππ=πͺπ«=ππ.πππ.π<br />Β <br />Hypotenuse<br />Adjacent<br />
33. 33. The Cosine Ratio<br />πosineπ=π¨πππππππ‘π―π¦πππ‘πππ’π π<br />Β <br />
34. 34. The Cosine Ratio<br />ο§<br />πosineπ=π¨πππππππ‘π―π¦πππ‘πππ’π π<br />Β <br />
35. 35. The Cosine Ratio<br />ο§<br />πosineπ=π¨π―<br />Β <br />πosineπ=π¨πππππππ‘π―π¦πππ‘πππ’π π<br />Β <br />
36. 36. The Cosine Ratio<br />ο§<br />πosineο§=π¨π―<br />Β <br />πosineπ=π¨πππππππ‘π―π¦πππ‘πππ’π π<br />Β <br />
37. 37. The Cosine Ratio<br />ο§<br />πosineο§=π¨π―<br />Β <br />πosineπ=π¨πππππππ‘π―π¦πππ‘πππ’π π<br />Β <br />
38. 38. The Cosine Ratio<br />ο§<br />πosineο§=ππ.ππ―<br />Β <br />πosineπ=π¨πππππππ‘π―π¦πππ‘πππ’π π<br />Β <br />
39. 39. The Cosine Ratio<br />ο§<br />πosineο§=ππ.ππ―<br />Β <br />πosineπ=π¨πππππππ‘π―π¦πππ‘πππ’π π<br />Β <br />
40. 40. The Cosine Ratio<br />ο§<br />πosineο§=ππ.ππ<br />Β <br />πosineπ=π¨πππππππ‘π―π¦πππ‘πππ’π π<br />Β <br />
41. 41. The Cosine Ratio<br />ο§<br />πosineο§=ππ.ππ<br />Β <br />πosineπ=π¨πππππππ‘π―π¦πππ‘πππ’π π<br />Β <br />
42. 42. The Cosine Ratio<br />ο§<br />πosineο§=ππ.ππ<br />Β <br />πosineπ=π¨πππππππ‘π―π¦πππ‘πππ’π π<br />Β <br />ο‘<br />
43. 43. The Cosine Ratio<br />ο§<br />πosineο§=ππ.ππ<br />Β <br />πosineπ=π¨πππππππ‘π―π¦πππ‘πππ’π π<br />Β <br />πosineπ=π¨π―<br />Β <br />ο‘<br />
44. 44. The Cosine Ratio<br />ο§<br />πosineο§=ππ.ππ<br />Β <br />πosineπ=π¨πππππππ‘π―π¦πππ‘πππ’π π<br />Β <br />πosineο‘=π¨π―<br />Β <br />ο‘<br />
45. 45. The Cosine Ratio<br />ο§<br />πosineο§=ππ.ππ<br />Β <br />πosineπ=π¨πππππππ‘π―π¦πππ‘πππ’π π<br />Β <br />πosineο‘=π¨π―<br />Β <br />ο‘<br />
46. 46. The Cosine Ratio<br />ο§<br />πosineο§=ππ.ππ<br />Β <br />πosineπ=π¨πππππππ‘π―π¦πππ‘πππ’π π<br />Β <br />πosineο‘=ππ―<br />Β <br />ο‘<br />
47. 47. The Cosine Ratio<br />ο§<br />πosineο§=ππ.ππ<br />Β <br />πosineπ=π¨πππππππ‘π―π¦πππ‘πππ’π π<br />Β <br />πosineο‘=ππ―<br />Β <br />ο‘<br />
48. 48. The Cosine Ratio<br />ο§<br />πosineο§=ππ.ππ<br />Β <br />πosineπ=π¨πππππππ‘π―π¦πππ‘πππ’π π<br />Β <br />πosineο‘=ππ<br />Β <br />ο‘<br />
49. 49. The Cosine Ratio<br />ο§<br />πosineο§=ππ.ππ<br />Β <br />πosineπ=π¨πππππππ‘π―π¦πππ‘πππ’π π<br />Β <br />πosineο‘=ππ<br />Β <br />ο‘<br />
50. 50. The Cosine Ratio<br />ο§<br />πosineο§=ππ.ππ<br />Β <br />πosineπ=π¨πππππππ‘π―π¦πππ‘πππ’π π<br />Β <br />πosineο‘=ππ<br />Β <br />ο‘<br />ο’<br />
51. 51. The Cosine Ratio<br />ο§<br />πosineπ=ππ.ππ<br />Β <br />πosineπ=π¨πππππππ‘π―π¦πππ‘πππ’π π<br />Β <br />πosineπ=π¨π―<br />Β <br />πosineο‘=ππ<br />Β <br />ο‘<br />ο’<br />
52. 52. The Cosine Ratio<br />ο§<br />πosineο§=ππ.ππ<br />Β <br />πosineπ=π¨πππππππ‘π―π¦πππ‘πππ’π π<br />Β <br />πosineο’=π¨π―<br />Β <br />πosineο‘=ππ<br />Β <br />ο‘<br />ο’<br />
53. 53. The Cosine Ratio<br />ο§<br />πosineο§=ππ.ππ<br />Β <br />πosineπ=π¨πππππππ‘π―π¦πππ‘πππ’π π<br />Β <br />πosineο’=π¨π―<br />Β <br />πosineο‘=ππ<br />Β <br />ο‘<br />ο’<br />
54. 54. The Cosine Ratio<br />ο§<br />πosineο§=ππ.ππ<br />Β <br />πosineπ=π¨πππππππ‘π―π¦πππ‘πππ’π π<br />Β <br />πosineο’=ππ―<br />Β <br />πosineο‘=ππ<br />Β <br />ο‘<br />ο’<br />
55. 55. The Cosine Ratio<br />ο§<br />πosineο§=ππ.ππ<br />Β <br />πosineπ=π¨πππππππ‘π―π¦πππ‘πππ’π π<br />Β <br />πosineο’=ππ―<br />Β <br />πosineο‘=ππ<br />Β <br />ο‘<br />ο’<br />
56. 56. The Cosine Ratio<br />ο§<br />πosineο§=ππ.ππ<br />Β <br />πosineπ=π¨πππππππ‘π―π¦πππ‘πππ’π π<br />Β <br />πosineο’=πππ.π<br />Β <br />πosineο‘=ππ<br />Β <br />ο‘<br />ο’<br />
57. 57. The Cosine Ratio<br />ο§<br />πosineο§=ππ.ππ<br />Β <br />πosineπ=π¨πππππππ‘π―π¦πππ‘πππ’π π<br />Β <br />πosineο’=πππ.π<br />Β <br />πosineο‘=ππ<br />Β <br />ο‘<br />ο’<br />
58. 58. The Cosine Ratio<br />ο±<br />ο§<br />πosineο§=ππ.ππ<br />Β <br />πosineπ=π¨πππππππ‘π―π¦πππ‘πππ’π π<br />Β <br />πosineο’=πππ.π<br />Β <br />πosineο‘=ππ<br />Β <br />ο‘<br />ο’<br />
59. 59. The Cosine Ratio<br />ο±<br />ο§<br />πosineπ=π¨π―<br />Β <br />πosineο§=ππ.ππ<br />Β <br />πosineπ=π¨πππππππ‘π―π¦πππ‘πππ’π π<br />Β <br />πosineο’=πππ.π<br />Β <br />πosineο‘=ππ<br />Β <br />ο‘<br />ο’<br />
60. 60. The Cosine Ratio<br />ο±<br />ο§<br />πosineπ=π¨π―<br />Β <br />πosineο§=ππ.ππ<br />Β <br />πosineπ=π¨πππππππ‘π―π¦πππ‘πππ’π π<br />Β <br />πosineο’=πππ.π<br />Β <br />πosineο‘=ππ<br />Β <br />ο‘<br />ο’<br />
61. 61. The Cosine Ratio<br />ο±<br />ο§<br />πosineπ=π¨π―<br />Β <br />πosineο§=ππ.ππ<br />Β <br />πosineπ=π¨πππππππ‘π―π¦πππ‘πππ’π π<br />Β <br />πosineο’=πππ.π<br />Β <br />πosineο‘=ππ<br />Β <br />ο‘<br />ο’<br />
62. 62. The Cosine Ratio<br />ο±<br />ο§<br />πosineπ=ππ.ππ―<br />Β <br />πosineο§=ππ.ππ<br />Β <br />πosineπ=π¨πππππππ‘π―π¦πππ‘πππ’π π<br />Β <br />πosineο’=πππ.π<br />Β <br />πosineο‘=ππ<br />Β <br />ο‘<br />ο’<br />
63. 63. The Cosine Ratio<br />ο±<br />ο§<br />πosineπ=ππ.ππ―<br />Β <br />πosineο§=ππ.ππ<br />Β <br />πosineπ=π¨πππππππ‘π―π¦πππ‘πππ’π π<br />Β <br />πosineο’=πππ.π<br />Β <br />πosineο‘=ππ<br />Β <br />ο‘<br />ο’<br />
64. 64. The Cosine Ratio<br />ο±<br />ο§<br />πosineπ=ππ.ππππ<br />Β <br />πosineο§=ππ.ππ<br />Β <br />πosineπ=π¨πππππππ‘π―π¦πππ‘πππ’π π<br />Β <br />πosineο’=πππ.π<br />Β <br />πosineο‘=ππ<br />Β <br />ο‘<br />ο’<br />
65. 65. The Cosine Ratio<br />ο±<br />ο§<br />πosineπ=ππ.ππππ<br />Β <br />πosineο§=ππ.ππ<br />Β <br />πosineπ=π¨πππππππ‘π―π¦πππ‘πππ’π π<br />Β <br />πosineο’=πππ.π<br />Β <br />πosineο‘=ππ<br />Β <br />ο‘<br />ο’<br />
66. 66. The Cosine Ratio<br />Remember:<br />πͺππ ππππ=π¨πππππππ‘π―π¦πππ‘πππ’π π ->CAH<br />Β <br />
67. 67. The Cosine Ratio<br />Remember:<br />πͺππ ππππ=π¨πππππππ‘π―π¦πππ‘πππ’π π ->CAH<br />Β <br />
68. 68. The Cosine Ratio<br />Remember:<br />πͺππ ππππ=π¨πππππππ‘π―π¦πππ‘πππ’π π ->CAH<br />Β <br />
69. 69. The Cosine Ratio<br />Remember:<br />πͺππ ππππ=π¨πππππππ‘π―π¦πππ‘πππ’π π ->CAH<br />Β <br />
70. 70. The Cosine Ratio<br />Remember:<br />πͺππ ππππ=π¨πππππππ‘π―π¦πππ‘πππ’π π ->CAH<br />Β <br />
71. 71. The Cosine Ratio<br />Remember:<br />πͺππ ππππ=π¨πππππππ‘π―π¦πππ‘πππ’π π ->CAH<br />Β <br />
72. 72. The Cosine Ratio<br />Remember:<br />πͺππ ππππ=π¨πππππππ‘π―π¦πππ‘πππ’π π ->CAH<br />Β <br />