Defining the Cosine ratio in Trigonometry. Small changes between slides so can be clicked through quickly.

1. Defining the sine, cosine and tangent ratios for angles in right-angled trianglesPart 2 - Cosine

2. The Cosine Ratio

3. The Cosine Ratio

4. The Cosine Ratio The Cosine of an angle is defined as the ratio between the Adjacent and the Hypotenuse

5. The Cosine Ratio The Cosine of an angle is defined as the ratio between the Adjacent and the Hypotenuse 𝐂osine𝜃=𝑨𝑑𝑗𝑎𝑐𝑒𝑛𝑡𝑯𝑦𝑝𝑜𝑡𝑒𝑛𝑢𝑠𝑒

6. The Cosine Ratio The Cosine of an angle is defined as the ratio between the Adjacent and the Hypotenuse 𝐂osine𝜃=𝑨𝑑𝑗𝑎𝑐𝑒𝑛𝑡𝑯𝑦𝑝𝑜𝑡𝑒𝑛𝑢𝑠𝑒

7. The Cosine Ratio The Cosine of an angle is defined as the ratio between the Adjacent and the Hypotenuse 𝐂osine𝜃=𝑨𝑑𝑗𝑎𝑐𝑒𝑛𝑡𝑯𝑦𝑝𝑜𝑡𝑒𝑛𝑢𝑠𝑒

8. The Cosine Ratio The Cosine of an angle is defined as the ratio between the Adjacent and the Hypotenuse 𝐂osine𝜃=𝑨𝑑𝑗𝑎𝑐𝑒𝑛𝑡𝑯𝑦𝑝𝑜𝑡𝑒𝑛𝑢𝑠𝑒

9. The Cosine Ratio The Cosine of an angle is defined as the ratio between the Adjacent and the Hypotenuse 𝐂osine𝜃=𝑨𝑑𝑗𝑎𝑐𝑒𝑛𝑡𝑯𝑦𝑝𝑜𝑡𝑒𝑛𝑢𝑠𝑒

10. The Cosine Ratio The Cosine of an angle is defined as the ratio between the Adjacent and the Hypotenuse 𝐂osine𝜃=𝑨𝑑𝑗𝑎𝑐𝑒𝑛𝑡𝑯𝑦𝑝𝑜𝑡𝑒𝑛𝑢𝑠𝑒 Remember:

11. The Cosine Ratio The Cosine of an angle is defined as the ratio between the Adjacent and the Hypotenuse 𝐂osine𝜃=𝑨𝑑𝑗𝑎𝑐𝑒𝑛𝑡𝑯𝑦𝑝𝑜𝑡𝑒𝑛𝑢𝑠𝑒 Remember:

12. The Cosine Ratio The Cosine of an angle is defined as the ratio between the Adjacent and the Hypotenuse 𝐂osine𝜃=𝑨𝑑𝑗𝑎𝑐𝑒𝑛𝑡𝑯𝑦𝑝𝑜𝑡𝑒𝑛𝑢𝑠𝑒 C Remember:

13. The Cosine Ratio The Cosine of an angle is defined as the ratio between the Adjacent and the Hypotenuse 𝐂osine𝜃=𝑨𝑑𝑗𝑎𝑐𝑒𝑛𝑡𝑯𝑦𝑝𝑜𝑡𝑒𝑛𝑢𝑠𝑒 C Remember:

14. The Cosine Ratio The Cosine of an angle is defined as the ratio between the Adjacent and the Hypotenuse 𝐂osine𝜃=𝑨𝑑𝑗𝑎𝑐𝑒𝑛𝑡𝑯𝑦𝑝𝑜𝑡𝑒𝑛𝑢𝑠𝑒 CA Remember:

15. The Cosine Ratio The Cosine of an angle is defined as the ratio between the Adjacent and the Hypotenuse 𝐂osine𝜃=𝑨𝑑𝑗𝑎𝑐𝑒𝑛𝑡𝑯𝑦𝑝𝑜𝑡𝑒𝑛𝑢𝑠𝑒 CA Remember:

16. The Cosine Ratio The Cosine of an angle is defined as the ratio between the Adjacent and the Hypotenuse 𝐂osine𝜃=𝑨𝑑𝑗𝑎𝑐𝑒𝑛𝑡𝑯𝑦𝑝𝑜𝑡𝑒𝑛𝑢𝑠𝑒 CAH Remember:

17. The Cosine Ratio Remember: CAH

18. The Cosine Ratio Remember: CAH

19. The Cosine Ratio Remember: CAH cosine of 𝜃 is equal to 𝑎𝑑𝑗h𝑦𝑝=𝐪𝐫=7.038.21

20. The Cosine Ratio Remember: CAH cosine of 𝜃 is equal to 𝑎𝑑𝑗h𝑦𝑝=𝐪𝐫=7.038.21

21. The Cosine Ratio Remember: CAH cosine of 𝜃is equal to𝑎𝑑𝑗h𝑦𝑝=𝐪𝐫=7.038.21

22. The Cosine Ratio Remember: CAH cosine of 𝜃is equal to𝑎𝑑𝑗h𝑦𝑝=𝐪𝐫=7.038.21 Adjacent

23. The Cosine Ratio Remember: CAH cosine of 𝜃is equal to𝒂𝒅𝒋h𝑦𝑝=𝐪𝐫=7.038.21 Adjacent

24. The Cosine Ratio Remember: CAH cosine of 𝜃is equal to𝒂𝒅𝒋h𝑦𝑝=𝐪𝐫=7.038.21 Adjacent

25. The Cosine Ratio Remember: CAH cosine of 𝜃is equal to𝒂𝒅𝒋𝒉𝒚𝒑=𝐪𝐫=7.038.21 Adjacent

26. The Cosine Ratio Remember: CAH cosine of 𝜃is equal to𝒂𝒅𝒋𝒉𝒚𝒑=𝐪𝐫=7.038.21 Hypotenuse Adjacent

27. The Cosine Ratio Remember: CAH cosine of 𝜃is equal to𝒂𝒅𝒋𝒉𝒚𝒑=𝐪𝐫=7.038.21 Hypotenuse Adjacent

28. The Cosine Ratio Remember: CAH cosine of 𝜃is equal to𝒂𝒅𝒋𝒉𝒚𝒑=𝐪𝐫=7.038.21 Hypotenuse Adjacent

29. The Cosine Ratio Remember: CAH cosine of 𝜃is equal to𝒂𝒅𝒋𝒉𝒚𝒑=𝐪𝐫=7.038.21 Hypotenuse Adjacent

30. The Cosine Ratio Remember: CAH cosine of 𝜃is equal to𝒂𝒅𝒋𝒉𝒚𝒑=𝐪𝐫=𝟔𝟐.𝟏8.21 Hypotenuse Adjacent

31. The Cosine Ratio Remember: CAH cosine of 𝜃is equal to𝒂𝒅𝒋𝒉𝒚𝒑=𝐪𝐫=𝟔𝟐.𝟏𝟔𝟕.𝟐 Hypotenuse Adjacent

32. The Cosine Ratio Remember: CAH cosine of 𝜃is equal to𝒂𝒅𝒋𝒉𝒚𝒑=𝐪𝐫=𝟔𝟐.𝟏𝟔𝟕.𝟐 Hypotenuse Adjacent

33. The Cosine Ratio 𝐂osine𝜃=𝑨𝑑𝑗𝑎𝑐𝑒𝑛𝑡𝑯𝑦𝑝𝑜𝑡𝑒𝑛𝑢𝑠𝑒

34. The Cosine Ratio  𝐂osine𝜃=𝑨𝑑𝑗𝑎𝑐𝑒𝑛𝑡𝑯𝑦𝑝𝑜𝑡𝑒𝑛𝑢𝑠𝑒

35. The Cosine Ratio  𝐂osine𝜃=𝑨𝑯 𝐂osine𝜃=𝑨𝑑𝑗𝑎𝑐𝑒𝑛𝑡𝑯𝑦𝑝𝑜𝑡𝑒𝑛𝑢𝑠𝑒

36. The Cosine Ratio  𝐂osine=𝑨𝑯 𝐂osine𝜃=𝑨𝑑𝑗𝑎𝑐𝑒𝑛𝑡𝑯𝑦𝑝𝑜𝑡𝑒𝑛𝑢𝑠𝑒

37. The Cosine Ratio  𝐂osine=𝑨𝑯 𝐂osine𝜃=𝑨𝑑𝑗𝑎𝑐𝑒𝑛𝑡𝑯𝑦𝑝𝑜𝑡𝑒𝑛𝑢𝑠𝑒

38. The Cosine Ratio  𝐂osine=𝟏𝟗.𝟏𝑯 𝐂osine𝜃=𝑨𝑑𝑗𝑎𝑐𝑒𝑛𝑡𝑯𝑦𝑝𝑜𝑡𝑒𝑛𝑢𝑠𝑒

39. The Cosine Ratio  𝐂osine=𝟏𝟗.𝟏𝑯 𝐂osine𝜃=𝑨𝑑𝑗𝑎𝑐𝑒𝑛𝑡𝑯𝑦𝑝𝑜𝑡𝑒𝑛𝑢𝑠𝑒

40. The Cosine Ratio  𝐂osine=𝟏𝟗.𝟏𝒇 𝐂osine𝜃=𝑨𝑑𝑗𝑎𝑐𝑒𝑛𝑡𝑯𝑦𝑝𝑜𝑡𝑒𝑛𝑢𝑠𝑒

41. The Cosine Ratio  𝐂osine=𝟏𝟗.𝟏𝒇 𝐂osine𝜃=𝑨𝑑𝑗𝑎𝑐𝑒𝑛𝑡𝑯𝑦𝑝𝑜𝑡𝑒𝑛𝑢𝑠𝑒

42. The Cosine Ratio  𝐂osine=𝟏𝟗.𝟏𝒇 𝐂osine𝜃=𝑨𝑑𝑗𝑎𝑐𝑒𝑛𝑡𝑯𝑦𝑝𝑜𝑡𝑒𝑛𝑢𝑠𝑒 

43. The Cosine Ratio  𝐂osine=𝟏𝟗.𝟏𝒇 𝐂osine𝜃=𝑨𝑑𝑗𝑎𝑐𝑒𝑛𝑡𝑯𝑦𝑝𝑜𝑡𝑒𝑛𝑢𝑠𝑒 𝐂osine𝜃=𝑨𝑯 

44. The Cosine Ratio  𝐂osine=𝟏𝟗.𝟏𝒇 𝐂osine𝜃=𝑨𝑑𝑗𝑎𝑐𝑒𝑛𝑡𝑯𝑦𝑝𝑜𝑡𝑒𝑛𝑢𝑠𝑒 𝐂osine=𝑨𝑯 

45. The Cosine Ratio  𝐂osine=𝟏𝟗.𝟏𝒇 𝐂osine𝜃=𝑨𝑑𝑗𝑎𝑐𝑒𝑛𝑡𝑯𝑦𝑝𝑜𝑡𝑒𝑛𝑢𝑠𝑒 𝐂osine=𝑨𝑯 

46. The Cosine Ratio  𝐂osine=𝟏𝟗.𝟏𝒇 𝐂osine𝜃=𝑨𝑑𝑗𝑎𝑐𝑒𝑛𝑡𝑯𝑦𝑝𝑜𝑡𝑒𝑛𝑢𝑠𝑒 𝐂osine=𝒄𝑯 

47. The Cosine Ratio  𝐂osine=𝟏𝟗.𝟏𝒇 𝐂osine𝜃=𝑨𝑑𝑗𝑎𝑐𝑒𝑛𝑡𝑯𝑦𝑝𝑜𝑡𝑒𝑛𝑢𝑠𝑒 𝐂osine=𝒄𝑯 

48. The Cosine Ratio  𝐂osine=𝟏𝟗.𝟏𝒇 𝐂osine𝜃=𝑨𝑑𝑗𝑎𝑐𝑒𝑛𝑡𝑯𝑦𝑝𝑜𝑡𝑒𝑛𝑢𝑠𝑒 𝐂osine=𝒄𝒇 

49. The Cosine Ratio  𝐂osine=𝟏𝟗.𝟏𝒇 𝐂osine𝜃=𝑨𝑑𝑗𝑎𝑐𝑒𝑛𝑡𝑯𝑦𝑝𝑜𝑡𝑒𝑛𝑢𝑠𝑒 𝐂osine=𝒄𝒇 

50. The Cosine Ratio  𝐂osine=𝟏𝟗.𝟏𝒇 𝐂osine𝜃=𝑨𝑑𝑗𝑎𝑐𝑒𝑛𝑡𝑯𝑦𝑝𝑜𝑡𝑒𝑛𝑢𝑠𝑒 𝐂osine=𝒄𝒇  

51. The Cosine Ratio  𝐂osine𝜃=𝟏𝟗.𝟏𝒇 𝐂osine𝜃=𝑨𝑑𝑗𝑎𝑐𝑒𝑛𝑡𝑯𝑦𝑝𝑜𝑡𝑒𝑛𝑢𝑠𝑒 𝐂osine𝜃=𝑨𝑯 𝐂osine=𝒄𝒇  

52. The Cosine Ratio  𝐂osine=𝟏𝟗.𝟏𝒇 𝐂osine𝜃=𝑨𝑑𝑗𝑎𝑐𝑒𝑛𝑡𝑯𝑦𝑝𝑜𝑡𝑒𝑛𝑢𝑠𝑒 𝐂osine=𝑨𝑯 𝐂osine=𝒄𝒇  

53. The Cosine Ratio  𝐂osine=𝟏𝟗.𝟏𝒇 𝐂osine𝜃=𝑨𝑑𝑗𝑎𝑐𝑒𝑛𝑡𝑯𝑦𝑝𝑜𝑡𝑒𝑛𝑢𝑠𝑒 𝐂osine=𝑨𝑯 𝐂osine=𝒄𝒇  

54. The Cosine Ratio  𝐂osine=𝟏𝟗.𝟏𝒇 𝐂osine𝜃=𝑨𝑑𝑗𝑎𝑐𝑒𝑛𝑡𝑯𝑦𝑝𝑜𝑡𝑒𝑛𝑢𝑠𝑒 𝐂osine=𝒄𝑯 𝐂osine=𝒄𝒇  

55. The Cosine Ratio  𝐂osine=𝟏𝟗.𝟏𝒇 𝐂osine𝜃=𝑨𝑑𝑗𝑎𝑐𝑒𝑛𝑡𝑯𝑦𝑝𝑜𝑡𝑒𝑛𝑢𝑠𝑒 𝐂osine=𝒄𝑯 𝐂osine=𝒄𝒇  

56. The Cosine Ratio  𝐂osine=𝟏𝟗.𝟏𝒇 𝐂osine𝜃=𝑨𝑑𝑗𝑎𝑐𝑒𝑛𝑡𝑯𝑦𝑝𝑜𝑡𝑒𝑛𝑢𝑠𝑒 𝐂osine=𝒄𝟐𝟑.𝟔 𝐂osine=𝒄𝒇  

57. The Cosine Ratio  𝐂osine=𝟏𝟗.𝟏𝒇 𝐂osine𝜃=𝑨𝑑𝑗𝑎𝑐𝑒𝑛𝑡𝑯𝑦𝑝𝑜𝑡𝑒𝑛𝑢𝑠𝑒 𝐂osine=𝒄𝟐𝟑.𝟔 𝐂osine=𝒄𝒇  

58. The Cosine Ratio   𝐂osine=𝟏𝟗.𝟏𝒇 𝐂osine𝜃=𝑨𝑑𝑗𝑎𝑐𝑒𝑛𝑡𝑯𝑦𝑝𝑜𝑡𝑒𝑛𝑢𝑠𝑒 𝐂osine=𝒄𝟐𝟑.𝟔 𝐂osine=𝒄𝒇  

59. The Cosine Ratio   𝐂osine𝜃=𝑨𝑯 𝐂osine=𝟏𝟗.𝟏𝒇 𝐂osine𝜃=𝑨𝑑𝑗𝑎𝑐𝑒𝑛𝑡𝑯𝑦𝑝𝑜𝑡𝑒𝑛𝑢𝑠𝑒 𝐂osine=𝒄𝟐𝟑.𝟔 𝐂osine=𝒄𝒇  

60. The Cosine Ratio   𝐂osine𝛉=𝑨𝑯 𝐂osine=𝟏𝟗.𝟏𝒇 𝐂osine𝜃=𝑨𝑑𝑗𝑎𝑐𝑒𝑛𝑡𝑯𝑦𝑝𝑜𝑡𝑒𝑛𝑢𝑠𝑒 𝐂osine=𝒄𝟐𝟑.𝟔 𝐂osine=𝒄𝒇  

61. The Cosine Ratio   𝐂osine𝛉=𝑨𝑯 𝐂osine=𝟏𝟗.𝟏𝒇 𝐂osine𝜃=𝑨𝑑𝑗𝑎𝑐𝑒𝑛𝑡𝑯𝑦𝑝𝑜𝑡𝑒𝑛𝑢𝑠𝑒 𝐂osine=𝒄𝟐𝟑.𝟔 𝐂osine=𝒄𝒇  

62. The Cosine Ratio   𝐂osine𝛉=𝟑𝟐.𝟗𝑯 𝐂osine=𝟏𝟗.𝟏𝒇 𝐂osine𝜃=𝑨𝑑𝑗𝑎𝑐𝑒𝑛𝑡𝑯𝑦𝑝𝑜𝑡𝑒𝑛𝑢𝑠𝑒 𝐂osine=𝒄𝟐𝟑.𝟔 𝐂osine=𝒄𝒇  

63. The Cosine Ratio   𝐂osine𝛉=𝟑𝟐.𝟗𝑯 𝐂osine=𝟏𝟗.𝟏𝒇 𝐂osine𝜃=𝑨𝑑𝑗𝑎𝑐𝑒𝑛𝑡𝑯𝑦𝑝𝑜𝑡𝑒𝑛𝑢𝑠𝑒 𝐂osine=𝒄𝟐𝟑.𝟔 𝐂osine=𝒄𝒇  

64. The Cosine Ratio   𝐂osine𝛉=𝟑𝟐.𝟗𝟏𝟓𝟏 𝐂osine=𝟏𝟗.𝟏𝒇 𝐂osine𝜃=𝑨𝑑𝑗𝑎𝑐𝑒𝑛𝑡𝑯𝑦𝑝𝑜𝑡𝑒𝑛𝑢𝑠𝑒 𝐂osine=𝒄𝟐𝟑.𝟔 𝐂osine=𝒄𝒇  

65. The Cosine Ratio   𝐂osine𝛉=𝟑𝟐.𝟗𝟏𝟓𝟏 𝐂osine=𝟏𝟗.𝟏𝒇 𝐂osine𝜃=𝑨𝑑𝑗𝑎𝑐𝑒𝑛𝑡𝑯𝑦𝑝𝑜𝑡𝑒𝑛𝑢𝑠𝑒 𝐂osine=𝒄𝟐𝟑.𝟔 𝐂osine=𝒄𝒇  

66. The Cosine Ratio Remember: 𝑪𝑜𝑠𝑖𝑛𝑒𝜃=𝑨𝑑𝑗𝑎𝑐𝑒𝑛𝑡𝑯𝑦𝑝𝑜𝑡𝑒𝑛𝑢𝑠𝑒 ->CAH

67. The Cosine Ratio Remember: 𝑪𝑜𝑠𝑖𝑛𝑒𝜃=𝑨𝑑𝑗𝑎𝑐𝑒𝑛𝑡𝑯𝑦𝑝𝑜𝑡𝑒𝑛𝑢𝑠𝑒 ->CAH

68. The Cosine Ratio Remember: 𝑪𝑜𝑠𝑖𝑛𝑒𝜃=𝑨𝑑𝑗𝑎𝑐𝑒𝑛𝑡𝑯𝑦𝑝𝑜𝑡𝑒𝑛𝑢𝑠𝑒 ->CAH

69. The Cosine Ratio Remember: 𝑪𝑜𝑠𝑖𝑛𝑒𝜃=𝑨𝑑𝑗𝑎𝑐𝑒𝑛𝑡𝑯𝑦𝑝𝑜𝑡𝑒𝑛𝑢𝑠𝑒 ->CAH

70. The Cosine Ratio Remember: 𝑪𝑜𝑠𝑖𝑛𝑒𝜃=𝑨𝑑𝑗𝑎𝑐𝑒𝑛𝑡𝑯𝑦𝑝𝑜𝑡𝑒𝑛𝑢𝑠𝑒 ->CAH

71. The Cosine Ratio Remember: 𝑪𝑜𝑠𝑖𝑛𝑒𝜃=𝑨𝑑𝑗𝑎𝑐𝑒𝑛𝑡𝑯𝑦𝑝𝑜𝑡𝑒𝑛𝑢𝑠𝑒 ->CAH

72. The Cosine Ratio Remember: 𝑪𝑜𝑠𝑖𝑛𝑒𝜃=𝑨𝑑𝑗𝑎𝑐𝑒𝑛𝑡𝑯𝑦𝑝𝑜𝑡𝑒𝑛𝑢𝑠𝑒 ->CAH