Defining the Sine 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 1 - Sine

2. The Sine Ratio

3. The Sine Ratio 𝐒ine𝜃=𝐎𝑝𝑝𝑜𝑠𝑖𝑡𝑒𝑯𝑦𝑝𝑜𝑡𝑒𝑛𝑢𝑠𝑒

4. The Sine Ratio The sine of an angle is defined as the ratio between the Opposite and Hypotenuse: 𝐒ine𝜃=𝐎𝑝𝑝𝑜𝑠𝑖𝑡𝑒𝑯𝑦𝑝𝑜𝑡𝑒𝑛𝑢𝑠𝑒

5. The Sine Ratio The sine of an angle is defined as the ratio between the Opposite and Hypotenuse: 𝐒ine𝜃=𝐎𝑝𝑝𝑜𝑠𝑖𝑡𝑒𝑯𝑦𝑝𝑜𝑡𝑒𝑛𝑢𝑠𝑒

6. The Sine Ratio The sine of an angle is defined as the ratio between the Opposite and Hypotenuse: 𝐒ine𝜃=𝐎𝑝𝑝𝑜𝑠𝑖𝑡𝑒𝑯𝑦𝑝𝑜𝑡𝑒𝑛𝑢𝑠𝑒

7. The Sine Ratio The sine of an angle is defined as the ratio between the Opposite and Hypotenuse: 𝐒ine𝜃=𝐎𝑝𝑝𝑜𝑠𝑖𝑡𝑒𝑯𝑦𝑝𝑜𝑡𝑒𝑛𝑢𝑠𝑒

8. The Sine Ratio The sine of an angle is defined as the ratio between the Opposite and Hypotenuse: 𝐒ine𝜃=𝐎𝑝𝑝𝑜𝑠𝑖𝑡𝑒𝑯𝑦𝑝𝑜𝑡𝑒𝑛𝑢𝑠𝑒

9. The Sine Ratio The sine of an angle is defined as the ratio between the Opposite and Hypotenuse: 𝐒ine𝜃=𝐎𝑝𝑝𝑜𝑠𝑖𝑡𝑒𝑯𝑦𝑝𝑜𝑡𝑒𝑛𝑢𝑠𝑒

10. The Sine Ratio The sine of an angle is defined as the ratio between the Opposite and Hypotenuse: 𝐒ine𝜃=𝐎𝑝𝑝𝑜𝑠𝑖𝑡𝑒𝑯𝑦𝑝𝑜𝑡𝑒𝑛𝑢𝑠𝑒 Remember:

11. The Sine Ratio The sine of an angle is defined as the ratio between the Opposite and Hypotenuse: 𝐒ine𝜃=𝐎𝑝𝑝𝑜𝑠𝑖𝑡𝑒𝑯𝑦𝑝𝑜𝑡𝑒𝑛𝑢𝑠𝑒 Remember:

12. The Sine Ratio The sine of an angle is defined as the ratio between the Opposite and Hypotenuse: 𝐒ine𝜃=𝐎𝑝𝑝𝑜𝑠𝑖𝑡𝑒𝑯𝑦𝑝𝑜𝑡𝑒𝑛𝑢𝑠𝑒 S Remember:

13. The Sine Ratio The sine of an angle is defined as the ratio between the Opposite and Hypotenuse: 𝐒ine𝜃=𝐎𝑝𝑝𝑜𝑠𝑖𝑡𝑒𝑯𝑦𝑝𝑜𝑡𝑒𝑛𝑢𝑠𝑒 S Remember:

14. The Sine Ratio The sine of an angle is defined as the ratio between the Opposite and Hypotenuse: 𝐒ine𝜃=𝐎𝑝𝑝𝑜𝑠𝑖𝑡𝑒𝑯𝑦𝑝𝑜𝑡𝑒𝑛𝑢𝑠𝑒 SO Remember:

15. The Sine Ratio The sine of an angle is defined as the ratio between the Opposite and Hypotenuse: 𝐒ine𝜃=𝐎𝑝𝑝𝑜𝑠𝑖𝑡𝑒𝑯𝑦𝑝𝑜𝑡𝑒𝑛𝑢𝑠𝑒 SO Remember:

16. The Sine Ratio The sine of an angle is defined as the ratio between the Opposite and Hypotenuse: 𝐒in𝑒𝜃=𝐎𝑝𝑝𝑜𝑠𝑖𝑡𝑒𝑯𝑦𝑝𝑜𝑡𝑒𝑛𝑢𝑠𝑒 SOH Remember:

17. The Sine Ratio Remember: SOH

18. The Sine Ratio Remember: SOH

19. The Sine Ratio Remember: SOH sineof𝛉isequalto 𝑶𝒑𝒑𝑯𝒚𝒑=𝒂𝒄=𝟓.𝟏𝟗𝟖.𝟕𝟒

20. The Sine Ratio Remember: SOH sineof𝛉isequalto 𝑶𝒑𝒑𝑯𝒚𝒑=𝒂𝒄=𝟓.𝟏𝟗𝟖.𝟕𝟒

21. The Sine Ratio Remember: SOH sineof𝛉isequalto 𝑶𝒑𝒑𝑯𝒚𝒑=𝒂𝒄=𝟓.𝟏𝟗𝟖.𝟕𝟒

22. The Sine Ratio Remember: SOH sineof𝛉isequalto 𝑶𝒑𝒑𝑯𝒚𝒑=𝒂𝒄=𝟓.𝟏𝟗𝟖.𝟕𝟒 Opposite

23. The Sine Ratio Remember: SOH Remember: SOH sineof𝛉isequalto 𝑶𝒑𝒑𝑯𝒚𝒑=𝒂𝒄=𝟓.𝟏𝟗𝟖.𝟕𝟒 Opposite

24. The Sine Ratio Remember: SOH sineof𝛉isequalto 𝑶𝒑𝒑𝑯𝒚𝒑=𝒂𝒄=𝟓.𝟏𝟗𝟖.𝟕𝟒 Hypotenuse Opposite

25. The Sine Ratio Remember: SOH sineof𝛉isequalto 𝑶𝒑𝒑𝑯𝒚𝒑=𝒂𝒄=𝟓.𝟏𝟗𝟖.𝟕𝟒 Hypotenuse Opposite

26. The Sine Ratio Remember: SOH sineof𝛉isequalto 𝑶𝒑𝒑𝑯𝒚𝒑=𝒂𝒄=𝟓.𝟏𝟗𝟖.𝟕𝟒 Hypotenuse Opposite

27. The Sine Ratio Remember: SOH sineof𝛉isequalto 𝑶𝒑𝒑𝑯𝒚𝒑=𝒂𝒄=𝟓.𝟏𝟗𝟖.𝟕𝟒 Hypotenuse Opposite

28. The Sine Ratio Remember: SOH sineof𝛉isequalto 𝑶𝒑𝒑𝑯𝒚𝒑=𝒂𝒄=𝟓.𝟏𝟗𝟖.𝟕𝟒 Hypotenuse Opposite

29. The Sine Ratio Remember: SOH sineof𝛉isequalto 𝑶𝒑𝒑𝑯𝒚𝒑=𝒂𝒄=𝟓.𝟏𝟗𝟖.𝟕𝟒 Hypotenuse Opposite

30. The Sine Ratio Remember: SOH sineof𝛉isequalto 𝑶𝒑𝒑𝑯𝒚𝒑=𝒂𝒄=𝟓.𝟏𝟗𝟖.𝟕𝟒 Hypotenuse Opposite

31. The Sine Ratio Remember: SOH sineof𝛉isequalto 𝑶𝒑𝒑𝑯𝒚𝒑=𝒂𝒄=𝟓.𝟏𝟗𝟖.𝟕𝟒 Hypotenuse Opposite

32. The Sine Ratio Remember: SOH sineof𝛉isequalto 𝑶𝒑𝒑𝑯𝒚𝒑=𝒂𝒄=𝟓.𝟏𝟗𝟖.𝟕𝟒 Hypotenuse Opposite

33. The Sine Ratio 𝐒ine𝜃=𝐎𝑝𝑝𝑜𝑠𝑖𝑡𝑒𝑯𝑦𝑝𝑜𝑡𝑒𝑛𝑢𝑠𝑒

34. The Sine Ratio  𝐒ine𝜃=𝐎𝑝𝑝𝑜𝑠𝑖𝑡𝑒𝑯𝑦𝑝𝑜𝑡𝑒𝑛𝑢𝑠𝑒

35. The Sine Ratio  𝐒ine𝜃=𝑶𝑯 𝐒ine𝜃=𝐎𝑝𝑝𝑜𝑠𝑖𝑡𝑒𝑯𝑦𝑝𝑜𝑡𝑒𝑛𝑢𝑠𝑒

36. The Sine Ratio  𝐒ine𝜽=𝑶𝑯 𝐒ine𝜃=𝐎𝑝𝑝𝑜𝑠𝑖𝑡𝑒𝑯𝑦𝑝𝑜𝑡𝑒𝑛𝑢𝑠𝑒

37. The Sine Ratio  𝐒ine𝜃=𝑶𝑯 𝐒ine𝜃=𝐎𝑝𝑝𝑜𝑠𝑖𝑡𝑒𝑯𝑦𝑝𝑜𝑡𝑒𝑛𝑢𝑠𝑒

38. The Sine Ratio  𝐒ine𝜃=𝟒.𝟔𝟔𝑯 𝐒ine𝜃=𝐎𝑝𝑝𝑜𝑠𝑖𝑡𝑒𝑯𝑦𝑝𝑜𝑡𝑒𝑛𝑢𝑠𝑒

39. The Sine Ratio  𝐒ine𝜃=𝟒.𝟔𝟔𝑯 𝐒ine𝜃=𝐎𝑝𝑝𝑜𝑠𝑖𝑡𝑒𝑯𝑦𝑝𝑜𝑡𝑒𝑛𝑢𝑠𝑒

40. The Sine Ratio  𝐒ine𝜃=𝟒.𝟔𝟔𝟖.𝟐𝟒 𝐒ine𝜃=𝐎𝑝𝑝𝑜𝑠𝑖𝑡𝑒𝑯𝑦𝑝𝑜𝑡𝑒𝑛𝑢𝑠𝑒

41. The Sine Ratio  𝐒ine𝜃=𝟒.𝟔𝟔𝟖.𝟐𝟒 𝐒ine𝜃=𝐎𝑝𝑝𝑜𝑠𝑖𝑡𝑒𝑯𝑦𝑝𝑜𝑡𝑒𝑛𝑢𝑠𝑒

42. The Sine Ratio  𝐒ine𝜃=𝟒.𝟔𝟔𝟖.𝟐𝟒  𝐒ine𝜃=𝐎𝑝𝑝𝑜𝑠𝑖𝑡𝑒𝑯𝑦𝑝𝑜𝑡𝑒𝑛𝑢𝑠𝑒

43. The Sine Ratio  𝐒ine𝜃=𝟒.𝟔𝟔𝟖.𝟐𝟒 𝐒ine=𝑶𝑯  𝐒ine𝜃=𝐎𝑝𝑝𝑜𝑠𝑖𝑡𝑒𝑯𝑦𝑝𝑜𝑡𝑒𝑛𝑢𝑠𝑒

44. The Sine Ratio  𝐒ine𝜃=𝟒.𝟔𝟔𝟖.𝟐𝟒 𝐒ine=𝑶𝑯  𝐒ine𝜃=𝐎𝑝𝑝𝑜𝑠𝑖𝑡𝑒𝑯𝑦𝑝𝑜𝑡𝑒𝑛𝑢𝑠𝑒

45. The Sine Ratio  𝐒ine𝜃=𝟒.𝟔𝟔𝟖.𝟐𝟒 𝐒ine=𝑶𝑯  𝐒ine𝜃=𝐎𝑝𝑝𝑜𝑠𝑖𝑡𝑒𝑯𝑦𝑝𝑜𝑡𝑒𝑛𝑢𝑠𝑒

46. The Sine Ratio  𝐒ine𝜃=𝟒.𝟔𝟔𝟖.𝟐𝟒 𝐒ine=𝒅𝑯  𝐒ine𝜃=𝐎𝑝𝑝𝑜𝑠𝑖𝑡𝑒𝑯𝑦𝑝𝑜𝑡𝑒𝑛𝑢𝑠𝑒

47. The Sine Ratio  𝐒ine𝜃=𝟒.𝟔𝟔𝟖.𝟐𝟒 𝐒ine=𝒅𝑯  𝐒ine𝜃=𝐎𝑝𝑝𝑜𝑠𝑖𝑡𝑒𝑯𝑦𝑝𝑜𝑡𝑒𝑛𝑢𝑠𝑒

48. The Sine Ratio  𝐒ine𝜃=𝟒.𝟔𝟔𝟖.𝟐𝟒 𝐒ine=𝒅𝒆  𝐒ine𝜃=𝐎𝑝𝑝𝑜𝑠𝑖𝑡𝑒𝑯𝑦𝑝𝑜𝑡𝑒𝑛𝑢𝑠𝑒

49. The Sine Ratio  𝐒ine𝜃=𝟒.𝟔𝟔𝟖.𝟐𝟒 𝐒ine=𝒅𝒆  𝐒ine𝜃=𝐎𝑝𝑝𝑜𝑠𝑖𝑡𝑒𝑯𝑦𝑝𝑜𝑡𝑒𝑛𝑢𝑠𝑒

50. The Sine Ratio  𝐒ine𝜃=𝟒.𝟔𝟔𝟖.𝟐𝟒 𝐒ine=𝒅𝒆  𝐒ine𝜃=𝐎𝑝𝑝𝑜𝑠𝑖𝑡𝑒𝑯𝑦𝑝𝑜𝑡𝑒𝑛𝑢𝑠𝑒 

51. The Sine Ratio  𝐒ine𝜃=𝟒.𝟔𝟔𝟖.𝟐𝟒 𝐒ine=𝒅𝒆  𝐒ine𝜃=𝐎𝑝𝑝𝑜𝑠𝑖𝑡𝑒𝑯𝑦𝑝𝑜𝑡𝑒𝑛𝑢𝑠𝑒 𝐒ine=𝑶𝑯 

52. The Sine Ratio  𝐒ine𝜃=𝟒.𝟔𝟔𝟖.𝟐𝟒 𝐒ine=𝒅𝒆  𝐒ine𝜃=𝐎𝑝𝑝𝑜𝑠𝑖𝑡𝑒𝑯𝑦𝑝𝑜𝑡𝑒𝑛𝑢𝑠𝑒 𝐒ine=𝑶𝑯 

53. The Sine Ratio  𝐒ine𝜃=𝟒.𝟔𝟔𝟖.𝟐𝟒 𝐒ine=𝒅𝒆  𝐒ine𝜃=𝐎𝑝𝑝𝑜𝑠𝑖𝑡𝑒𝑯𝑦𝑝𝑜𝑡𝑒𝑛𝑢𝑠𝑒 𝐒ine=𝑶𝑯 

54. The Sine Ratio  𝐒ine𝜃=𝟒.𝟔𝟔𝟖.𝟐𝟒 𝐒ine=𝒅𝒆  𝐒ine𝜃=𝐎𝑝𝑝𝑜𝑠𝑖𝑡𝑒𝑯𝑦𝑝𝑜𝑡𝑒𝑛𝑢𝑠𝑒 𝐒ine=𝒒𝑯 

55. The Sine Ratio  𝐒ine𝜃=𝟒.𝟔𝟔𝟖.𝟐𝟒 𝐒ine=𝒅𝒆  𝐒ine𝜃=𝐎𝑝𝑝𝑜𝑠𝑖𝑡𝑒𝑯𝑦𝑝𝑜𝑡𝑒𝑛𝑢𝑠𝑒 𝐒ine=𝒒𝑯 

56. The Sine Ratio  𝐒ine𝜃=𝟒.𝟔𝟔𝟖.𝟐𝟒 𝐒ine=𝒅𝒆  𝐒ine𝜃=𝐎𝑝𝑝𝑜𝑠𝑖𝑡𝑒𝑯𝑦𝑝𝑜𝑡𝑒𝑛𝑢𝑠𝑒 𝐒ine=𝒒𝟕.𝟑𝟐 

57. The Sine Ratio  𝐒ine𝜃=𝟒.𝟔𝟔𝟖.𝟐𝟒 𝐒ine=𝒅𝒆  𝐒ine𝜃=𝐎𝑝𝑝𝑜𝑠𝑖𝑡𝑒𝑯𝑦𝑝𝑜𝑡𝑒𝑛𝑢𝑠𝑒 𝐒ine=𝒒𝟕.𝟑𝟐 

58. The Sine Ratio  𝐒ine𝜃=𝟒.𝟔𝟔𝟖.𝟐𝟒 𝐒ine=𝒅𝒆  𝐒ine𝜃=𝐎𝑝𝑝𝑜𝑠𝑖𝑡𝑒𝑯𝑦𝑝𝑜𝑡𝑒𝑛𝑢𝑠𝑒  𝐒ine=𝒒𝟕.𝟑𝟐 

59. The Sine Ratio  𝐒ine𝜃=𝟒.𝟔𝟔𝟖.𝟐𝟒 𝐒ine=𝒅𝒆  𝐒ine𝜃=𝐎𝑝𝑝𝑜𝑠𝑖𝑡𝑒𝑯𝑦𝑝𝑜𝑡𝑒𝑛𝑢𝑠𝑒  𝐒ine=𝑶𝑯 𝐒ine=𝒒𝟕.𝟑𝟐 

60. The Sine Ratio  𝐒ine𝜃=𝟒.𝟔𝟔𝟖.𝟐𝟒 𝐒ine=𝒅𝒆  𝐒ine𝜃=𝐎𝑝𝑝𝑜𝑠𝑖𝑡𝑒𝑯𝑦𝑝𝑜𝑡𝑒𝑛𝑢𝑠𝑒  𝐒ine=𝑶𝑯 𝐒ine=𝒒𝟕.𝟑𝟐 

61. The Sine Ratio  𝐒ine𝜃=𝟒.𝟔𝟔𝟖.𝟐𝟒 𝐒ine=𝒅𝒆  𝐒ine𝜃=𝐎𝑝𝑝𝑜𝑠𝑖𝑡𝑒𝑯𝑦𝑝𝑜𝑡𝑒𝑛𝑢𝑠𝑒  𝐒ine=𝑶𝑯 𝐒ine=𝒒𝟕.𝟑𝟐 

62. The Sine Ratio  𝐒ine𝜃=𝟒.𝟔𝟔𝟖.𝟐𝟒 𝐒ine=𝒅𝒆  𝐒ine𝜃=𝐎𝑝𝑝𝑜𝑠𝑖𝑡𝑒𝑯𝑦𝑝𝑜𝑡𝑒𝑛𝑢𝑠𝑒  𝐒ine=𝟒.𝟒𝟑𝑯 𝐒ine=𝒒𝟕.𝟑𝟐 

63. The Sine Ratio  𝐒ine𝜃=𝟒.𝟔𝟔𝟖.𝟐𝟒 𝐒ine=𝒅𝒆  𝐒ine𝜃=𝐎𝑝𝑝𝑜𝑠𝑖𝑡𝑒𝑯𝑦𝑝𝑜𝑡𝑒𝑛𝑢𝑠𝑒  𝐒ine=𝟒.𝟒𝟑𝑯 𝐒ine=𝒒𝟕.𝟑𝟐 

64. The Sine Ratio  𝐒ine𝜃=𝟒.𝟔𝟔𝟖.𝟐𝟒 𝐒ine=𝒅𝒆  𝐒ine𝜃=𝐎𝑝𝑝𝑜𝑠𝑖𝑡𝑒𝑯𝑦𝑝𝑜𝑡𝑒𝑛𝑢𝑠𝑒  𝐒ine=𝟒.𝟒𝟑𝒕 𝐒ine=𝒒𝟕.𝟑𝟐 

65. The Sine Ratio  𝐒ine𝜃=𝟒.𝟔𝟔𝟖.𝟐𝟒 𝐒ine=𝒅𝒆  𝐒ine𝜃=𝐎𝑝𝑝𝑜𝑠𝑖𝑡𝑒𝑯𝑦𝑝𝑜𝑡𝑒𝑛𝑢𝑠𝑒  𝐒ine=𝟒.𝟒𝟑𝒕 𝐒ine=𝒒𝟕.𝟑𝟐 

66. The Sine Ratio Remember: 𝑺𝑖𝑛𝑒𝜃=𝑶𝑝𝑝𝑜𝑠𝑖𝑡𝑒𝑯𝑦𝑝𝑜𝑡𝑒𝑛𝑢𝑠𝑒 ->SOH

67. The Sine Ratio Remember: 𝑺𝑖𝑛𝑒𝜃=𝑶𝑝𝑝𝑜𝑠𝑖𝑡𝑒𝑯𝑦𝑝𝑜𝑡𝑒𝑛𝑢𝑠𝑒 ->SOH

68. The Sine Ratio Remember: 𝑺𝑖𝑛𝑒𝜃=𝑶𝑝𝑝𝑜𝑠𝑖𝑡𝑒𝑯𝑦𝑝𝑜𝑡𝑒𝑛𝑢𝑠𝑒->SOH

69. The Sine Ratio Remember: 𝑺𝑖𝑛𝑒𝜃=𝑶𝑝𝑝𝑜𝑠𝑖𝑡𝑒𝑯𝑦𝑝𝑜𝑡𝑒𝑛𝑢𝑠𝑒 ->SOH

70. The Sine Ratio Remember: 𝑺𝑖𝑛𝑒𝜃=𝑶𝑝𝑝𝑜𝑠𝑖𝑡𝑒𝑯𝑦𝑝𝑜𝑡𝑒𝑛𝑢𝑠𝑒 ->SOH

71. The Sine Ratio Remember: 𝑺𝑖𝑛𝑒𝜃=𝑶𝑝𝑝𝑜𝑠𝑖𝑡𝑒𝑯𝑦𝑝𝑜𝑡𝑒𝑛𝑢𝑠𝑒 ->SOH

72. The Sine Ratio Remember: 𝑺𝑖𝑛𝑒𝜃=𝑶𝑝𝑝𝑜𝑠𝑖𝑡𝑒𝑯𝑦𝑝𝑜𝑡𝑒𝑛𝑢𝑠𝑒 ->SOH