1. FUNDAMENTAL
Trigonometric
IDENTITIES

2. Trigonometric Identity
A Trigonometric Identity is a trigonometric equation that is true for all values of the variables for which the expressions in the equation are defined.

3. Reciprocal Identities

4. Reciprocal Identities

6. Reciprocal Identities
k odd integer

8. Reciprocal Identities
k odd integer
k an integer

10. Reciprocal Identities
k odd integer
k an integer
k an integer

11. Reciprocal Identities
k odd integer
k an integer
k an integer

12. We Could Also Say

13. Reciprocal Identities

14. Reciprocal Identities

15. Ratio Identities

16. Ratio Identities
Recall
The Unit Circle

17. 1

18. 1

19. 1

20. 1

21. 1

22. 1

23. 1

24. 1

25. 1

26. 1

27. 1

28. 1

29. 1

30. 1

31. Ratio Identities
k odd integer

32. Ratio Identities
k odd integer
k an integer

33. Pythagorean Identities

34. Pythagorean Identities1

35. Pythagorean Identities1

36. Pythagorean Identities1

37. Pythagorean Identities1

38. Pythagorean Identities1

39. Pythagorean Identities1

40. Pythagorean Identities1

41. Pythagorean Identities1

42. Pythagorean Identities1

43. Pythagorean Identities
Most Important!!
Most Important!!
Most Important!!

44. Pythagorean Identities
Other Two

45. Proof of the Indentity

46. What Are Proofs?
A proof of an identity may be written using a vertical line to separate the expressions to be proved equivalent.
Use known algebraic and trigonometric identities to replace on the expressions with an equivalent express.
Repeat the process until an expression is obtained that is the same as that on the other side of the line
DO NOT Add, Subtract, Multiply or Divided Both Sides by the Same Thing.

48. USE

50. Common Denominator

53. QED

54. quod erat demonstrandum
QED
quod erat demonstrandum
 Meaning
"which was to be proved"

55. Proof of the Indentity

56. USE

58. Common Denominator

61. QED

62. quod erat demonstrandum
QED
quod erat demonstrandum
 Meaning
"which was to be proved"

63. Odd-Even Identities

64. Odd-Even Identities
Recall

65. Odd-Even Identities
Odd
Even

66. Odd Identities

67. Even Identities

68. Proof

69. Where's