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PreCalculus 89-R 8 – Solving Trig Equations 9 – Trig Identities and Proof Review Problems.

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Presentation on theme: "PreCalculus 89-R 8 – Solving Trig Equations 9 – Trig Identities and Proof Review Problems."— Presentation transcript:

1 PreCalculus 89-R 8 – Solving Trig Equations 9 – Trig Identities and Proof Review Problems

2 Simplify the following trigonometric expressions tan x 1 sin 2 x

3 Review Problems tan x cos x csc x 1 sin(z) + cos(–z) + sin(–z) cos z Simplify the following trigonometric expressions 2

4 Review Problems 1 Simplify the following trigonometric expressions cos B + sin B tan B sec B 3

5 Review Problems cos 2 x Simplify the following trigonometric expressions (1 – cos 2 x)(1 + cot 2 x) 1 4

6 Review Problems sin 2 t + cos 2 t + tan 2 t sec 2 t Simplify the following trigonometric expressions sec A 5

7 Review Problems 2 csc x Simplify the following trigonometric expressions cot x 6

8 Review Problems sin 2 x Simplify the following trigonometric expressions tan 2 t 7

9 Review Problems find the exact value of the expression. 8

10 Review Problems Write the expression as a trigonometric function of one number. 9

11 Review Problems Simplify the following expressions as much as possible. cot(x) cos(p + z) – cos(p – z)–2sin(p)sin(z) 10

12 Review Problems tan z Simplify the following expressions as much as possible. 0 11

13 Review Problems Write the following expression in terms of sine only. sin z + cos z 12

14 Review Problems Find the exact value of the expression. 13

15 Review Problems Evaluate the expressions by sketching a triangle 0 14

16 Review Problems Rewrite the expressions as an algebraic expression in x. tan (sin – 1 x) sin (2 cos – 1 x) cos (sin – 1 x + cos – 1 x) 0 15

17 Review Problems Find all solutions of the following equations. 16

18 Review Problems Find all solutions of the following equations. 4 cos 2 x – 4 cos x + 1 = 0 17

19 Review Problems cos 2 4 x – sin 2 4 x = 0 Find all solutions of the following equations. 2 cos x cot x – cot x = 1 – 2 cos x 18

20 Review Problems Find all solutions of the following equation in the interval. tan x – 3 cot x = 0 Find all solutions of the following equation in the interval. cos x cos 7 x – sin x sin 7 x = 0 19

21 Review Problems Simplify completely the trigonometric expressions 1 1 20

22 Review Problems 1 Simplify completely the trigonometric expressions 21

23 Review Problems Simplify completely the trigonometric expressions 22

24 Review Problems Simplify completely the trigonometric expressions 23

25 Review Problems Simplify completely the trigonometric expressions 24

26 Review Problems Simplify completely the trigonometric expressions 25

27 Review Problems Simplify completely the trigonometric expressions 26

28 Review Problems Find the exact value of the expressions 27

29 Review Problems Simplify completely the trigonometric expressions 28

30 Review Problems Simplify completely the trigonometric expressions 29

31 Review Problems Simplify completely the trigonometric expressions 30

32 Review Problems Use an appropriate half-angle formula to find the exact value of the expression. 31

33 Review Problems Use an appropriate half-angle formula to find the exact value of the expression. 32

34 Review Problems Write the products as a sum. 33

35 Review Problems Write the sum as a product. 34

36 Review Problems Find the value of the product. Find the value of the sum. 35

37 Review Problems Simplify the expressions. 36

38 Review Problems Simplify the expressions. 37

39 Review Problems Find all solutions of the equation. 38

40 Review Problems Find all solutions of the equation. 39

41 Review Problems Find all solutions of the equation. 40

42 Review Problems Find all solutions of the equation. 41

43 Review Problems Find all solutions of the equation. 42

44 Review Problems Find all solutions of the equation. 43

45 Review Problems Solve the equation by first using a sum-to-product formula 44

46 Review Problems Find the exact value for each trigonometric function. sec 120° tan 390° cos 315° –2 45

47 Review Problems Find the exact value of the expressions. 46

48 Review Problems Find the exact value of the expressions. 47

49 Review Problems Find the exact value of the expressions. 48

50 Review Problems Evaluate the expressions by sketching a triangle. 49

51 Review Problems 0 Evaluate the expressions by sketching a triangle. 50

52 Review Problems Rewrite the expression as an algebraic expression in x. sin (cos – 1 x) tan (sin – 1 x) 51

53 Review Problems Verify the identity 52

54 Review Problems Verify the identity 53

55 Review Problems Verify the identity 54

56 Review Problems Verify the identity 55

57 Review Problems Verify the identity 56

58 Review Problems Find all real solutions, to four decimal places 57

59 Review Problems Find all real solutions, to two decimal places 58

60 Answers 1. 2. 3. 4. 5. 6. 7. 8. 9. 10. 11. 12. 13. 14. 15. 16. 17. 18. tan x sin 2 x 1cos z 1sec B cos 2 x1 sec 2 tsec A 2 csc x cot x sin 2 xtan 2 t cot(x)–2sin(p)sin(z) tan z 0 0 0

61 Answers 19. 20. 21. 22. 23. 24. 25. 26. 27. 28. 29. 30. 31. 32. 33. 34. 35. 36. 11 1

62 Answers 37. 38. 39. 40. 41. 42. 43. 44. 45. 46. 47. 48. 49. 50. –2 0

63 Answers 51. 52. 53. 54. 55.

64 Answers 56. 57. 58.

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