1. 1 + tan2u = sec2u 1 + cot2u = csc2u
Ch5.1A – Using Fundamental Identities
Reciprocal Identities
Quotient Identities
Pythagorean Identities
sin2u + cos2u = 1
1 + tan2u = sec2u
1 + cot2u = csc2u

2. sec(–u) = sec(u) tan(–u) = –tan(u)
Cofunction Identities
Even/Odd Identities
Even Odd
cos(–u) = cos(u) sin(–u) = –cos(u)
sec(–u) = sec(u) tan(–u) = –tan(u)
cot(–u) = –cot(u)
csc(–u) = –csc(u)

3. Ex1) find all six trigs.
Ex2) Simplify: sinx.cos2x – sinx

4. Ex3) Use ur calc to determine if the following are identities:
a) cos3x = 4cos3x – 3cosx
b) cos3x = sin(3x – )
Ex4) Verify by hand:
Ch5.1A p – 43odd

5. Ch5.1A p – 43odd Do 19,21,29,31,37,39,41 in class

6. Ch5.1A p – 43odd Do 19,21,29,31,37,39,41 in class

7. Ch5.1A p – 43odd Do 19,21,29,31,37,39,41 in class

8. Ch5.1A p – 43odd Do 19,21,29,31,37,39,41 in class

9. Ch5.1B – More Identities
Ex5) Factor:
a) sec2θ – 1 b) 4tan2θ + tanθ – 3
Ex6) Factor: csc2x – cotx – 3

10. Ex7) Simplify: sint + cott.cost
Ex8) Rewrite not as a fraction

11. Ex9) If x = 2tanθ, use substitution to express
as a trig function. (0 < θ < π/2)
Ch5.1B p odd,71-75odd

12. Ch5.1B p odd,71-75odd

13. Ch5.1B p odd,71-75odd

14. Ch5.1B p odd,71-75odd

15. Ch5.1B p odd,71-75odd

16. Ch5.1B p odd,71-75odd

17. Ch5.1C p – 62 even

18. Ch5.1C p – 62 even

19. Ch5.1C p – 62 even

20. Ch5.1C p – 62 even

21. Ch5.1C p – 62 even

22. Ch5.1C p – 62 even

23. Ch5.1C p – 62 even

24. Ch5.1C p – 62 even

25. Ch5.2A – Verifying Trig Identities
Guidelines:
1. Work one side at a time, usually the most complicated 1st.
2. Look to:
- Factor
- Add fractions
- Square a binomial
- Get a monomial denominator
3. Use fundamental identities
4. Head toward sine and cosine
5. But try SOMETHING!

26. Ex1) Verify:

27. Ex2) Verify:

28. Ex3) Verify: (tan2x + 1)(cos2x – 1) = –tan2x

29. Ex4) Verify: tanx + cotx = secx.cscx

30. HW#25) Verify:
Ch5.2A p421 1 – 10 all

31. Ch5.2A p421 1 – 10 all

32. Ch5.2A p421 1 – 10 all

33. Ch5.2B – More Verifying Trig ID’s
Ex5) Verify:

34. Ex6) Verify:

35. Ex7) Verify: tan4x = tan2x.sec2x – tan2x
Verify: sin3x.cos4x = (cos4x – cos6x).sinx

36. HW#46) Verify:
Ch5.2B p – 39 odd

37. Ch5.2B p – 39 odd

38. Ch5.2B p – 39 odd

39. Ch5.2B p – 39 odd

40. Ch5.2B p – 39 odd

41. Ch5.2C p all

42. Ch5.3A – Solving Trig Functions
Ex1) Solve: 2sinx – 1 = 0
Ex2) Solve:

43. Ex3) Solve: 3tan2x – 1 = 0
Ex4) Solve: cotx.cos2x = 2cotx

44. Ex5) Solve: 2sin2x – sinx – 1 = 0 over [0,2π]
Ex6) Solve: 2sin2x + 3cosx – 3 = 0
Ch5.3A p – 29odd,60

45. Ch5.3A p – 29odd,60

46. Ch5.3A p – 29odd,60

48. Ch5.3B – Solving Trig Functions cont
HW#18) Solve: tan23x = 3
#24) Solve: cos2x.(2cosx + 1) = 0

49. #35) Solve:
#37) Solve:
Ch5.3B p – 22even, 31 – 37odd

50. Ch5.3B p – 22even, 31 – 37odd

51. Ch5.3B p – 22even, 31 – 37odd

52. sin(u + v) = sinu.cosv + cosu.sinv
Ch5.4A – Sum and Difference Formulas
sin(u + v) = sinu.cosv + cosu.sinv
sin(u – v) = sinu.cosv – cosu.sinv
cos(u + v) = cosu.cosv – sinu.sinv
cos(u – v) = cosu.cosv + sinu.sinv
Ex1) Find the exact value of cos75˚.

53. sin(u + v) = sinu.cosv + cosu.sinv cos(u + v) = cosu.cosv – sinu.sinv
Ex2) Find the exact value of , given that

54. sin(u + v) = sinu.cosv + cosu.sinv cos(u + v) = cosu.cosv – sinu.sinv
Ex3) Find the exact value of sin42˚.cos12˚ – cos42˚.sin12˚

55. sin(u + v) = sinu.cosv + cosu.sinv cos(u + v) = cosu.cosv – sinu.sinv
Ex4) Prove the cofunction identity

56. sin(u + v) = sinu.cosv + cosu.sinv cos(u + v) = cosu.cosv – sinu.sinv
Ex5) Simplify tan(θ + 3π)

57. Ex6) Solve
Ch5.4A p440 7 – 25odd (7-sin,9-cos,11-sin,13-cos,15-tan)

58. Ch5.4A p440 7 – 25odd (7-sin,9-cos,11-sin,13-cos,15-tan)

59. Ch5.4A p440 7 – 25odd (7-sin,9-cos,11-sin,13-cos,15-tan)

60. Ch5.4A p440 7 – 25odd (7-sin,9-cos,11-sin,13-cos,15-tan)

61. sin(u + v) = sinu.cosv + cosu.sinv cos(u + v) = cosu.cosv – sinu.sinv
Ch5.4B – Sum and Difference Formulas cont
sin(u + v) = sinu.cosv + cosu.sinv
sin(u – v) = sinu.cosv – cosu.sinv
cos(u + v) = cosu.cosv – sinu.sinv
cos(u – v) = cosu.cosv + sinu.sinv
HW#12) Solve: tan255˚.

62. sin(u + v) = sinu.cosv + cosu.sinv cos(u + v) = cosu.cosv – sinu.sinv
HW#14) Solve:

63. sin(u + v) = sinu.cosv + cosu.sinv cos(u + v) = cosu.cosv – sinu.sinv
HW#32) Prove: sin(x+π).sin(x–π) = sin2x

64. sin(u + v) = sinu.cosv + cosu.sinv cos(u + v) = cosu.cosv – sinu.sinv
HW#44) Prove: cos(x+y) + cos(x–y) = 2cosx.cosy
Ch5.4B p440 8 – 26 even, 32,44
(8-sin,10-cos,12-tan,14-sin,16-cos)

65. Ch5.4B p440 8 – 26 even, 32,44 (8-sin,10-cos,12-tan,14-sin,16-cos)

66. Ch5.4B p440 8 – 26 even, 32,44 (8-sin,10-cos,12-tan,14-sin,16-cos)

67. sin(2u) = 2sinu.cosu cos(2u) = cos2u – sin2u or = 2cos2u – 1
Ch5.5A – Multiple Angle Formulas
sin(2u) = 2sinu.cosu
cos(2u) = cos2u – sin2u
or = 2cos2u – 1
or = 1 – 2sin2u
Ex1) Find all the solutions of: 2cosx + sin2x = 0

68. sin(2u) = 2sinu.cosu cos(2u) = cos2u – sin2u or = 2cos2u – 1
or = 1 – 2sin2u
Ex2) Find sin2θ, cos2θ, and tan2θ,
given

69. sin(2u) = 2sinu.cosu cos(2u) = cos2u – sin2u or = 2cos2u – 1
or = 1 – 2sin2u
Ex3) Express sin3x in terms of sinx.
Ch5.5A p451 1 – 25odd, not 15
Quiz tomorrow on Sum/Diff/Double Angle Formulas

70. Ch5.5A p451 1 – 25odd, not 15
Quiz tomorrow on Sum/Diff/Double Angle Formulas

71. Ch5.5A p451 1 – 25odd, not 15
Quiz today on Sum/Diff/Double Angle Formulas

72. Ch5.5A p451 1 – 25odd, not 15
Quiz today on Sum/Diff/Double Angle Formulas

73. Ch5.5A p451 1 – 25odd, not 15
Quiz today on Sum/Diff/Double Angle Formulas

74. Ch5.4,5.5 Quiz Name____________
Form A Form B
1. sin(u + v) = 1. cos2θ =
2. cos(u + v) = 2. tan2θ =
3. sin(u – v) = 3. sin2θ =
4. cos(u – v) = 4. cos(u + v) =
5. tan(u – v) = 5. cos(u – v) =
6. sin2θ = 6. sin(u + v) =
7. tan2θ = 7. sin(u – v) =
8. cos2θ = 8. tan(u – v) =

75. Ch5.5B – Multiple Angle Formulas cont
Power Reducing Formulas:
Half Angle Formulas
HW#29) Simplify: sin2x.cos2x

76. Power Reducing Formulas:
Half Angle Formulas
HW#28) Simplify: sin4x

77. Power Reducing Formulas:
Half Angle Formulas
HW#33) Simplify: 5 θ 12

78. Power Reducing Formulas:
Half Angle Formulas
HW#37) Simplify: 5 θ 12

79. Power Reducing Formulas:
Half Angle Formulas
HW#39) Simplify: sin105˚

80. Power Reducing Formulas:
Half Angle Formulas
HW#43) Simplify:
Ch5.5B p452 27,28,29,33,34,35,37,39,40,41,43,44,45

81. Ch5.5B p452 27,28,29,33,34,35,37,39,40,41,43,44,45

82. Ch5.5B p452 27,28,29,33,34,35,37,39,40,41,43,44,45

84. Ch5 Rev p455 1 – 49 eoo, + 31

85. Ch5 Rev p455 1 – 49 eoo, + 31

86. Ch5 Rev p455 1 – 49 eoo, + 31

87. Ch5 Rev p455 1 – 49 eoo, + 31

88. Ch5 Rev p455 1 – 49 eoo, + 31

89. Ch5 Rev p455 1 – 49 eoo, + 31

90. Ch5 Rev p455 1 – 49 eoo, + 31

91. Ch5 Rev p455 1 – 49 eoo, + 31