Lesson 7.0 Wks. €
€
7.1 part 1 €
€
€
7.1 part 2 €
The unit circle 7.2 part 1 7.3 part 1 7.4 part 1 €
Answers 1. h = 3 3 2. d = 10 2 3. x = 14, y = 14 2 4. x = 10, y = 5 5. u = 16,v = 8 3 6. x = 3 2, y = 3 2 7. x = 8 3, y = 4 3 8. x =€6, y = 3 2 9€. y = 8, x = 8 3 10. x = 4 €15, y = 4 5 Pg. 513
€
π
11π
−5π
35.
38. € 41. π 44.
47. 60
6
6
4
50. -120 53. 15 56. -180 59. .30 62. -.89
65. 179.91 68. 171.89
Pg. 514 €
€s=5 meters 74.€R=24 cm 75. .6 radians
71.
79. A=25 sq meters 82. r=6.928 vm
83. .24 radians
88. s=2.094 meters, A=4.189 sq meters
90. s=7.854 cm, A=35,343 sq cm
91. 9.42 in, 15.71 in 95. A=1060.29 sq feet
Fill out unit circle neatly and memorize it! Pg. 526
11. sin=5/13, cos=12/13, tan=5/12
12. sin=3/5, cos=4/5, tan=3/4
7
3 7
16. sin=3/4, cos=
, tan=
4
7
5
2 5
19. sin=
, cos=
, tan=1/2 5
5
2
€
25. cos=€ , tan=1
2
€27. sin= 2€ 2 , tan= 2 2 3
€30. sin= 2 5 , cos= 5 , tan=2
5
5
€
2
6
6
€32. sin=1/5, cos=
, tan=
5
12
€Pg. 536 €
3
3 2+4 3
17. 2 19. 2 20.
21.
3
€
€ 2
23. -8/3 25. ½ 28. -2/3 29. ? 31. ? 33. ? 36.
? 38. ? 40. ? 41. ? 43. ?
€
Pg. 548 €
11. sin=4/5, cos=-3/5, tan=-4/3
−3 13
2 13
, cos=
, tan=-3/2
13
13
3
3
17. sin=1/2, cos=
, tan=
2
3
−
2
−
2
€20. sin= € , cos=
, tan= 1
2
2
33. 2 €
35. 4 36.€1
40. 2
13. sin=
€ Find two positive
€
and two negative coterminal
angles. (*Answers will vary*)
1. 40°
2. 2π/3
3. -17π/6
4. -690°
5. 9π/2
6. 495°
Pg. 548
2
21.
26. -1
2
Pg. 549
41. 30 43. 60
7.4 part 2 €
56. 50
29.
2
32. 1
2
46. 30 47. Pi/4 54. Pi/6
2
57.€Pi/4 59. 1/2 61. 64. -1/2
2
3
2
2
71. 73. 3 80. − 2
83. 0 87. -1
2
92. cos=-12/13, tan=5/12
15
98. sin=
, tan= 15
4
− 3
99. sin=
, cos=1/2, tan= − 3
2
€
€103. sin= 10 , cos= −3 10
10
10
€
Pg.
558
€
66. 7.5 23. 1 27.
32. 1
€
€
51.
7.2 part 2 Pg. 526
55. -1
56.
39.
40.
57. -2
58.
39. 1
7.3 part 2 42. 0
45. 1
48. 0
51. 1
54. 1
Use trig properties to simplify each expression.
1.tan58
2. 3cot
3. 1
4. cot 2 θ
5. csc 2 θ
6. -3
Pg. 538
€
59. 70.02 feet 60. 83.91 feet 61. 985.91 feet
€
63. 137.37 m 64. 20.67 feet 65. 1978.09 feet
67. 60.27 feet 69. 203.52 feet
8.3-­‐8.5 Assignments 8.3 Pg. 625 Hints 19. Change to sine and cosine 21. Even/Odd and Pythagorean 23. Change to sine and cosine, Pythagorean 25. Pythagorean 27. Multiply, Pythagorean 29. Multiply, Pythagorean 31. Pythagorean 33. Multiply, Factor, Pythagorean 34. Change to sine and cosine, Pythagorean 43. Change to Cotangent 44. Change to Sine 49. Common Denominator 50. Common Denominator 52. Common Denominator 8.4 Pg. 634 1
1
1
9. ( 6 − 2) 10. ( 6 − 2) 11. ( 2 − 6) 12. −2 − 3 4
4
4
1
1
13. − ( 2 + 6) 14. ( 2 + 6) 15. 2 − 3 16. 2 − 3 4
4
1
17. − ( 2€+ 6) 21. ½ €
23. 0 25. 1 €
27. -­‐1 €
4
€
2 5
11 5
2 5 €
2 5
11 5
2 5
€ 31. a) €
b) c) d) 2 32. a) b) c) d) -­‐2 25
25
5
25
25
5
€ 54. sin θ 55. 2sin α cos β 59. 1− tan α tan β 60. cot α + tan β 8.5 Pg. 643 10
3 10 €
€ 7. a) 2€
€
4/25 b) €
7/25 c) d) €
10
10
€
€
€
€
5
2 5
8. a) 24/25 b) -­‐7/25 c) d) 5
5
2 5
− 5
9. a) 24/25 b) -­‐€
7/25 c) € d) 5
5
− 3
3
16. a) b) €-­‐1/2 €
c) ½ d) 2
2
€
€
17. a) -­‐3/5 b) -­‐4/5 c) €
19. 21. €
23. d) 24. 8.1 8.2 €
8.7 8.8 €
13. 0 14. 0 15. –pi/2 16. Pi 17. 0 18. –pi/4 19. Pi/4 20. pi/6 21. Pi/3 22. –pi/3 23. 5pi/6 24. –pi/4 42. Pi/3 44. Pi/3 2
3
5
9. 12. −
15. Pi/4 18. ½ 21. 3pi/4 24. Pi/3 27. 2
3
2
5
30. −
33. 5 36. 2pi/3 39. –pi/2 42. 2pi/3 45. 1.32 48. 1.91 2
Extras € €
2 5
105
1. 4/5 € 2. 12/13 3. 3 4. 11 7. 7pi/6, 11pi/6 8. Pi/3, 5pi/3 10. Pi/6, 5pi/6, 7pi/6, 11pi/6 11. pi/4, 3pi/4, 5pi/4, 7pi/4 12. Pi/6, 5pi/6, 7pi/6, 11pi/6 15. pi/3, 2pi/3, 4pi/3, 5pi/3 16. 3pi/8, 7pi/8, 11pi/8, 15pi/8 €
€
19. 7pi/6, 11pi/6 22. 2pi/3, 5pi/3 23. 2pi/3, 4pi/3 25. 3pi/4, 5pi/4 26. 4pi/3, 5pi/3 37. Pi/3 + kpi, 2pi/3 + kpi 38. 3pi/4 + kpi 5. pi/2, 2pi/3, 4pi/3, 3pi/2 6. Pi/2, 3pi/2 8. Pi/3, pi, 5pi/3 9. 0, pi/4, 5pi/4 16. No real Solution 20. Pi/6, pi/2, 5pi/6, 3pi/2 23. 0, 2pi/3, 4pi/3 24. Pi/4, pi/2, 3pi/4, 5pi/4, 3pi/2, 7pi/4 31. pi/2 32. 2pi/3, 4pi/3 Chapter 9 9.1 11. b=5.03, c=7.83, A=50 17. b=3.08, a=8.46, A=70 22. A=48.3, B=41.8, a=4.47 32. a) 2150 b) 1450 c)38.4 9.2 11. B=45, a=3.35, c=4.23 19. A=100, a=5.24, c=.92 21. B=40, a=5.64, b=3.86 26. One triangle: A=111.2, C=28.8, a=5.80 29. No triangle 30. Tri 1: A=65.4, C=74.6, a=2.83 – Tri 2: A=34.6, C=105.4, a=1.77 35. Tri 1: A=57.7, B=97.3, b=2.35 – Tri 2: A=122.3, B=32.7, b=1.28 38. B=95, c=76.90 39. C=1490.48 40. H=629.90 ft. 41. 381.69 ft. 9.3 11. c=3.75, A=32.1, B=52.9 13. A=48.5, B=38.6, C=92.9 17. c=2.57, A=48.6, B=91.4 21. b=4.14, C=27, A=43 28. A=70.5, B=70.5, C=39 31. A=97.9, B=52.4, C=29.7 33. 165 34. 227.56 miles 37. 63.7 feet 9.4 7. 2.99 9. 14.98 17. 2.82 23. 19.9 35. $5446.38 37. 216.5 38. 15.27