9781285774770_AppC_ans.qxd
9/11/13
10:37 AM
Page A143
A143
Answers to Odd-Numbered Exercises
Appendix C
(page A14)
1
2
3
(− 1, 1)
−2
0
1
2
3
4
5
The interval is unbounded.
6
21. y ⱖ 4; 关4, ⬁兲
25. x ⱖ 12
23. 0.03 < r ⱕ 0.07; 共0.03, 0.07兴
27. ⫺ 12 < x < 72
1
2
1
−1
0
1
−2
2
0
2
−1
0
a
−2
0
2
4
x
−4
2
−2
0
2
47. (a) ⫺51; 51; 51 (b) 51; ⫺51; 51
4; ⫺4; 4
51. x ⫺ 2 > 2
x ⱕ 2
(a) x ⫺ 12 ⱕ 10 (b) x ⫺ 12 ⱖ 10
1
57. (a) 14
(b) 10
61. x ⱕ 41 or x ⱖ 59
x ⱖ 36 units
(a) 355
(b) 22
65. b
113 > ␲
7 > ␲
False. The reciprocal of 2 is 12, which is not an integer.
True
71. True
73–79. Proofs
⫺3 ⫺ 1 > ⫺3 ⫺ 1 ; 3 ⫺ 1 ⫽ 3 ⫺ 1 ; Proof
ⱍⱍ
ⱍ
ⱍ
ⱍ
ⱍ
ⱍ
ⱍ
ⱍ ⱍⱍ ⱍⱍ
(page A21)
Appendix C.2
1
2
3. (a)
冣 冢
冣
冣
2
−4
(3, 3)
2
x
1
(b) 2冪5
(c) 共3, 3兲
2
3
4
5
3
− , −5
2
2
3
x
−2 −1
(1, − 3)
1
3
(1, − 3)
−3
45. 共x ⫺
2
−2
4
−4
−5
(2, 1)
1
1
x
−2
1
− , −2
2
2
x
−2 −1
1
,1
2
4
3
y
y
(4, 5)
5
10 12
3
y
y
1. (a)
8
Year (2 ↔ 2002)
冢
冢
ⱍ
ⱍ ⱍ ⱍ ⱍⱍ ⱍ
6
17. d1 ⫽ 2冪5, d2 ⫽ 冪5, d3 ⫽ 3冪5
Collinear, because d1 ⫹ d2 ⫽ d3.
19. d1 ⫽ 冪2, d2 ⫽ 冪13, d3 ⫽ 5
Not collinear, because d1 ⫹ d2 > d3.
21. x ⫽ ± 3
23. y ⫽ ± 冪55
3x1 ⫹ x2 3y1 ⫹ y2
x ⫹ x2 y1 ⫹ y2
25.
,
, 1
,
,
4
4
2
2
x1 ⫹ 3x2 y1 ⫹ 3y2
,
4
4
27. c
28. b
29. a
30. d
31. x 2 ⫹ y 2 ⫺ 9 ⫽ 0
2
2
33. x ⫹ y ⫺ 4x ⫹ 2y ⫺ 11 ⫽ 0
35. x 2 ⫹ y 2 ⫹ 2x ⫺ 4y ⫽ 0
37. x 2 ⫹ y 2 ⫺ 6x ⫺ 4y ⫹ 3 ⫽ 0
39. x 2 ⫹ y 2 ⫽ 26,0002
2
2
41. 共x ⫺ 1兲 ⫹ 共 y ⫹ 3兲 ⫽ 4 43. 共x ⫺ 1兲2 ⫹ 共 y ⫹ 3兲2 ⫽ 0
43. ⫺3 ⱕ x ⱕ 2
0
4
x
(0, 0)
x
x
−2
x
2
(2, 1)
39. 0 < x < 3
2
x
(4, 0)
1800
1700
1600
1500
1400
1300
1200
1100
1000
2
1
41. ⫺3 ⱕ x ⱕ 1
45.
49.
53.
55.
59.
63.
67.
69.
81.
(1, 2)
10
0
d2
y
15.
a+b
x
−4
(3, 3)
3
x
a−b
37. ⫺3 < x < 2
−2
冪
x
2
35. a ⫺ b < x < a ⫹ b
x
−4
2
y
1
13
0
1
−1
x
−2
8
33. x ⱖ 13, x ⱕ ⫺7
− 10
1+ 3
2
13. Rhombus: the length of
each side is 冪5.
31. ⫺1 < x < 1
−7
冢0, 1 ⫹2 3冣
(− 1, − 5)
4
x
6
(c)
x
29. x > 6
4
0,,
7
2
−2
x
−2
3)
7. Quadrant II
9. Quadrants I and III
y
11. Right triangle:
2
d1 ⫽ 冪45
(2, 1)
d2 ⫽ 冪5
d1 2
−2
d3 ⫽ 冪50
−
2
d3
共d1兲2 ⫹ 共d2兲2 ⫽ 共d3兲2
19. x is no more than 5.
−1
冪8 ⫺ 2冪3
−1
4
x
(1,
2
1. Rational
3. Irrational
5. Rational
7. Rational
4
9. Rational
11. 11
13. 11
37
15. (a) True
(b) False
(c) True
(d) False
(e) False
(f) False
17. x is greater than ⫺3 and less than 3.
x
The interval is bounded.
0
(b)
3
Number of stores
Appendix C.1
−4 −3 −2 −1
y
5. (a)
−5
兲
1 2
2
⫹ 共y ⫺
兲
1 2
2
⫽2
47. 共x ⫹ 12 兲 ⫹ 共y ⫹ 54 兲 ⫽ 94
2
2
y
−6
(b) 2冪10
1
(c) 共⫺ 2, ⫺2兲
y
1 1
,
2 2
2
1
1
−2
−3
−2
x
−1
1
x
−1
1
2
−1
−2
−2
1 5
− ,−
2 4
−3
9781285774770_AppC_ans.qxd
A144
9/11/13
10:37 AM
Page A144
Answers to Odd-Numbered Exercises
49.
51.
3
−9
y
1
29.
x
−1
−9
−2
1
3
5
(2, − 1)
31.
−3
35.
−4
53. Proof
55. True
Appendix C.3
57. True
59–61. Proofs
␪
12 ft
1.5
41.
(page A31)
1. (a) 396⬚, ⫺324⬚ (b) 240⬚, ⫺480⬚
19␲ 17␲
10␲ 2␲
3. (a)
(b)
,⫺
,⫺
9
9
3
3
␲
5␲
5. (a) ; 0.524 (b)
; 2.618
6
6
7␲
2␲
(c)
; 5.498 (d)
; 2.094
4
3
7. (a) 270⬚ (b) 210⬚ (c) ⫺105⬚ (d) ⫺151.1⬚
9.
12,963
r
8 ft
15 in.
85 cm
24 in.
mi
␲
s
24 in.
63.75␲ cm
1.6
3␲
4
␲ 7␲
3␲ 5␲
(b) ␪ ⫽
,
,
4 4
4 4
␲ 5␲
5␲ 11␲
(a) ␪ ⫽ ,
(b) ␪ ⫽
,
4 4
6 6
␲ 3␲ 5␲ 7␲
␲
5␲
33. ␪ ⫽ 0, , ␲,
␪⫽ , , ,
4 4 4 4
4
4
␲ 5␲
␲
␪⫽ ,
37. ␪ ⫽ 0, , ␲
39. 5099 ft
3 3
2
(a) Period: ␲
43. Period: 12
Amplitude: 2
Amplitude: 3
(b) Period: 2
Amplitude: 12
␲
2␲
Period:
47. Period:
2
5
1
2.5
(a)
(b)
c = −2
27. (a) ␪ ⫽
2
9
96 in.
8642 mi
4
2␲
3
5
11. (a) sin ␪ ⫽ 45 csc ␪ ⫽ 54 (b) sin ␪ ⫽ ⫺ 13
csc ␪ ⫽ ⫺ 13
5
3
5
12
cos ␪ ⫽ 5 sec ␪ ⫽ 3
cos ␪ ⫽ ⫺ 13 sec ␪ ⫽ ⫺ 13
12
5
12
tan ␪ ⫽ 43 cot ␪ ⫽ 34
tan ␪ ⫽ 12
cot ␪ ⫽ 5
13. (a) Quadrant III
(b) Quadrant IV
冪3
4
15.
17.
2
3
冪3
冪3
19. (a) sin 60⬚ ⫽
(b) sin 120⬚ ⫽
2
2
1
1
cos 60⬚ ⫽
cos 120⬚ ⫽ ⫺
2
2
tan 60⬚ ⫽ 冪3
tan 120⬚ ⫽ ⫺ 冪3
冪2
␲ 冪2
5␲
(c) sin ⫽
(d) sin
⫽⫺
4
2
4
2
冪2
␲ 冪2
5␲
cos ⫽
⫽⫺
cos
4
2
4
2
␲
5␲
tan ⫽ 1
⫽1
tan
4
4
冪2
冪2
21. (a) sin 225⬚ ⫽ ⫺
(b) sin共⫺225⬚兲 ⫽
2
2
冪2
冪2
cos 225⬚ ⫽ ⫺
cos共⫺225⬚兲 ⫽ ⫺
2
2
tan共⫺225⬚兲 ⫽ ⫺1
tan 225⬚ ⫽ 1
冪3
5␲
1
11␲
(c) sin
(d) sin
⫽⫺
⫽⫺
3
2
6
2
5␲ 1
11␲ 冪3
cos
⫽
⫽
cos
3
2
6
2
冪3
5␲
11␲
tan
⫽ ⫺ 冪3
⫽⫺
tan
3
6
3
23. (a) 0.1736
(b) 5.7588
25. (a) 0.3640
(b) 0.3640
45.
49.
c = ±2
c = −1
c=1
−
c = ±1
−
c=2
−1
− 2.5
Change in amplitude
(c)
Change in period
1.5
c = −2
c=2
−
2
2
c = −1
c=1
− 1.5
Horizontal translation
51.
53.
y
y
1
1
π
3π
x
x
3
2
−1
55.
3
−1
57.
y
y
3
2
1
−1
1
π
x
3π
59.
π
2
61.
y
π
3π
2
x
y
1
2
x
π
2
π
2
−1
x
−π
2
1
␲
63. a ⫽ 3, b ⫽ , c ⫽
2
2
π
2
π
3π
2
9781285774770_AppC_ans.qxd
9/11/13
10:37 AM
Page A145
Answers to Odd-Numbered Exercises
65.
y
y
2
2
f(x) = sin x
g(x) = ⏐sin x⏐
1
−π
π
x
2π
−2π
−π
π
2π
x
−1
−2
−2
y
h(x) = sin (⏐x⏐)
2
π
2π
ⱍ
ⱍ
x
−1
−2
The graph of f 共x兲 will reflect any parts of the graph of f 共x兲
below the x-axis about the x-axis. The graph of f 共 x 兲 will
reflect the part of the graph of f 共x兲 right of the y-axis about the
y-axis.
67.
ⱍⱍ
100
0
12
0
January, November, December
4
1
1
69. f 共x兲 ⫽
sin ␲x ⫹ sin 3␲x ⫹ sin 5␲x ⫹ . . .
␲
3
5
冢
2
−1
3
−2
冣
A145