Ans-1
Answers to Odd-Numbered Exercises
APPENDIX D
Section D.1 (page D8)
1. Rational
Section D.2 (page D15)
1. d 5 2!5
3. Irrational
9. Rational
4
11
11.
15. (a) True
5. Rational
13.
(b) False
(e) False
7. Rational
11
37
(c) True
(d) False
1
2
3
−4
1
2
3
4
5
21. y ≥ 4, f4, `d
1
25. x ≥ 2
0
2
4
5
y
6
23. 0.03 < r ≤ 0.07, s0.03, 0.07g
1
7
27. 2 2 < x < 2
1
3
5. 8!8 2 2!3
3
(1,
2
( 1, 1)
x
−1
3
,
2
x
7
2
3)
0,,
1
3
2
x
−2
2
0
2
x
2
4
1
1
2
1
31. 21 < x < 1
29. x > 6
x
4
6
−2
8
33. x ≥ 13, x ≤ 27
−7
−1
0
1
2
35. a 2 b < x < a 1 b
13
0
y
x
x
− 10
7. Right triangle:
d1 5 !45, d2 5 !5
d3 5 !50
sd1d2 1 sd2d2 5 sd3d2
x
a
b
a
a
b
2
10
37. 23 < x < 2
39. 0 < x < 3
(2, 1)
d2
−2
x
d1
2
2
x
−2
0
−2
2
41. 23 ≤ x ≤ 1
0
2
4
43. 23 ≤ x ≤ 2
( 1,
x
−4
45.
49.
55.
59.
63.
67.
68.
72.
79.
81.
−2
0
x
−4
2
−2
0
|
|
|
|
||
|
|
| | | ||
| || ||
|
5)
9. Rhombus: the length of each side is !5.
2
4, 24, 4
47. (a) 251, 51, 51
(b) 51, 251, 51
1
51. (a) 14
(b) 10
53. x ≤ 2
x22 > 2
57. (a) x 2 12 ≤ 10 (b) x 2 12 ≥ 10
61. x ≤ 41 or x ≥ 59
x ≥ 36 units
22
(a) 355
(b)
65. b
>
p
112
7 > p
False: the reciprocal of 2 is 12 , which is not an integer.
True
69. True
70. False: 0 5 0.
71. True
True
73. Proof
75. Proof
77. Proof
Proof
23 2 1 > 23 2 1
321 5 3 2 1
||
(4, 0)
d3
x
|
y
(3, 3)
3
(1, 2)
2
1
(2, 1)
x
(0, 0)
1
2
3
11. Quadrant II
13. Quadrants I and III
15. x 5 0 ↔ 1990
y
2000
Number of
Wal-Mart stores
−4
2
2
(2, 1)
1
The interval is unbounded.
1
2
1
, 1
2
x
−2
1
,
2
2
1
1
2
−2
(3, 3)
4
x
0
(4, 5)
3
19. x is no more than 5.
−1
y
2
4
17. x is greater than 23 and less than 3.
The interval is bounded.
x
0
y
5
(f) False
−4 −3 −2 −1
3. d 5 2!10
1500
500
−2
x
2
4
Year (0 ↔ 1990)
6
5
6
4
Ans-2
Answers to Odd-Numbered Exercises
17. d1 5 2!5, d2 5 !5, d3 5 3!5
Collinear, because d1 1 d2 5 d3
19. d1 5 !2, d2 5 !13, d3 5 5
Not collinear, because d1 1 d2 > d3
21. x 5 ± 3
23. y 5 ± !55
3x1 1 x2 3y1 1 y2
x1 1 x2 y1 1 y2
25.
,
,
4
4
2
2
2 1
1
1
x1 1 3x2 y1 1 3y2
,
4
4
27. c
28. b
7. (a) 2708
r
8 ft
15 in.
85 cm
24 in.
s
12 ft
24 in.
63.75p cm
96 in.
1.6
3p
4
4
u
2
1.5
csc u 5 54
5
(b) sin u 5 2 13
csc u 5 2 13
5
5
3
3
4
2 12
13
5
12
sec u 5 2 13
12
tan u 5
31. x 2 1 y 2 2 9 5 0
sec u 5
cot u 5
13. (a) Quadrant III
35. x 2 1 y 2 1 2x 2 4y 5 0
15.
41. sx 2 1d 1 sy 1 3d 5 4
2
2
39. x 2 1 y 2 5 26,0002
43. sx 2 1d2 1 s y 1 3d2 5 0
y
x
2
1
1
2
(1,
2
1
−1
1
2
3
−3
(1,
3)
1
1
45. s x 2 2 d 1 s y 2 2 d 5 2
2
2
1
5
9
47. s x 1 2 d 1 s y 1 4 d 5 4
2
2
y
y
1 1
,
2 2
2
1
1
−3
−2
1
2
3
5
4
51.
−9
9
y
x
−1
−2
1
3
(2,
23. (a) 0.1736
−4
57. True
| |
56. False: the distance is 2b .
58. True
59. Proof
Section D.3 (page D25)
1. (a) 3968, 23248
(b) 2408, 24808
19p 17p
3. (a)
,2
9
9
10p 2p
(b)
,2
3
3
5. (a)
(c)
p
, 0.524
6
7p
, 5.498
4
(b)
(d)
5p
, 2.618
6
2p
, 2.094
3
61. Proof
5
1)
−3
55. True
!2
(b) sins22258d 5
2
!2
29. (a) u 5
2
!2
2
tans22258d 5 21
11p
1
52
6
2
11p !3
5
cos
6
2
!3
11p
tan
52
6
3
(d) sin
(b) 5.759
p 7p
27. (a) u 5 ,
4 4
!2
coss22258d 5 2
2
!3
5p
52
3
2
5p 1
cos
5
3
2
5p
tan
5 2 !3
3
1
53. Proof
!2
5p
52
4
2
!2
5p
cos
52
4
2
5p
51
tan
4
(c) sin
2
−9
tan 1208 5 2 !3
tan 2258 5 1
−3
!3
(d) sin
cos 2258 5 2
−2
1
,
2
(b) sin 1208 5
2
1
cos 1208 5 2
2
1
2
1
49.
21. (a) sin 2258 5 2
x
−1
x
−1
2
!3
(c) sin
−5
cot u 5 12
5
4
3
p !2
5
4
2
p !2
cos 5
4
2
p
tan 5 1
4
−4
−5
tan u 5
tan 608 5 !3
−2
3)
17.
2
cos u 5
(b) Quadrant IV
2
1
cos 608 5
2
x
3
!3
19. (a) sin 608 5
y
2p
3
3
5
4
3
33. x 2 1 y 2 2 4x 1 2y 2 11 5 0
37. x 2 1 y 2 2 6x 2 4y 1 3 5 0
12,963
mi
p
8642 mi
11. (a) sin u 5 45
cos u 5
30. d
(d) 2135.68
9.
2
29. a
(c) 21058
(b) 2108
25. (a) 0.3640
(b) 0.3640
3p 5p
(b) u 5
,
4 4
p 5p
,
4 4
(b) u 5
31. u 5
p 3p 5p 7p
, , ,
4 4 4 4
35. u 5
p 5p
,
3 3
5p 11p
,
6 6
p
5p
33. u 5 0, , p,
4
4
p
37. u 5 0, , p
2
39. 5099 feet
Ans-3
Answers to Odd-Numbered Exercises
41. (a) Period: p
43. Period: 12
(b) Period: 2
Amplitude: 2
p
45. Period:
2
Amplitude:
1
2
65.
y
Amplitude: 3
y
f )x)
2
2p
47. Period:
5
sin x
2
2.5
−3.14
x
2
2
(b) Change in period
1
2
1
c = −2
c = ±2
c = −1
c=1
sin x
x
2
49. (a) Change in amplitude
g)x)
1
3.14
2
c = ±1
−3.14
y
3.14
h )x)
2
c=2
− 2.5
sin x
−1
x
(c) Horizontal translation
2
1
1.5
c = −2
c=2
−1.57
2
|
1.57
c = −1
c=1
− 1.5
51.
53.
y
|
The graph of f sxd will reflect any parts of the graph of f sxd
below the x-axis about the x-axis. The graph of f s x d will
reflect the part of the graph of f sxd left of the y-axis about the
x-axis.
||
y
67.
100
1
1
x
3
x
3
2
1
0
3
12
0
1
January, November, December
55.
57.
y
69. f sxd 5
y
1
4
1
1
sin px 1 sin 3px 1 sin 5px 1 . . .
p
3
5
2
3
2
2
1
1
−1
x
3
x
1
3
3
2
2
−2
59.
61.
y
APPENDIX E (page E6)
y
2
1.
1
sy9d2 sx9d2
2
51
2
2
x
2
y
y
2
2
3
2
y
x
y
2
1
p
63. a 5 3, b 5 , c 5
2
2
sx9d2 sy9d2
2
51
1y4
1y6
x
2
1
3.
45
x
2
x
2
θ
2
4
θ
45
2
4
x
Ans-4
5.
Answers to Odd-Numbered Exercises
s x9 2 3!2d 2 2 s y9 2 !2 d2 5 1
16
31. Two lines
33. Proof
y
16
3
y
x
2
8
1
y
4
45
4
8
1
2
3
−1
x
4
x
−1
θ
4
7.
APPENDIX F (page F10)
sx9d2 sy9d2
1
51
3
2
9. x9 5 2 sy9d2
1. 11 2 i
9.
y
y
y
x
y
2
45
4
60
2
x
2
11. 22!3
25. 34
x
θ
6
2
4
35.
16
41
1 20
41 i
41.
9
2 1681
13. u 5 458
1
−2 −1
−1
−6
6
y
θ
53.13
2
57. 25i
45.
62
949
1 297
949 i
5
3
51. 2 2 , 2 2
1 !11
±
i
8
8
53.
59. 2375!3i
61. i
Imaginary
axis
1
2
3
4
Real
axis
5
−4 + 4i
4
−2
3
−3
2
−4
−4
1
−5i
−5
x
4
39. 27 2 6i
1
5
43. 2 2 2 2 i
1
49. 22 ± 2 i
23. 210
33. 26i
31. 8
Imaginary
axis
6
2
15. 5 1 i
65. 4!2
4
x
1 45 i
63. 5
y
4
3
5
37.
55. 21 1 6i
sx9d2 x9
11. y9 5
2
6
3
29. 400
40
1681 i
7. 214 1 20i
13. 210
21. 29 1 40i
19. 24
27. 9
47. 1 ± i
2
5. 3 2 3!2i
3. 4
1 76 i
17. 12 1 30i
x
θ
2
1
6
−5 −4 −3 −2 −1
−1
−6
4
1
Real
axis
2
15. u < 26.578
1
67. !85
17. u < 31.728
69. 3!2 cos
4
4
Imaginary
axis
−6
6
−6
6
Imaginary
axis
2
4
6
Real
axis
8
−2
21. Ellipse
23. Hyperbola
25. Parabola
y
1
y
6 − 7i
71. 2 cos
2
−3
3 − 3i
2
3
2
1
73. 4 cos
4p
4p
1 i sin
3
3
2
1
1
2
2
−4
1
−3
−2
Real
axis
−1
3+i
1
3
2
−2
−1
1
−1
2
Imaginary
axis
x
x
1
p
p
1 i sin
6
6
Imaginary
axis
1
1
Real
axis
−2
−8
2
2
3
29. Two parallel lines
3
3
2
−1
−6
27. Two lines
1
−4
−4
−4
19. Parabola
7p
7p
1 i sin
4
4
2
Real
axis
−3
−2 (1 +
3i)
−4
2
Ans-5
Answers to Odd-Numbered Exercises
p
p
1 i sin
2
2
1
75. 6 cos
2
3
Imaginary
axis
Imaginary
axis
8
1
−3
2
2
−2
4
−2
Real
axis
6
−1
Real
axis
1
(c) 1 1 !3i, 2 !3 1 i, 21 2 !3i, !3 2 i
−1
Imaginary
axis
Imaginary
axis
3.75 cos 34π + i sin 34π
(
1
−1
1
1
87. 24 2 4i
2
−4
6
4
2
−6
4
−2
Real
axis
6
−4
−6
−3
−2
Real
axis
−1
−1
85.
89. 232i
10
scos 2008 1 i sin 2008d
9
91. 2128!3 2 128i
95. (a) !5 scos 608 1 i sin 608d
!5 scos 2408 1 i sin 2408d
93. i
p
p
1 i sin
8
8
5p
5p
cos
1 i sin
8
8
9p
9p
cos
1 i sin
8
8
13p
13p
cos
1 i sin
8
8
1 p5 1 i sin p5 2
3p
3p
31cos
1 i sin 2
5
5
103. 3 cos
101. cos
3scos p 1 i sin pd
1 75p 1 i sin 75p2
9p
9p
31cos
1 i sin 2
5
5
3 cos
Imaginary
axis
Imaginary
axis
(b)
Imaginary
axis
1
3 (cos 300° + i sin 300°)
2
p
p
1 i sin
2
2
(b)
2
Real
axis
2
(
−1
83. 12 cos
1 49p 1 i sin 49p2
10p
10p
1 i sin
51cos
9
9 2
16p
16p
1 i sin
51cos
9
9 2
99. (a) 5 cos
215!2 15!2
1
i
81.
8
8
3 3!3
i
79. 2
4
4
−2
Real
axis
−3
2
−2
3
1
4
−4
−1
2(cos 150 ° + i sin 150°)
6i
6
Imaginary
axis
(b)
77. 2 !3 1 i
2
Imaginary
axis
3
4
Real
axis
1
−3
−1
1
3
−2
Real
axis
2
−2
−4
−2
2
4
Real
axis
−3
−4
(c)
!5
2
1
!15
2
i, 2
!5
2
p
p
97. (a) 2 cos 1 i sin
3
3
1
2
2
1
4p
4p
1 i sin
3
3
2
1
11p
11p
1 i sin
6
6
1
2 cos
2
2
5p
5p
2 cos
1 i sin
6
6
2 cos
!15
i
1 p2 1 i sin p2 2
7p
7p
41cos
1 i sin 2
6
6
11p
11p
41cos
1 i sin
6
6 2
105. 4 cos
6 2 scos 1058 1 i sin 1058d
107. !
6 2 scos 2258 1 i sin 2258d
!
6 2 scos 3458 1 i sin 3458d
!
Imaginary
axis
2
Imaginary
axis
2
5
−2
3
2
1
−5
3
−2
−3
−5
5
Real
axis
2
−2
Real
axis