Coburn J.W. Algebra and Trigonometry
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SA30 Student Answer Appendix
73. Since
avg. shifted up 3 units;
avg. amplitude is
“centered” on average value.
75. g(t) has the shortest period;
77.
79. a.
b. c. d.
Exercises 5.6, pp. 582–587
1.
;
3. odd,
;
5. a. use
b. use reciprocals of tan t 7.
0, , 1, , und.
9. 1.6, 0.8, 0.5, 1.4, 0.7, 1.2 11. a. b. c. d.
13. a.
b. c. d. 15. und., , 1, , 0
17. 19. 4.6, 7.8 21.
23.
25. 27.
29. 31.
33. 35.
37. 39.
41. 43. 45.
47. about 137.8 ft
8
,
3
8
y 2 cota
2
3
tby 3 tana
1
2
tb
t
y
2
1
1
2
t
y
1
4
1
4
1
2
1
2
3
t
y
5
3
3
2
t
y
2
4
8
t
y
1
4
8
t
y
1
4
2
4
2
t
y
3
4
5
2
1
3
4
5
2
1
2
2
3
2
3
2
2
2
y
cot xh(t)
t
y
3
4
5
2
1
3
4
5
2
1
2
2
3
2
3
2
2
2
y
2 tan ty
tan t
12
k, k Z
10
k, k Z1.6,
59
24
35
24
,
13
24
,
1
13
13
3
4
5
3
7
6
7
4
131131
13
1
13
cos t
sin t
0.268f1t2P
B
3 7i
2
7 3i1 6i3 4i
distance
200
13
yd 115.5 yd
y
t
1
1
1
2954
1
1477
value 1;
value 3;
m M, 0;
49. asymptotes at using
(3, 5.2), at model gives at ,
model gives answers will vary.
51. Answers will vary; asymptotes at
from pen is
cm long
53. a. cm b. 80 cm; it is a square
c.
getting close to
55.
a. no; b. 1.05
c. Angles will be greater than soft rubber on sandstone
57. a. 5.67 units b.
c.
Yes. Range of is ( ).
d. The closer gets to the longer the line segment gets.
59. m/sec; m/sec;
m/sec. The velocity of the beam is increasing dramatically,
m/sec
61. a. x-intercepts: (0, 0), (3, 0); y-intercept: (0, 0); vertical
asymptotes: horizontal asymptote:
b. x-intercept: ( ; y-intercept: none; vertical asymptotes:
horizontal asymptote:
c. x-intercepts: ( (1, 0); y-intercept: vertical
asymptote:
,
slant asymptote:
63.
Exercises 5.7, pp. 596–600
1.
;
3.
5.
Answers will vary.
7. a. b. c. [1.6, 10.4]
9. a. b. c. [1.75, 2.75]
11.
13.
15. a. b.
c. A.M., 10:30 A.M.
17. a.
b. c. 134 days
t
y
16
20
12
8
4
2 4 6 8 10 12
y 6.4 cosa
6
tb 12.4
1:30
t
y
32
40
24
16
8
5101520
25
y 5 sina
12
tb 34
t
y
16
20
12
8
4
60 120 180 240 300 360
y 8 sina
180
tb 12
t
y
80
100
60
40
20
6121824
30
y 40 sina
15
tb 60
175
A
200, P 3
25
A
50, P 24
0 Bt C 6 2
y A cos1Bt C2 Dy A sin1Bt C2 D
7.37 hr
y x 2x 2
a0,
1
2
b;1, 02,
y 0x 0, x 4;
1, 02
y
3
2
x 2, x 2;
33.9, 3.994S 12,733
33.5, 3.84S 12833, 3.54S 26.132, 34S 7.1
90°,
q, qtan 86.5°
68.2°;
35°
tan
2
2.5
1.5
1
0.5
1002030405060
20
20 cm 62.8
12
130°, 6.9 cm2;
A
11.95 90° 180°k;
P 180°;y 11.95 tan ;
y 3.002;
x 2y 3.002;x 2,
A
5.2;
x 6 12k, k ;y 5.2 tana
12
xb; P 12;
ty
03
5
3
1
32
3
2
2
nP
10 64.984
20 63.354
30 63.063
100 62.853
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Student Answer Appendix SA31
19. a. c.
b. d. about 2 yr.
21.
23. HS: 6 units right; VS: (none); PI:
25. HS: 2 units right; VS: (none); PI:
27. HS: unit right; VS: (none); PI:
29. HS: 2.5 units right;
VS: 15.5 units up; PI:
31. HS: units right; VS: 92 units up; PI:
33. HS: unit left;
VS: 3150 units up; PI:
35. 37.
39. 41.
43.
45.
47. a. b. , moving away
c. , moving toward d. about ,
greater, still gaining speed
49. 51.
53.
55. a. Caracas: , Tokyo:
b. (i) Same # of hours on 79th day & 261st day
(ii) Caracas: , Tokyo:
57. a. Adds 12 hr. The sinusoidal behavior is actually based on hours
more/less than an average of 12 hr of light.
b. Means 12 hr of light and dark on March 20, day 79 (Solstice!).
c. Additional hours of deviation from average. In the north, the planet
is tilted closer toward the Sun or farther from Sun,
depending on date. Variations will be greater!
59. QIII;
61. sum: , difference:
, product: 6, quotient:
2
3
i25
3
2i252
3.7 0.5584
0 365
11
13
158 days81 days
9.9 hr11.4 hr
G
4
: y sin3392 12t24; P 0.00255 sec
D
3
: y sin3146.84 12t24; P 0.0068 sec;
red S D
3
; blue S A#
3
d1t2 15 cosa
5
4
tb
1.76 cm. avg. vel. 3.52 cm/sec4.24 cm
4.24 cmP 4 sec, f
1
4
cycle/sec
A sin1Bt2 A sin312f 2t4
P
2
B
, B
2
P
; f
1
P
, P
1
f
; B
2
1/f
2f.
t
y
0
1
2
3
4
1
2
3
4
4
2
2
3
t
y
80
100
60
40
20
2468
10
y 4 sina
180
t
4
b 7
y 5 sina
50
t
2
b 13y 250 sina
12
tb 350
1
3
t 6
23
3
1
3
A
2500; P 8;
5
2
t 6
29
2
5
2
A
28; P 12;
2.5 t 6 22.5
A
24.5; P 20;
2
3
t 6
26
3
2
3
A
1; P 8;
2 t 6 14
A
1; P 12;
6 t 6 30
A
120; P 24;
P1t2 250 cosc
2
11
1t 2.752d 950; P1t2 250 sina
2
11
tb 950
t
P
1200
1500
900
600
300
2 4 6 8 10 12
max 1200, min 700
P 11 yr
Summary and Concept Review, pp. 601–608
1.
2. 3.
4.
approx. 692.82 yd 5.
6.
7. approx. 4.97 units 8.
9.
10.
11.
12. a. approx. 9.4248 rad/sec
b. approx. 3.9 ft/sec c. about 15.4 sec 13. a.
b.
14. a. b.
15. 16.
17. approx. 5.18 m 18. a. approx. 239.32 m b. approx. 240.68 m apart
19. approx. and
20.
; answers will vary.
21.
22. a.
b.
23. a. ; QIV;
b. ; QIV;
24. a.
b.
or
c. d.
or
25.
, and
26.
27.
and 28.
29.
a. approx. 19.67 rad b. 25 rad
30. 31.
32. 33.
34. 35.
y
t
2
4
2
0
4
1
398
1
199
t
y
1
8
1
8
1
4
1
4
1
2
1
2
A
3, P
1
199
A
2, P
1
2
y
t
1
0
2
1
2
4
3
8
8
2
t
y
2
2
0.5
1
0.5
1
A
1.7, P
2
A
1, P
t
y
2
4
6
8
10
4
6
8
10
2
2
2
3
2
y
t
1
2
3
4
1
2
3
4
2
3
2
2
P 2
A
3, P 2
t 2.44
2
3
3
sec t
4
3
, tan t
17
3
, cot t
3
17
sin t
17
4
, csc t
4
27
cos t
3
4
,
a
113
7
,
6
7
by
6
7
, a
113
7
,
6
7
b, a
113
7
,
6
7
b
207.0° 360°k 27.0° 360°k 76.0° 180°k
330° 360°k 30° 360°k 135° 180°k
cos
5
13
, sec
13
5
, tan
12
5
, cot
5
12
sin
12
13
, csc
13
12
,x 5, y 12, r 13
cos
4
5
, sec
5
4
, tan
3
4
, cot
4
3
sin
3
5
, csc
5
3
,x 4, y 3, r 5
sec
113
2
, tan
3
2
, cot
2
3
sin
3
113
, csc
113
3
, cos
2
113
,
sec
37
12
, tan
35
12
, cot
12
35
sin
35
37
, csc
37
35
, cos
12
37
,
28°, 19°, 30°
207° 360°k35.5°54.5°
cos170°29¿45–2cot 32.6°
A 64.3°A 0.80
4.75 rad, s 38 m
r 41.74 in., A 2003.48 in
2
s 25.5 cm. A 191.25 cm
2
1
2
7
6
120°
10.125 13.5 16.87532°52¿12–147.613
Angles Sides
c 117.93 in.C 90°
b 77.37 in.B 41°
a 89 in.A 49°
Angles Sides
c 29 mC 90°
c 21 mB 46.4°
a 20 mA 43.6°
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SA32 Student Answer Appendix
36. 37. 38.
green, red
39. 40.
41. 42.
43. radians;
44.
3.5860 45.
46.
; asymptotes
47. a. , HS: 3 units right, VS: 520 units up
b.
48. a. , HS: 6 units left, VS: 6.4 units up
b.
49. , HS: 3 units right, VS: 175 units up,
50. , HS: (none), VS: 105 units up,
51. a.
b. August: 1.81 in., Dec: 0.44 in.
Mixed Review, pp. 607–609
1. a. b. c. d.
3. and 5.
7.
9. arc length: ; area: 11.
13.
15.
17. a. HS: (none); b. HS: 1 unit right;
VS: 8 units down; PI: VS: (none); PI:
19. a. rad/sec b. 20162 cm/sec 377 cm/sec6
y
t
1
2
3
4
2
246810
3
1
4
y
t
3
6
9
12
15
6
9
3
12
15
2
3
2
2
1 t 6 50 t 6
A
7
2
; P 4;
A
5; P ;
60°cot
15
8
tan
8
15
,csc
17
8
,
cos
15
17
,sec
17
15
,sin
8
17
,
86.915°
112
3
117.3 units
2
28
3
29.3 units
1212 in.; 6012 84.9 in.
220°48¿50–t
4
3
t
2
3
f142 20P 6D 15A 10
P1t2 0.91 sin a
6
tb 1.35y 75 sin a
16
3
tb 105
A 75, P
3
8
y 125 cosc
12
1t 32d 175
A
125, P 24
y
t
2
4
6
8
22
4
6
8
A
3.2, P 8
t
y
760
280
520
30691215
A
240, P 12
x 6, x 6y 5.2 tana
12
xb; period 12; A 5.2
151.14 mkZ1.55 k
t
y
2
1
3
4
5
2
3
1
4
5
0.5
0.5 1
1
t
y
6
12
6
12
2
2
2
3
;
2
3
tana
7
4
b1; cota
3
b
1
13
y 4 csc13t2y 0.75 sin16t2
c. : NA; ; HS: none; d. : NA; ; HS: to the
VS: none; PI: ( ) right; VS: none; PI: ( )
Practice Test, pp. 609–610
1. complement: ; supplement:
2. a. b. c.
d.
3. 4. a.
b.
5.
a. 430 mi b.
6.
7.
8.
9. a. or 225 ft 9.6 in. b.
c.
10.
11. about 67 cm,
12.
57.9 m 13. a. b. c.
14. a.
b. 433,000 gal; 249,000 gal
15. a.
y
t
1
2
1
246810
2
P 10,
A
2;
D: t R, R: y 32, 24,
W1t2 18.4 sina
12
tb 34.1
3
4
11
6
7
6
49.6°
11.29 ft/sec 7.7 mph
23
480
0.1505 rad/sec
225.8 ft
sec t 3, csc t
312
4
, cot t
12
4
a
1
3
b
2
a
212
3
b
2
1
9
8
9
1; cos t
1
3
, sin t
212
3
, tan t 212,
cot
2
121
csc
5
121
,
tan
121
2
,sin
121
5
,sec
5
2
,
21513 372 mi
48°12¿45–100.755°
30° 360°k; k Z
3
6
30°45°145°
55°
x
y
4
2
6
4
6
8
2
10
1234
1
2
4
3
556
6
x
y
4
2
6
8
10
4
6
2
8
10
2468
2
4
6
810
10
, 2, 2
2
P 2
A
P 4
A
t sin t cos t tan t csc t sec t cot t
0
13
6
5
3
5
4
7
6
2
3
0 1 0 undefined 1 undefined
11
2
2 13
213
3
13
3
13
2
1
2
13
3
213
3
13
1
2
13
2
1212
12
2
12
2
13
213
3
2
13
3
13
2
1
2
13
3
2
213
3
13
1
2
13
2
Angles Sides
c 15.0 cmC 90°
b 12.6 cmB 57°
a 8.2 cmA 33°
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Student Answer Appendix SA33
b. for
c. for
16. HS: units right, VS: 19 units up
PI:
17.
18. a.
b.
19. 20. a. b.
Strengthening Core Skills, pp. 612–613
Exercise 1:
t 0
01
10
01—
0
01
13
3
13
3
113
12
2
13
2
1
13
2
12
2
1
2
12
2
1
2
1
2
12
2
13
2
5
4
7
6
5
6
3
4
2
3
13
13
3
tan t
y
x
1
2
12
2
13
2
cos t x
13
2
12
2
1
2
sin t y
2
3
4
6
t 2.3
t 4
y 7.5 sina
6
t
2
b 12.5
y
t
2
4
2
4
2
3
2
2
D: t 2k, k Z; R: y R, P 2,
y
t
4
8
4
8
2
3
2
2
D: t
4
12k 12, k Z; R: y R; P
2
;
1260°
t
y
32
24
16
8
6
2
3
2
3
5
3
7
7
12
,
31
4
,
12
t 6
3
4
12
A
12, P
2
3
,
y
t
4
8
4
8
3
5
3
4
3
2
3
2
k Z, R: y R, P
3
D: t
6
12k 12
y
t
1
2
3
1
2
3
2
2
3
2
R: y 1q, 14 ´ 31, q2, P 2
k Z,D: t
2
12k 12
Exercise 2:
a. b. c. d.
Exercise 3:
a. no solution b.
c. ,
d. ,
Cumulative Review Chapters 1–5, pp. 613–614
1.
3.
5.
7. a.
b.
9. a. max: ( , 4), endpoint max: (4, 0)
min: (2, ), endpoint min: ( , 0)
b.
c.
d. function is odd:
11. 13.
15. , QII;
17. 19.
21. 23.
,
y-intercept (0, )
25. about 6.85%
2m
3
4
,y
3
4
x 2
x
y
54321
5
4
3
2
1
1
2
3
4
5
2
3
4
5
1
f
1
(x)
f(x)
y
3
2
sina4t
2
b
1
2
S 18 m; A 135 m
2
102.7°cot
9
40
,
csc
41
40
,sec
41
9
,tan
40
9
,sin
40
41
,cos
9
41
,
x 9, y 40, r 41
x
y
5
(0, 1)
5
5
5
y 2
x 1
114.3 ft
f 1x2f 1x2
f 1x2T: x 12, 22
f 1x2c: x 14, 22 ´ 12, 42
f 1x26 0: x 10, 42
f 1x2 0: x 34, 04 ´ 546
44
2
D: x 1q, 72 ´ 17, 72 ´ 17, q2, R: y 1q, q2
D: x c
3
2
, qb, R: y 30, q2
cot t
3
17
317
7
csc t
4
17
417
7
,
sec t
4
3
,tan t
17
3
,sin t
17
4
,cos t
3
4
,
hyp 89; 64°; 90 26°
89
80
39
5 6 x 6 3
t 4.3009t 1.9823
t 2.8966t 6.0382t 5.0522t 1.2310,
t
4
,
7
4
t
6
,
7
6
t
4
,
7
4
t
4
3
,
5
3
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SA34 Student Answer Appendix
CHAPTER 6
Exercises 6.1, pp. 620–623
1. . 3. one, false 5. Answers will vary.
7. Answers may vary;
9.
11.
13.
15.
17.
19.
21.
23.
25.
27.
29.
31.
33.
35.
37.
39.
41. 43. 45.
47.
49.
51.
53.
csc
13
7
, cot
2130
7
cos
1120
13
2130
13
, tan
7
2130
, sec
13
2130
,
sec
2x
2
25
x
, csc
2x
2
25
5
cos
x
2x
2
25
, sin
5
2x
2
25
, tan
5
x
,
cos
8
17
, sin
15
17
, sec
17
8
, csc
17
15
, cot
8
15
sin
21
29
, tan
21
20
, sec
29
20
, csc
29
21
, cot
20
21
21 sin
2
x
sin x
B
1
cot
2
x
1
sin x
21 sin
2
x
sec x
sin x
csc x
sec x
sec
2
x sin x csc x
sin x sec x
sec
2
x 1
sin x
1
cos x
tan
2
x
tan x
tan x
tan x
csc x
sin x
cos x
tan x cos xsin x csc x
csc x cos x
sin x
cos x
cos x1
1
sin x
cos x
sin x1
cot x
cos
2
x
sin x
sin x
1
cos
2
x sin
2
x
sin x
1
sin x
csc x
1csc x cot x21csc x cot x2
tan x
csc
2
x cot
2
x
tan x
1
tan x
cot x
11 sin x231 sin1x24 11 sin x211 sin x2 1 sin
2
x cos
2
x
1
cos x
2 sin x cos x
cos x
sec x 2 sin x
sin
2
x cos
2
x 2 sin x cos x
cos x
1 2 sin x cos x
cos x
1sin x cos x2
2
cos x
sin
2
x 2 sin x cos x cos
2
x
cos x
sin x
sin x/cos x
sin x cos x
sin x
cos x
sin x tan x sin x
tan x tan
2
x
sinx 1tan x 12
tan x11 tan x2
sin x
tan x
1 sin x
cos x cos x sin x
11211 sin x2
1cos x211 sin x2
1
cos x
sec x
sin x cos x sin x
cos x cos
2
x
sin x 1cos x 12
cos x 11 cos x2
tan x;
sin x
cos x
tan x
tan
2
x csc
2
x tan
2
x tan
2
x 1csc
2
x121; tan
2
x 1cot
2
x21
sin x
cos x
1
sin x
sin x
cos x
cos x
sin x
1
cos x
1 sec x 1
tan x1csc x cot x2 tan x csc x tan x cot x
sin x1csc x sin x2 1 sin
2
x cos
2
x
cos x
1
cos x
cos
2
x 1 cos
2
x sin
2
x
cosx 1sec x cos x2 cos x sec x cos
2
x
sec
2
x cot
2
x
1
cos
2
x
cos
2
x
sin
2
x
1
sin
2
x
csc
2
x
sin x cot x sin x
cos x
sin x
cos x
1 1sec x tan x21sec x tan x2; tan x 2sec
2
x 1
1 sec
2
x tan
2
x; tan
2
x sec
2
x 1;
tan x
sec x
csc x
;
sin x
cos x
sec x
csc x
;
1
cot x
sec x
csc x
;
1
cot x
sin x
cos x
1 sin
2
x
sin x sec x
;sin ; sec ; cos
55.
57. Answers will vary.
59. Answers will vary. 61. Answers will vary.
63. a. b.
c.
65.
67.
69.
71.
73. a. b.
c. 75. 77.
79. 81. about 1148 ft
83.
Exercises 6.2, pp. 627–630
1. substituted 3. complicated; simplify; build
5. Because we don’t know if the equation is true. 7.
9. 11.
13.
15.
17.
cos x
tan x
cos x
sin x
cos x
cos
2
x
sin x
1 sin
2
x
sin x
1
sin x
sin x csc x sin x
sec x csc x
1
cos x
1
sin x
1
cos x sin x
sin
2
x cos
2
x
cos x sin x
sin x
cos x
cos x
sin x
tan x cot x
1 cos
2
x
sin
2
x
cos
2
x
sin
2
x
cos
2
x
cos
2
x tan
2
x
1 cos x
sin x
cos x
1 sin x
cos x
y = 2 sin(2t)
2
3
2
2
y
t
2
1
2
1
0,
3
,
2
,
2
3
, ,
3
2
45°tan
1 m
1
m
2
m
2
m
1
A 51.45 m
2
A 4
#
4
2
tana
4
b 64 m
2
A nr
2
tana
n
b
11211 sin x211 sin x2
2
11sin x211 sin x211211 sin x2
11sin x211sin x21sin x12
11 sin
2
x21sin x 12
cos
2
x sin x cos
2
x 1cos
2
x21sin x 12
1sec x 421sec x 121sec x 12
1sec x 421sec
2
12 1sec x 421tan
2
x2
tan
2
x sec x 4 tan
2
x 1tan
2
x21sec x 42
tan x tan
3
x 1tan x211 tan
2
x2 1tan x21sec
2
x2
cos
3
x 1cos x21cos
2
x2 1cos x211 sin
2
x2
A 119.62 in
2
A
4
18 m2
2
4
cota
4
b 64 m
2
#
1 64 m
2
A
nx
2
4
cota
n
b
csc
9
412
, cot
7
412
sin
412
9
, cos
7
9
, tan
412
7
,
cob19529_saa_SA34-SA48.qxd 1/16/09 18:15 Page SA34 User-S178 MAC-OSX_1:broker:MH-DUBUQUE:MHDQ092:MHDQ092-SAA:MHDQ092-SAA:
Student Answer Appendix SA35
19.
21.
23.
25.
27.
29.
tan
2
x
sin
2
x
cos
2
x
1
cos
2
x
1
sin
2
x
sec
2
x
csc
2
x
sec
2
x
1 cot
2
x
2 sec x
2
cos x
2
1
sin x
cos x
sin x
2 csc x
cot x
2 cot x csc x
cot
2
x
cot x
cot x csc x cot x cot x csc x
1 csc
2
x
cot x11 csc x2 cot x 11 csc x2
11 csc x211 csc x2
cot x
1 csc x
cot x
1 csc x
2 tan
2
x
2 sin
2
x
cos
2
x
sin x
sin
2
x sin x sin
2
x
1 sin
2
x
sin x11 sin x2 sin x 11 sin x2
11 sin x211 sin x2
sin x
1 sin x
sin x
1 sin x
cot
2
x sin
2
x
cot x
csc
2
x 1 sin
2
x
cot x
csc
2
x 11 sin
2
x2
cos x
1
sin x
csc
2
x cos
2
x
cos x csc x
csc x
cos x
cos x
csc x
cos x
1 sin x
cos
2
x
cos x11 sin x2
1 sin
2
x
cos x 11 sin x2
11 sin x211 sin x2
cos x11 sin x2
1 sin x
cos x
cos
1 sin
cos
2
cos 11 sin 2
1 sin
2
cos 11 sin 2
11 sin 211 sin 2
cos 11 sin 2
1 sin
cos
1
cos
sin
cos
sec tan
31.
33.
35.
37.
39.
41.
43.
cos x sin x
1 tan x
1cos x sin x2
1cos x sin x2
1cos x sin x211 tan x2
1cos x sin x21cos x sin x2
cos x11 tan x211 tan x2
1cos x sin x21cos x sin x2
cos x11 tan
2
x2
1cos x sin x21cos x sin x2
cos xa1
sin
2
x
cos
2
x
b
1cos x sin x21cos x sin x2
cos x sin x sin x
sin
2
x
cos x
1cos x sin x2
11 tan x2
1cos x sin x2
1cos x sin x2
cos x sin x
1 tan x
1tan x sec x2
2
1sec x tan x2
2
sec
2
x 2 tan x sec x tan
2
x
1
cos
2
x
2
sin x
cos x
1
cos x
sin
2
x
cos
2
x
1 2 sin x sin
2
x
cos
2
x
1 2 sin x sin
2
x
1 sin
2
x
11 sin x2
11 sin x2
11 sin x2
11 sin x2
1 sin x
1 sin x
tan x sec x
sin x
cos x
1
cos x
sin x
cos
2
x
sin x
1 sin
2
x
1
1csc x sin x2
sin x
sin x
1
csc x sin x
cos
2
x
sin
2
x 1
sin x
csc x
csc x
csc x
sin x csc x
csc x
sin x
sin x
1
sin x
cos
2
x sin
2
x
1
cos x
1sin x21cos x2
a
cos x
sin x
sin x
cos x
b1sin x21cos x2
sec x
cot x tan x
csc x
1
sin x
cos
2
x sin
2
x
sin x
cos
2
x
sin x
sin x
cos x
cos x
sin x
sin xcos x cot x sin x
sin
2
x
cos
2
x 1
sin
2
x
cos
2
x
sin
2
x
sin
2
x
1
sin
2
x
sin
2
x cot
2
x sin
2
x csc
2
xsin
2
x1cot
2
x csc
2
x2
cob19529_saa_SA01-SA68.qxd 1/5/09 13:20 Page SA35 User-S178 MAC-OSX_1:Users:user-s178:Desktop:
SA36 Student Answer Appendix
45.
47.
49.
51.
53.
55.
57.
59. a.
800 40x1cos sin 2 x
2
800 40x1cos sin 2 x
2
1cos
2
sin
2
2
400 40x cos x
2
cos
2
400 40 x sin x
2
sin
2
d
2
120 x cos 2
2
120 x sin 2
2
sin x cos x
1 sin x cos x
1121sin x cos x2
1sin x cos x2
1sin x cos x21sin
2
x cos
2
x sin x cos x2
1sin
2
x cos
2
x21sin
2
x cos
2
x2
1sin x cos x21sin
2
x sin x cos x cos
2
x2
sin
4
x cos
4
x
sin
3
x cos
3
x
sec x cos x
sin x
sec x1cos
2
x sin
2
x2 112cos x
sin x112
cos
2
x sec x sin
2
x sec x csc x sin x cos x
sin x cos x sec x
cos x
sin x
sin x
cos x
csc x
sec x
1sin x 12
2
cos
2
x
11 sin x2
2
cos
2
x
1 2 sin x sin
2
x
cos
2
x
1
cos
2
x
2 sin x
cos
2
x
sin
2
x
cos
2
x
sec
2
x 2 sec x tan x tan
2
x1sec x tan x2
2
2 sec
2
x
1 sec
2
x 1
1 1sec
2
x 12
1 tan
2
x
cos
2
x
cos
2
x
sin
2
x
cos
2
x
1cos
2
x sin
2
x2112
cos
2
x
1cos
2
x sin
2
x21cos
2
x sin
2
x2
cos
2
x
cos
4
x sin
4
x
cos
2
x
1
sec
2
x tan
2
x
1sec
2
x tan
2
x21sec
2
x tan
2
x2
1sec
2
x tan
2
x2
sec
4
x tan
4
x
sec
2
x tan
2
x
1 sin
2
x
cos
2
x
1
cos
2
x
cos
2
x sin
2
x
cos x
sin x
cos x
sin x
sin x
cos x
1cos x21sin x2
1cos x21sin x2
cot x
cot x tan x
csc x sec x
sec x csc x
1
cos x
1
sin x
1
cos x sin x
sin
2
x cos
2
x
cos x sin x
sin x
cos x
cos x
sin x
tan x cot x
1tan x cot x21tan x cot x2
1tan x cot x2
tan
2
x cot
2
x
tan x cot x
b.
61. a.
b.
63.
65. 67. Answers will vary.
69.
71.
73.
Exercises 6.3, pp. 635–639
1. false; QII 3. repeat; opposite 5. Answers will vary.
7. 9.
11. a.
b.
13. 15. 17. 19. 21.
23. 25. sin(8x) 27. 29. 1 31.
33. a. b. 35. 37.
39. 41.
43. a.
b.
45. 47. a. b. c.
49. a. b. c.
51. a. b. c.
53. a. b. c.
55.
sin
0 112sin
sin1 2 sin cos cos sin
247
96
96
265
247
265
190° 2 190° 2 180°
12 513
1213 5
1213
5
26
12 513
26
3416
2937
1767
4505
3416
4505
319
360
480
481
319
481
12 16
4
16
12
4
12
4
16
4
a
12
2
ba
1
2
b a
12
2
ba
13
2
b
sin1135° 120°2 sin 135° cos 120° cos 135° sin 120°
sin145° 30°2 sin 45° cos 30° cos 45° sin 30°
16
12
4
13
1
13
13
3
16
12
4
16 12
4
304
297
304
425
13
tan132cosa
3
b
cota
12
bsin 33°
16
65
13
2
cos152
22 26
4
26 22
4
cos1120° 45°2 cos 120° cos 45° sin 120° sin 45°
cos145° 30°2 cos 45° cos 30° sin 45° sin 30°
26
22
4
12
16
4
12 16
4
x
y
654321
4
3
2
11
1
2
3
4
3
4
5
6
2
1
sin t
3
4
, cos t
17
4
, tan t
3
17
1sin
2
x cos
2
x2
2
112
2
1
sin cos
D 40.5 ft
D
2
400 40x cos x
2
h 3.76; yes
h 1csc x sec x
csc x sec x;
1
sin x cos x
cos
2
x sin
2
x
sin x cos x
cot x tan x
cos x
sin x
sin x
cos x
h 3.76
h 1cot x tan x;
42.2 ft
cob19529_saa_SA01-SA68.qxd 1/5/09 13:20 Page SA36 User-S178 MAC-OSX_1:Users:user-s178:Desktop:
Student Answer Appendix SA37
57.
59.
61.
63.
65.
67.
69.
71.
73.
75. verified using sum identity for sine
77.
79. 81.
1
2
12
2
sin x1cos h 12 cos x sin h
h
sin x
cos h 1
h
cos x
sin h
h
sin x cos h cos x sin h sin x
h
sin x cos h sin x cos x sin h
h
f 1x h2 f 1x2
h
sin1x h2 sin x
h
tan
2
sin
2
cos
2
sin 10 sin 2
cos 1cos 02
A
B
sin 1cos 90° cos sin 90° sin 2
cos 1sin 90° cos cos 90° sin 2
A
B
sin cos190° 2
cos sin190° 2
1
C1tan s tan t2
1
Ca
sin s cos t
cos s cos t
cos s sin t
cos s cos t
b
cos s cos t
1
cos s cos t
C1sin s cos t cos s sin t2
1
cos s cos t
cos s cos t
C1sin s cos t cos s sin t2
R
cos s cos t
C sin1s t2
F
Wk
c
1 13
1 13
12
2
1cos x sin x2
cos xa
12
2
b sin xa
12
2
b
cosax
4
b cos x cosa
4
b sin x sina
4
b
4 sin
3
t 3 sin t
3 sin t 3 sin
3
t sin
3
t
3 sin t11 sin
2
t2 sin
3
t
3 sin t cos
2
t sin
3
t
2 sin t cos
2
t sin t cos
2
t sin
3
t
2 sin t cos t cos t 1cos
2
t sin
2
t2 sin t
sin12t2 cos t cos12t2 sin t
sin12t t2sin13t2
cos
2
t sin
2
t
cos t cos t sin t sin t
cos1t t2cos12t2
2 cos cos
cos cos sin sin
cos cos sin sin
cos1 2 cos1 2
tanax
4
b
tan x tana
4
b
1 tan x tana
4
b
tan x 1
1 tan x
1 tan x
1 tan x
cos xa
12
2
b sin xa
12
2
b
12
2
1cos x sin x2
cosax
4
b cos x cosa
4
b sin x sina
4
b
83. so and
so
85. 87. about 19.3 ft
Exercises 6.4, pp. 648–652
1. sum; 3. 2x; x 5. Answers will vary
7.
9.
11.
13.
15.
17.
19.
21.
23. 25. 27. 1 29. 4.5 sin(6x) 31.
33.
35.
37.
39.
41.
43.
45. 47. 49.
51. 53. tan x
55.
57.
59.
61. sin a
2
b
1
1226
, cos a
2
b
15
1226
, tan a
2
b
1
15
sin a
2
b
7
174
, cos a
2
b
5
174
, tan a
2
b
7
5
sin a
2
b
3
110
, cos a
2
b
1
110
, tan a
2
b 3
sin a
2
b
3
113
, cos a
2
b
2
113
, tan a
2
b
3
2
tan 2
cos 15°
1
2 12
13
2
1
2 12
12
2
sin
12
12
2
, cos
12
12
2
, tan 12 1
tan 12 1cos
12
12
2
,sin
12
12
2
,
tan 2 13cos
12
13
2
,sin
12
13
2
,
tan 12 1cos
12
12
2
,sin
12
12
2
,
5
8
7
8
cos12x2
3
8
cos14x2
1
8
cos12x2cos14x2
9
8
3
2
cos12x2
3
8
cos14x2
1
8
1
8
cos14x2
12
2
1
4
3 sin 4 sin
3
2 sin 2 sin
3
sin 2 sin
3
2 sin 11 sin
2
2 sin 2 sin
3
2 sin cos
2
sin 2 sin
3
12 sin cos 2cos 11 2 sin
2
2sin
sin122cos cos122sin
sin12 2sin132
tan
21
20
cos
20
29
,sin
21
29
,
tan
4
3
cos
3
5
,sin
4
5
,
tan122
24
7
cos122
7
25
,sin122
24
25
,
tan122
5280
721
cos122
721
5329
,sin122
5280
5329
,
tan122
2184
6887
cos122
6887
7225
,sin122
2184
7225
,
tan122
720
1519
cos122
1519
1681
,sin122
720
1681
,
tan122
120
119
cos122
119
169
,sin122
120
169
,
P 16
cos cos sin sin cos1 2
2 cos cos 2 sin sin
2
2 cos1 2
2
2 2 cos cos 2 sin sin 2 2 cos1 2
D
2
d
2
2 2 cos1 2
sin
2
1 2 cos
2
1 2 2 cos1 2 1
d
2
sin
2
1 2 3cos1 2 14
2
2 2 cos cos 2 sin sin
2 sin sin sin
2
cos
2
2 cos cos cos
2
sin
2
D
2
1cos cos 2
2
1sin sin 2
2
D
2
d
2
,D d,
cob19529_saa_SA01-SA68.qxd 1/5/09 13:20 Page SA37 User-S178 MAC-OSX_1:Users:user-s178:Desktop:
SA38 Student Answer Appendix
63.
65. 67.
69. 71. 73.
75. 77.
79. 81.
83.
85.
87.
89.
91.
93.
95.
97.
99.
cot 120t2
cos120t2
sin120t2
2 sin1100t2
cos120t2
2 sin1100t2sin 120t2
sin1120t2 sin 180t2
cos 1120t2 cos 180t2
1 sin
2
122
cos
2
122
3cos 1224
2
11 2 sin
2
2
2
1 4 sin
2
4 sin
4
cos x
cos a2
#
x
2
bcos
2
a
x
2
b sin
2
a
x
2
b
tan x cot x
sin x
cos x
cos x
sin x
sin
2
x
sin x cos x
cos
2
x
sin x cos x
sin
2
x cos
2
x
sin x cos x
1
sin x cos x
2
2 sin x cos x
2
sin 12x2
2 csc 12x2
2
cot tan
2
1
tan
tan
12 tan 2
1
tan
11 tan
2
2
1
tan
2 tan
1 tan
2
tan 122
cot
2
1
cos
2
sin
2
sin
2
sin
2
cos
2
sin
2
sin
2
cos 122
sin
2
cos
2
142 sin
2
142
cos12
#
42cos182
1 sin12x2
1 2 sin x cos x
sin
2
x cos
2
x 2 sin x cos x
sin
2
x 2 sin x cos x cos
2
x1sin x cos x2
2
tan12x2
sin12x2
cos12x2
2 sin x cos x
cos
2
x sin
2
x
12
2
2 cos a
2061
2
tb cosa
357
2
tb
2 sin x sin a
x
6
b2 sin a
55
2
kbcos a
27
2
kb
1
4
1 13
2
cos11540t2 cos12418t2
cos12t2 cos15t2
1
2
3cos1122 cos1424
sin a
2
b
5
129
, cos a
2
b
2
129
, tan a
2
b
5
2
101.
103.
105.
107. a.
b. c.
109. a. b.
111. the * key
113.
115. a.
b.
c.
d.
117. a.
b.
119. Must be a unit circle with in radians. Must use a right triangle
definition of tangent:
121. x 1; x 2; x 16
; x 16
tangent a
2
b
opposite side
adjacent side
sin
1 cos
.
2 13
4
2 13
4
2 13
4
8 413
16
2 13
4
6 2112 2
16
a
12
13
2
b
2
a
16
12
4
b
2
0.9659; 0.9659
1 cos122 1 cos122
1 cos122
1 1cos
2
sin
2
21 sin
2
cos
2
1 cos122
1 1cos
2
sin
2
2
1 cos
2
sin
2
sin
2
sin
2
2 sin
2
1 cos 122
0 cos 122 1
sin 122cos 90° cos 122sin 90° 1
sin12 90°2 1
A
18
c
1 cos
a
t
30
bd
R
36
1 cosa
t
30
b
2
6
R
1 cosa
t
30
b
2
†
6
°
Q
1 cosa
t
30
b
2
¢†
`6 sin a
1
2
#
t
30
b`
d1t2 `6 sina
t
60
b`
cos32112092t4 cos3219412t4;
288 14412 ft 84.3 ft288 14412 ft 84.3 ft
60°M 2.6M
2
22 12
,
M 3.9M
2
22 13
,
1
2
3cos 1 2 cos 1 24 sin sin
tan 122
2 tan
1 tan
2
tan tan
1 tan tan
tan1 2 tan 1 2
2 sin cos
sin cos sin cos
sin cos cos sin
sin122 sin 1 2
2 11 cos 2 4 a
1 cos
2
b 4 sin
2
a
2
b c2 sina
2
bd
2
sin
2
cos
2
1 2 cos 1 1 2 cos 2 2 cos
sin
2
11 cos 2
2
sin
2
1 2 cos cos
2
cob19529_saa_SA01-SA68.qxd 1/5/09 13:20 Page SA38 User-S178 MAC-OSX_1:Users:user-s178:Desktop:
Student Answer Appendix SA39
123.
Mid-Chapter Check, pp. 652–653
1.
2.
3.
4.
5. a.
b.
6. a.
cos
2
x
1 sin
2
x
1
sin
2
x
cos
2
x
1
cos
2
x
sec
2
x
sec
2
x
tan
2
x
sec
2
x
sec
2
x tan
2
x
sec
2
x
0
sin x
sin x
cos x
sin x
cos x
sin x
asin x
sin x
cos x
b a
sin x
cos x
sin xb
1
1
cos x
1
sin x
1 cos x
cos x
sin x
1 sec x
csc x
1 cos x
cot x
1 sin x cos x
1sin
2
x cos
2
x sin x cos x2
1sin x cos x2
1sin
2
x sin x cos x cos
2
x2
1sin x cos x2
sin
3
x cos
3
x
sin x cos x
2 0 False
1 1 0
1 1
2
0
2
1 sec
2
0 tan
2
0
1 sec
2
x tan
2
x
cos x sin x
1
sec x csc x
2112 1
sec x csc x
2 sin x csc x cos x sec x
sec x csc x
2 sin x
sec x
cos x
csc x
cos
2
x cot
2
x
cos
2
x1cot
2
x2
cos
2
x11 csc
2
x2
cos
2
xa1
1
sin
2
x
b
cos
2
x
cos
2
x
sin
2
x
cos
2
x cot
2
x
cos
2
x
1 sin
2
x
sin x
1
sin x
sin
2
x
sin x csc x sin
2
xsin x3csc x sin x4
256
256
3969
256
4225
256
1
3969
256
4225
256
1 a
63
16
b
2
a
65
16
b
2
tan
63
16
; sec
65
16
a
16
65
b
2
a
63
65
b
2
256
4224
3969
4225
4225
4225
1,
b.
7. a. b. c.
8.
9.
10.
Reinforcing Basic Concepts, pp. 653–654
1.
✓
✓
2.
Exercises 6.5, pp. 665–670
1. horizontal; line; one; one 3.
;
5.
7. 0; ; ; 9. 11. 13. 1.0956,
15. 0.3876, 17. 19. 21. 23. 0.8205
25. 0; 27. 29. 31. 1.4352;
33. 0.7297; 35. 37. 0.5560 39. 41.
43. 0; 45. 47. 49.
51. 53. 55. 57. 59.
61. cannot evaluate
63. , not in domain of .
65.
67. sin
2x
2
36
x
, cos
6
x
, tan
2x
2
36
6
sin
3
5
, cos
4
5
, tan
3
4
sin
1
xcsc
4
12
7 1
tan a
2
b
30°12
13
3
6
0.9441, 54.1°
1.1170, 64.0°
3
6
13; 30°; 13;
3
3
4
12
2
4
41.8°
82.2°
3
13
2
; 120°;
45°
3
12
2
22.2°
62.8°
2
4
2
6
1
2
cos
1
1
1
5
2c
2
,
2
d31, 14
1 2 sin
2
11 sin
2
2 sin
2
cos
2
sin
2
2 cos
2
1
cos
2
11 cos
2
2
cos
2
sin
2
cos 1 2 cos cos sin sin cos 1 2
tan
2
x 1 sec
2
x
sin
2
x
cos
2
x
cos
2
x
cos
2
x
1
cos
2
x
sin
2
x cos
2
x 1
1 cot
2
x csc
2
x
sin
2
x
sin
2
x
cos
2
x
sin
2
x
1
sin
2
x
sin
2
x cos
2
x 1
sin 122
336
625
, cos 122
527
625
, tan 122
336
527
sin a
2
b
4
117
, cos a
2
b
1
117
sin A
7 2413
50
, cos A
24 713
50
, tan A
7 2413
24 713
456
5767
3193
5785
456
5785
cos
2
x sin
2
x
cos
2
x sin x
sin x
sin
2
x cos x
cos x
cos x
sin x
1
sin x
#
1
cos x
sin x
cos x
1
sin x
#
1
cos x
cot x
csc x sec x
tan x
csc x sec x
cot x tan x
csc x sec x
cob19529_saa_SA01-SA68.qxd 1/5/09 13:20 Page SA39 User-S178 MAC-OSX_1:Users:user-s178:Desktop: