Precalculus: An Investigation of Functions by David Lippman and Melonie Rasmussen - HTML preview
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7. ( x − )2 +( y − )2
5
8 =1 3
9.
11. (0, 3+ 5) and (0, 3− 5)
13. (1.3416407865, 7.683281573)
15. (-1.07335, 2.8533)
17. 29.87 miles
Section 5.2
70°
30°
-135°
300°
1.
3. π
5. 150°
7. 325°
π
π
9. 54°
11. 8
13.
9
2
15. 35 miles
17. 8π cm
19. 5.7596 miles
21. 28.6479°
23. 14.1372 cm2
25. 3960 rad/min 630.254 RPM
27. 2.094 in/sec, π/12 rad/sec, 2.5 RPM
29. 75,398.22 mm/min = 1.257 m/sec
31. Angular speed: π/12 rad/hr. Linear speed: 1036.73 miles/hr
540
Section 5.3
1. a. III b. II
3. 4
−
5
5. 4 3
−
7.
55
−
7
8
9.
a. reference: 45°. Quadrant III.
( °)
2
sin 225 = −
.
( °)
2
cos 225 = −
2
2
b. reference: 60°. Quadrant IV.
( °)
3
sin 300 = −
.
( °) 1
cos 300 =
2
2
c. reference: 45°. Quadrant II.
( °)
2
sin 135 =
.
( °)
2
cos 135 = −
2
2
d. reference: 30°. Quadrant III.
( °)
1
sin 210 = − .
( °)
3
cos 210 = −
2
2
π
π
π
11. a. reference: . Quadrant III.
5
2
sin
= −
.
5
2
cos
= −
4
4
2
4
2
π
π
π
b. reference: . Quadrant III.
7
1
sin
= − .
7
3
cos
= −
6
6
2
6
2
π
π
π
c. reference: . Quadrant IV.
5
3
sin
= −
.
5 1
cos
=
3
3
2
3 2
π
π
π
d. reference: . Quadrant II.
3
2
sin
=
.
3
2
cos
= −
4
4
2
4
2
π
π
13. a.
3
2
sin −
= −
3
2
cos −
= −
4
2
4
2
π
π
b.
23
1
sin
= −
23
3
cos
=
6
2
6
2
π
π
c. sin
−
=
1
−
cos −
=
0
2
2
d. sin (5π ) = 0 cos(5π ) = 1
−
π
π
15. a. 2
b. 100°
c. 40°
d. 5
e. 235°
3
3
π
π
17. a. 5
b. 280°
c. 220°
d. 2
e. 55°
3
3
19. (-11.491, -9.642)
541
Section 5.4
1. sec(θ ) = 2 , csc(θ ) = 2 , tan (θ ) =1, cot (θ ) =1
3.
(θ )
2 3
sec
= −
, csc(θ ) = 2,
(θ )
3
tan
= −
, cot (θ ) = − 3
3
3
5. sec(θ ) = 2
− ,
(θ ) 2 3
csc
=
, tan (θ ) = − 3 ,
(θ )
3
cot
= −
3
3
7. a. sec(135°) = − 2 b. csc(210°) = 2
− c. tan (60°) = 3 . d. cot (225°) =1
9.
(θ )
7
cos
= −
,
(θ )
4 7
sec
= −
,
(θ ) 4
csc
= ,
(θ )
3 7
tan
= −
,
(θ )
7
cot
= −
4
7
3
7
3
11.
(θ )
2 2
sin
= −
, csc(θ )
3 2
= −
, se (
c θ ) = 3
− , tan (θ ) = 2 2 ,
(θ )
2
cot
=
3
4
4
13.
(θ ) 12
sin
=
,
(θ ) 5
cos
=
,
(θ ) 13
sec
=
,
(θ ) 13
csc
=
,
(θ ) 5
cot
=
13
13
5
12
12
15. a. sin(0.15) = 0.1494 cos(0.15) = 0.9888 tan(0.15) = 0.1511
b. sin(4) = -0.7568
cos(4) = -0.6536
tan(4) = 1.1578
c. sin(70°) = 0.9397
cos(70°) = 0.3420 tan(70°) = 2.7475
d. sin(283°) = -0.9744
cos(283°) = 0.2250 tan(283°) = -4.3315
17. sec( t)
19. tan( t)
21. tan( t)
23. cot( t)
25. (
t )2
sec( )
Section 5.5
sin( A) 5 41
=
,cos( A) 4 41
=
,
( A) 5
tan
=
1.
41
41
4
( A)
41
sec
=
,
( A)
41
csc
=
,
( A) 4
cot
=
5
4
5
3. c =14, b = 7 3, B = 60°
5. a = 5.3171, c =11.3257, A = 28°
7. a = 9.0631, b = 4.2262, B = 25°
9. 32.4987 ft
11. 836.2698 ft
13. 460.4069 ft
15. 660.35 feet
17. 28.025 ft
19. 143.0427
21. 86.6685
542
Chapter 6
Section 6.1
1.
2.
3.
4.
5. Amp: 3. Period= 2. Midline: y= -4. f ( t) = 3sin (π t) − 4
π
6. Amp: 2. Period= 4. Midline: y= -3. f ( t) 2sin
t
=
−
3
2
7. Amp: 2. Period= 4π. Midline: y= 1. f ( t)
1
2cos
t
=
+
1
2
8. Amp: 3. Period= π. Midline: y= -1. f ( t) = 3cos(2 t) −1
π
9. Amp: 2. Period= 5. Midline: y= 3. f ( t)
2
2cos
t
= −
+
3
5
π
10. Amp: 1. Period= 3. Midline: y= -1. f ( t)
2
sin
t
= −
−
1
3
π
11. Amp: 3, Period = , Shift: 4 left, Midline: y = 5
4
12. Amp: 4, Period = 4, Shift: 3 right, Midline: y = 7
π
13. Amp: 2, Period = 2 , Shift: 7 right, Midline: y = 4
3
543
π
14. Amp: 5, Period = 2 , Shift: 4 left, Midline: y = -2
5
15. Amp: 1, Period = 12, Shift: 6 left, Midline: y = -3
16. Amp: 8, Period = 12 , Shift: 3 left, Midline: y = 6
7
π
17. f ( x) 4sin
( x )1
=
+
5
π
18. f ( x) 3sin
( x )1
=
+
3
π
19. f ( x) cos
( x 2)
=
+
5
π
20. f ( x)
2cos
( x )1
= −
−
3
π
21. D( t) 50 7sin
t
=
−
12
π
22. D( t) 68 12sin
t
=
−
12
23. a. Amp: 12.5. Midline: y = 13.5. Period: 10
π
b. h( t)
12.5cos
t
= −
+
13.5
5
c. h(5) = 26 meters
24. a. Amp: 17.5. Midline: y = 20.5. Period: 8
π
b. h( t)
17.5cos
t
= −
+
20.5
8
c. h(4) = 38 meters
Section 6.2
1. II
3. I
π
5. Period: . Horizontal shift: 8 right
4
7. Period: 8. Horizontal shift: 1 left
9. Period: 6. Horizontal shift: 3 left
544
11.
13.
15.
π
π
17. f ( x) 2sec
x
=
−
1
19. f ( x) = 2csc
x +
1
2
4
21. tan (− x) =1.5
23. sec(− x) = 2
25. csc(− x) = 5
27. −csc( x)
Section 6.3
π
π
π
1.
3. −
5.
4
6
3
π
π
π
7. 3
9.
11. −
4
4
3
13. 1.9823
15. -0.9273
17. 44.427°
π
π
19.
21. −
23. 2 10
25. 1
4
6
7
17
−
27. 25
2
x
29.
3 x
5
9 2
x +1
545
Section 6.4
π π
π π
π
π π
1. 5 7
,
3.
5
,
5.
7.
3
,
4 4
3 3
2
2 2
π
π
9.
7
+ 2π k,
+ 2π k , where k is an integer
4
4
π
π
11. 7
11
+ 2π k,
+ 2π k , where k is an integer
6
6
π
π
π
π
13.
2
5
2
+
k,
+
k , where k is an integer
18
3
18
3
π
π
π
π
15. 5
2
7
2
+
k,
+
k , where k is an integer
12
3
12
3
π
π
17.
5
+ π k,
+ π k , where k is an integer
6
6
π
π
π
π
19.
2
5
2
+
k,
+
k , where k is an integer
4
3
12
3
21. 4 + 8 k , where k is an integer
23. 1
5
+ 2 k, + 2 k , where k is an integer
6
6
25. 0.2734, 2.8682
27. 3.7603, 5.6645
29. 2.1532, 4.1300
31. 0.7813, 5.5019
33. 0.04829, 0.47531
35. 0.7381, 1.3563
37. 0.9291, 3.0709
39. 1.3077, 4.6923
Section 6.5
1. c = 89 , A = 57.9946°, B = 32.0054°
3. b = 1 76 , A = 27.8181°, B = 62.1819°
π
5. y ( x) 6sin
( x )1
=
−
+
4
2
7. D( t)
π
50 13cos
(t 5)
=
−
−
12
π
π
9. a. P( t) 129 25cos
t
=
−
b. P( t) =129 − 25cos
( t −
3)
6
6
11. 75 degrees
13. 8
15. 2.80869431742
17. 5.035 months
546
Chapter 7
Section 7.1
π
π
π π
1. 7 11
,
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