Download MAC 1114 Fall 10 Ref:579973 Mr. Guillen Review for Exam 1 Exam

MAC 1114 Fall 10 Ref:579973
Review for Exam 1
Mr. Guillen
Exam 1 will be on 09/21/10 and cover the following sections: 6.1, 6.2, 6.3, 6.4.
SHORT ANSWER. Write the word or phrase that best completes each statement or answers the question.
Find the requested function value of θ.
12
1) If csc θ =
, find cot θ.
7
2) If sin θ =
3) If cos α =
8
, find cos θ.
11
7
, then find sec α.
8
4) If tan θ = 1.9, then find csc θ.
5) If sin θ =
11
5
11
, cos θ = , and tan θ =
, then find csc θ, sec θ, and cot θ.
6
5
6
1)
2)
3)
4)
5)
Without using a calculator, give the exact trigonometric function values with rational denominators.
6) cos 60°
6)
7) tan 60°
7)
8) cot 45°
8)
9) csc 45°
9)
10) cos 30°
10)
11) sec 30°
11)
12) sec 45°
12)
13) tan 45°
13)
Express the angle in degrees to the nearest hundredth.
14) 52°25'20''
14)
15) 91°48'28''
15)
16) 32°47'51''
16)
17) 17°4'53''
17)
Convert the angle measures to degrees, minutes, and seconds. Round seconds to whole units.
18) 56.83°
18)
19) 24.41°
19)
20) 30.31°
20)
21) 79.02°
21)
Answer the question.
22) Given that sin 72° = .9511 and cos 72° = .3090, find the six function values of 18°.
22)
23) Given that sin 64° = .8988 and cos 64° = .4384, find the six function values of 26°.
23)
24) Given that sin 2° = .0349 and cos 2° = .9994, find the six function values of 88°.
24)
25) Given that sin 40° = .6428 and cos 40° = .7660, find the six function values of 50°.
25)
Solve the right triangle for all missing sides and angles to the nearest tenth.
26)
26)
c=6
A = 51°
27)
27)
c = 11
B = 54°
28)
28)
c = 17
B = 24.1°
Solve the right triangle.
29) b = 120, c = 490
29)
30) a = 15.3, b = 18.6
30)
31) a = 12.9, b = 18.9
31)
Solve the problem.
32) Find h as indicated in the figure. Round your answer to the hundredths place.
25.7°
154 ft
57.9°
32)
33) Find h as indicated in the figure. Round your answer to the hundredths place.
26.6°
33)
58.3°
105 ft
34) Find h as indicated in the figure. Round your answer to the hundredths place.
25.3°
34)
50.4°
160 ft
35) A tree 490 m away subtends an angle of 4°. Find the height of the tree.
35)
36) A tree 500 m away subtends an angle of 2°. Find the height of the tree.
36)
Find the measures of two angles, one positive and one negative, that are coterminal with the given angle.
37) 118°
37)
38) 244°
38)
39) -49°
39)
40) -193°
40)
Find the exact function value if it exists.
41) cot 0°
41)
42) cos 90°
42)
43) sin 225°
43)
44) sin 270°
44)
45) cos 210°
45)
46) tan 300°
46)
47) cot 150°
47)
48) sin (-150°)
48)
49) sec (-225°)
49)
50) cot (-120°)
50)
51) sin (-630°)
51)
Find the exact function value.
52) cos -330°
52)
53) sin 780°
53)
54) tan -675°
54)
55) csc 405°
55)
56) sec 1110°
56)
Find the reference angle for the given angle.
57) A = 166°
57)
58) A = 35°
58)
59) A = 216.8°
59)
60) A = -83.2°
60)
61) A = 431°
61)
62) A = -391°
62)
Find the measures of two angles, one positive and one negative, that are coterminal with the given angle.
π
63)
63)
6
64)
2π
5
64)
65)
10π
7
Convert to radian measure. Leave your answer in terms of π.
66) 90°
65)
66)
67) -60°
67)
68) -610°
68)
69) -79.9°
69)
Convert to radian measure. Round to two decimal places.
70) -151.3°
70)
71) -182.4°
71)
72) 117.4°
72)
73) -358.8°
73)
Convert to degree measure. Round to two decimal places, if necessary.
π
74) 2
74)
28
π
9
75)
76) 1.7744
76)
77) -2.5
77)
78) A wheel is rotating at 8 radians/sec, and the wheel has a 25-inch diameter. To the nearest
foot per minute, what is the velocity of a point on the rim?
78)
79) A wheel is rotating at 2 radians/sec, and the wheel has a 75-inch diameter. To the nearest
foot per minute, what is the velocity of a point on the rim?
79)
80) A wheel with a 16-inch diameter is turning at the rate of 36 revolutions per minute. To the
nearest inch per minute, what is the velocity of a point on the rim?
80)
81) A wheel with a 15-inch diameter is turning at the rate of 34 revolutions per minute. To the
nearest inch per minute, what is the velocity of a point on the rim?
81)
75) -
Solve.
82) A cylinder on John Lennon Guttenbergʹs printing press has a 43.3 cm diameter. The linear
speed of a point on the cylinderʹs surface is 126 meters per minute. What is the angular
speed of the cylinder in revolutions per hour? Round to the nearest tenth.
82)
83) A cylinder on John Lennon Guttenbergʹs printing press has a 44.9 cm diameter. The linear
speed of a point on the cylinderʹs surface is 133 meters per minute. What is the angular
speed of the cylinder in revolutions per hour? Round to the nearest tenth.
83)
84) A bicyclistʹs average linear speed during a race was 31 mph. His bicycle wheel has a 16-in.
diameter. What was the angular speed of the wheel in revolutions per hour? Round to the
nearest tenth.
84)
85) A bicyclistʹs average linear speed during a race was 31 mph. His bicycle wheel has a 17-in.
diameter. What was the angular speed of the wheel in revolutions per hour? Round to the
nearest tenth.
85)
Answer Key
Testname: MAC_1114_FALL_10_TR_EXAM_1_REVIEW
1)
95
7
2)
57
11
3)
8 7
7
4) 1.1
5) csc θ =
6)
6 11
6
5 11
; sec θ = ; cot θ =
11
11
5
1
2
7) 3
8) 1
9) 2
3
10)
2
11)
12)
13)
14)
15)
16)
17)
18)
19)
20)
21)
22)
23)
24)
25)
26)
27)
28)
29)
30)
31)
32)
33)
34)
35)
36)
37)
2 3
3
2
1
52.42
91.81
32.80
17.08
56°49'48''
24°24'36''
30°18'36''
79°1'12''
sin 18° = .3090; cos 18° = .9511; tan 18° = .3249
csc 18° = 3.2361; sec 18° = 1.0515; cot 18° = 3.0777
sin 26° = .4384; cos 26° = .8988; tan 26° = .4877
csc 26° = 2.2812; sec 26° = 1.1126; cot 26° = 2.0503
sin 88° = .9994; cos 88° = .0349; tan 88° = 28.6363
csc 88° = 1.0006; sec 88° = 28.6537; cot 88° = .0349
sin 50° = .7660; cos 50° = .6428; tan 50° = 1.192
csc 50° = 1.305; sec 50° = 1.556; cot 50° = .8391
B = 39°, a = 4.7, b = 3.8
A = 36°, a = 6.5, b = 8.9
A = 65.9°, a = 15.5, b = 6.9
A = 75.8, B = 14.2, a = 475.1
A = 39.4, B = 50.6, c = 24.1
A = 34.3, B = 55.7, c = 22.9
106.17 ft
76.12 ft
124.2 ft
34 m
17 m
478°; -242°
Answer Key
Testname: MAC_1114_FALL_10_TR_EXAM_1_REVIEW
604°; -116°
311°; -409°
167°; -553°
Undefined
0
2
43) 2
38)
39)
40)
41)
42)
44) -1
45) -
3
2
46) 47) -
3
3
1
2
48) 49) -
2
3
3
50)
51) 1
52)
3
2
53)
3
2
54) 1
55) 2
2 3
56)
3
57)
58)
59)
60)
61)
62)
14°
35°
36.8°
83.2°
71°
31°
13π
11π
63)
;6
6
64)
12π
8π
;5
5
65)
24π
4π
;7
7
66)
π
2
67) -
π
3
68) -
61
π
18
69)
280.1
π
180
Answer Key
Testname: MAC_1114_FALL_10_TR_EXAM_1_REVIEW
70)
71)
72)
73)
74)
75)
76)
77)
78)
79)
80)
81)
82)
83)
84)
85)
-2.64
-3.18
2.05
-6.26
-90°
-560°
101.67°
-143.24°
500 ft/min
375 ft/min
1810 in./min
1602 in./min
1.5 revolutions per hour
1.6 revolutions per hour
39,075.8 revolutions per hour
36,777.2 revolutions per hour
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