Review Test 1
MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question. Convert the angle to a decimal in degrees. Round the answer to two decimal places.
1) 22°54ʹ35ʹʹ
A) 22.97° B) 22.87° C) 22.91° D) 22.92°
1)
2) 291°26ʹ12ʹʹ
A) 291.44° B) 291.40° C) 291.50° D) 291.45°
2)
3) 21°17ʹ34ʹʹ
A) 21.22° B) 21.37° C) 21.29° D) 21.34°
3)
Convert the angle to D° Mʹ Sʹʹ form. Round the answer to the nearest second. 4) 14.93°
A) 14°55ʹ93ʹʹ B) 14°55ʹ54ʹʹ C) 14°55ʹ48ʹʹ D) 14°55ʹ36ʹʹ
4)
5) 183.82°
A) 183°49ʹ82ʹʹ B) 183°47ʹ82ʹʹ C) 183°50ʹ12ʹʹ D) 183°49ʹ12ʹʹ
5)
6) 217.03°
A) 217°47ʹ3ʹʹ B) 217°1ʹ3ʹʹ C) 217°2ʹ47ʹʹ D) 217°1ʹ48ʹʹ
6)
If s denotes the length of the arc of a circle of radius r subtended by a central angle θ, find the missing quantity. Round to one decimal place, if necessary.
7) r = 12.17 centimeters, θ = 1.8 radians, s = ?
A) 20.9 cm B) 21.9 cm C) 22.9 cm D) 23.9 cm
7)
8) r = 1
3 feet, s = 5 feet, θ = ?
A) 15° B) 15 radians C) 5
3 radians D)
5 3°
8)
9) s = 2.85 meters, θ = 1.9 radians, r = ?
A) 1.5 m B) 0.67 m C) 0.75 m D) 1 m
Find the length s. Round the answer to three decimal places. 10)
s
π 4
2 ft
A) 6.283 ft B) 1.571 ft C) 3.142 ft D) 2.546 ft
10)
11)
s
70°
10 m
A) 13.439 m B) 9.774 m C) 12.217 m D) 10.995 m
11)
Solve the problem.
12) For a circle of radius 4 feet, find the arc length s subtended by a central angle of 30 °. Round to the nearest hundredth.
A) 4.19 ft B) 376.99 ft C) 2.09 ft D) 6.28 ft
12)
SHORT ANSWER. Write the word or phrase that best completes each statement or answers the question. 13) Salt Lake City, Utah, is due north of Flagstaff, Arizona. Find the distance between Salt
Lake City (40°45ʹ north latitude) and Flagstaff (35°16ʹ north latitude). Assume that the radius of the Earth is 3960 miles. Round to nearest whole mile.
13)
MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question. Convert the angle in degrees to radians. Express the answer as multiple of π.
14) 36°
A) π
7 B)
π
6 C)
π
4 D)
π 5
14)
15) 54°
A) 3π
10 B)
10π
3 C)
2π
9 D)
4π 11
16) 87°
A) 29π
30 B)
29π
120 C)
29π
60 D)
29π 90
16)
17) 6°
A) π
15 B)
π
60 C)
π
30 D)
π 18
17)
Convert the angle in radians to degrees. 18)- 5π
12
A)-74° B)-76° C) -77° D)-75°
18)
19)- π 2
A)-90π° B)-2° C) -90° D) 2°
19)
20) 23
9 π
A) 230° B) 460° C) 920π° D) 8°
20)
Convert the angle in degrees to radians. Express the answer in decimal form, rounded to two decimal places. 21) 55°
A) 0.95 B) 0.94 C) 0.93 D) 0.96
21)
22)-335°
A)-5.83 B)-5.85 C) -5.84 D)-5.82
22)
Convert the angle in radians to degrees. Express the answer in decimal form, rounded to two decimal places. 23) 2
A) 113.75° B) 0.09° C) 114.59° D) 0.03°
23)
24) 6
A)-0.15° B) 0.04° C) 139.27° D) 140.35°
24)
If A denotes the area of the sector of a circle of radius r formed by the central angle θ, find the missing quantity. If necessary, round the answer to two decimal places.
25) r = 7 feet, A = 56 square feet, θ = ?
A) 1372 radians B) 2744 radians C) 2.29 radians D) 1.14 radians
25)
26)θ = π
6 radians, A = 62 square meters, r = ?
A) 64.93 m B) 16.23 m C) 4.03 m D) 15.39 m
26)
27) r = 5 feet, A = 33 square feet, θ = ?
A) 47,292.99° B) 75.67° C) 23,646.5° D) 151.34°
28) r = 44.2 centimeters, θ = π
8 radians, A = ?
A) 122.1 cm2 B) 8.7 cm2 C) 767.2 cm2 D) 383.6 cm2
28)
Find the area A. Round the answer to three decimal places. 29)
π 6
9 yd
A) 2.356 yd2 B) 42.412 yd2 C) 13.5 yd2 D) 21.206 yd2
29)
30)
50°
9 ft
A) 35.343 ft2 B) 3.927 ft2 C) 11.25 ft2 D) 70.686 ft2
30)
Solve the problem.
31) A circle has a radius of 11 centimeters. Find the area of the sector of the circle formed by an angle of 55°. If necessary, round the answer to two decimal places.
A) 58.08 cm2 B) 116.15 cm2 C) 5.28 cm2 D) 18.49 cm2
31)
32) An irrigation sprinkler in a field of lettuce sprays water over a distance of 25 feet as it rotates through an angle of 135°. What area of the field receives water? If necessary, round the answer to two decimal places.
A) 1472.62 ft2 B) 29.45 ft2 C) 736.31 ft2 D) 234.38 ft2
32)
33) An object is traveling around a circle with a radius of 10 centimeters. If in 20 seconds a central
angle of 1
3 radian is swept out, what is the linear speed of the object?
A) 6 radians/sec B) 1
6 cm/sec C)
1
6 radians/sec D) 6 cm/sec
34) An object is traveling around a circle with a radius of 20 meters. If in 10 seconds a central angle of 1
5 radian is swept out, what is the linear speed of the object?
A) 2
5 m/sec B)
1
5 m/sec C)
1
8 m/sec D)
1 4 m/sec
34)
35) An object is traveling around a circle with a radius of 10 meters. If in 15 seconds a central angle of 3 radians is swept out, what is the linear speed of the object?
A) 1
3 m/sec B)
2
3 m/sec C) 3 m/sec D) 2 m/sec
35)
Find the value of the indicated trigonometric function of the angle θ in the figure. Give an exact answer with a rational denominator.
36)
7
6 Find sin θ.
A) sin θ = 85
7 B) sin θ =
7 85
85 C) sin θ =
6 85
85 D) sin θ =
85 6
36)
37)
7
9 Find cos θ.
A) cos θ = 9 130
130 B) cos θ =
130
7 C) cos θ =
7 130
130 D) cos θ =
130 9
37)
38)
8
5 Find tan θ.
A) tan θ = 39
8 B) tan θ =
5 39
39 C) tan θ =
8 39
39 D) tan θ =
5 8
39)
9
2 Find csc θ.
A) csc θ = 2 85
85 B) csc θ =
85
2 C) csc θ =
85
9 D) csc θ =
9 85 85
39)
40)
7
4
Find sec θ.
A) sec θ = 65
7 B) sec θ =
4 65
65 C) sec θ =
7 65
4 D) sec θ =
7 65 65
40)
41)
8
7
Find cot θ.
A) cot θ = 7 113
113 B) cot θ =
7
8 C) cot θ =
8 113
113 D) cot θ =
8 7
41)
Use identities to find the exact value of the indicated trigonometric function of the acute angle θ. 42) sin θ = 5
3 , cos θ = 2
3 Find tan θ.
A) 5
2 B)
3
2 C)
2 5
5 D)
3 5 5
42)
43) sin θ = 2 2
3 , cos θ = 1
3 Find sec θ.
A) 3 2
4 B)
2
4 C) 3 D) 2 2
44) sin θ = 1
4, cos θ = 15
4 Find csc θ.
A) 15 B) 4 C) 4 15
15 D)
15 15
44)
Use Fundamental Identities to find the exact value of the expression. Do not use a calculator. 45) sin2 65° + cos2 65°
A)-1 B) 2 C) 1 D) 0
45)
46) sec2 25° - tan2 25°
A) 1 B) 2 C) -1 D) 0
46)
47) tan 55° - sin 55° cos 55°
A) 0 B) 55 C) 1 D) undefined
47)
Use the definition or identities to find the exact value of the indicated trigonometric function of the acute angle θ. 48) sin θ = 4
5 Find tan θ.
A) 3
4 B)
4
3 C)
5
3 D)
5 4
48)
49) cos θ = 3
5 Find sec θ.
A) 5
4 B)
4
3 C)
3
4 D)
5 3
49)
50) tan θ = 3 Find sin θ.
A) 1
2 B) 2 C)
2 3
3 D)
3 2
50)
51) cot θ = 12
5 Find sin θ.
A) 5
13 B)
5
12 C)
13
12 D)
12 13
51)
52) sec θ = 5
3 Find csc θ.
A) 3
4 B)
5
4 C)
3
5 D)
4 5
52)
53) csc θ = 2 3
3 Find cos θ.
A) 3
3 B) 2 C)
3
2 D)
1 2
Use Fundamental Identities and/or the Complementary Angle Theorem to find the exact value of the expression. Do not use a calculator.
54) csc2 20° - tan2 70°
A) 0 B) 1 C) -1 D) 2
54)
55) cos 30°sin 60° + sin 30°cos 60°
A) 0 B)-1 C) 2 D) 1
55)
56) If tan θ = 10, find the exact value of cot (π 2 - θ).
A) 11 B) 1
10 C) 9 D) 10
56)
Solve the problem.
57) Given sin 30° = 1
2 , use trigonometric identities to find the exact value of tan π 6.
A) 3 3 B) 3 C) 3 D) 3
3
57)
58) Given csc θ = 2 , use trigonometric identities to find the exact value of sec2 θ.
A) 1
3 B)
1
2 C)
4
3 D)
1 4
58)
59) Given tan θ = 2, use trigonometric identities to find the exact value of cot (90° - θ).
A) 5
2 B)
1
2 C) 5 D) 2
59)
Find the exact value. Do not use a calculator. 60) sin π
4
A) 1
2 B) 2 C)
-2
2 D)
2 2
60)
61) csc 45°
A) 2
2 B)
3
2 C) 2 D) 3
61)
62) sin 30°
A) 2
2 B)
3
3 C)
3
2 D)
1 2
62)
63) csc π 6
A) 2 3
3 B)
1
2 C) 2 D) 2
Find the exact value of the expression if θ = 60°. Do not use a calculator.
64) f(θ) = tan θ Find f(θ).
A) 2 B) 3
3 C) 3 D)
3 2
64)
65) f(θ) = sin θ Find 6f(θ).
A) 3 3 B)- 3
2 C) 3 D)-
1 2
65)
Find the exact value. Do not use a calculator. 66) csc 60° - sin 45°
A) 4 3 - 3 2
6 B)
4 - 2
2 C)
4 2 - 3 3
6 D)
4 - 3 2
66)
67) cot π 3 - cos
π 6
A) 3 B)- 3
6 C) -
6
2 D)
2 3 - 3 2
6
67)
68) 1 + cot2 30° - sec2 45°
A) 0 B) 3 C) 1 D) 2
68)
69) sin2 π 3 - cos2
π 4 - sin2
π 6
A)-1 B) 0 C) 1
2 D) 1
69)
Solve the problem.
70) A boat leaves the entrance of a harbor and travels 83 miles on a bearing of N 19° E. How many miles north and how many miles east from the harbor has the boat traveled? Round to the nearest tenth of a mile.
A) 27 miles north and 78.5 miles east B) 78.5 miles north and 27 miles east
C) 83 miles north and 83 miles east D) 241 miles north and 28.6 miles east
70)
71) A building 230 feet tall casts a 80 foot long shadow. If a person looks down from the top of the building, what is the measure of the angle between the end of the shadow and the vertical side of the building (to the nearest degree)? (Assume the personʹs eyes are level with the top of the building.)
A) 20° B) 19° C) 71° D) 70°
71)
72) A photographer points a camera at a window in a nearby building forming an angle of 42 ° with the camera platform. If the camera is 52 m from the building, how high above the platform is the window, to the nearest hundredth of a meter?
A) 57.75 m B) 0.9 m C) 46.82 m D) 1.11 m
72)
73) A tree casts a shadow of 26 meters when the angle of elevation of the sun is 24 °. Find the height of the tree to the nearest meter.
A) 13 m B) 12 m C) 10 m D) 11 m
74) A twenty-five foot ladder just reaches the top of a house and forms an angle of 41.5° with the wall of the house. How tall is the house? Round your answer to the nearest 0.1 foot.
A) 19 ft B) 18.6 ft C) 18.7 ft D) 18.8 ft
74)
A point on the terminal side of angle θ is given. Find the exact value of the indicated trigonometric function.
75) (9, 12) Find sin θ.
A) 4
5 B)
3
4 C)
3
5 D)
4 3
75)
76) (9, -8) Find tan θ.
A)- 2
3 B)-
8
9 C) -
9
8 D)
3 4
76)
77) (-3, -2) Find sec θ.
A) 2
3 B)-
13
3 C) -
3 13
13 D)
13 2
77)
78) - 1 2,
3
2 Find cot θ.
A)-2 B)- 3
3 C)
2 3
3 D)- 3
78)
79) (-5, -12) Find cot θ.
A)- 12
13 B)-
5
13 C)
12
5 D)
5 12
79)
Use a coterminal angle to find the exact value of the expression. Do not use a calculator. 80) sin -315°
A)- 2
2 B)-
1
2 C)
2
2 D)
1 2
80)
81) csc -660°
A) 2 B) 1
2 C)
2 3
3 D) 3
81)
82) cot 720°
A) 1 B) 0 C) -1 D) undefined
82)
83) csc 25π 4
A) 2 B) 2 C) 2
2 D)
2 3 3
83)
84) tan (49π)
A) 0 B)-1 C) 1 D) undefined
Name the quadrant in which the angle θ lies. 85) cos θ < 0, csc θ < 0
A) I B) II C) III D) IV
85)
86) cot θ < 0, cos θ > 0
A) I B) II C) III D) IV
86)
87) tan θ < 0, sin θ < 0
A) I B) II C) III D) IV
87)
88) sin θ > 0, cos θ > 0
A) I B) II C) III D) IV
88)
Find the reference angle of the given angle. 89) 78°
A) 12° B) 168° C) 78° D) 102°
89)
90) 426°
A) 156° B) 114° C) 24° D) 66°
90)
91)-260°
A) 100° B) 10° C) 80° D) 170°
91)
92) 2π
3
A) 4π
3 B)
π
6 C)
2π
3 D)
π 3
92)
93)- 2π 3
A) 2π
3 B)
π
6 C)
4π
3 D)
π 3
93)
94)- 42π 8
A) π
4 B)
π
2 C)
π
8 D)
π 3
94)
Use the reference angle to find the exact value of the expression. Do not use a calculator. 95) sin 765°
A) 1
2 B)
2
2 C) -
2
2 D)-
1 2
95)
96) csc -2π 3
A)- 2 3
3 B)-
1
2 C) - 2 D)- 3
97) cot -11π 6
A) 3
3 B)- 3 C) 3 D)-
3 3
97)
f(x) = sin x, g(x) = cos x, h(x) = tan x, F(x) = csc x, G(x) = sec x, H(x) = cot x. Provide an appropriate response. 98) Find f(225°). What point is on the graph of f?
A)- 2
2 ; 225°, - 2
2 B)-
2 2 ; -
2 2 , 225°
C) 2
2 ; 225°, 2 2 D) 2 2 ; 2 2 , 225° 98)
99) Find g 5π
3 . What point is on the graph of g? A) 3 2 ; 5π 3 , 3 2 B) 1 2; 5π 3 , 1 2
C)- 3
2 ; 5π
3 , - 3
2 D)-
1 2;
5π 3 , -
1 2
99)
Find the exact value of the indicated trigonometric function of θ. 100) cos θ = 2
5, tan θ < 0 Find sin θ.
A)- 21
5 B)-
5
2 C) - 21 D)-
21 2
100)
101) sec θ = 9
2 , θ in quadrant IV Find tan θ.
A)- 77
9 B)-
9
2 C) -
77
2 D)- 77
101)
102) cos θ = 24 25,
3π
2 < θ < 2π Find cot θ.
A)- 7
24 B)-24 C)
25
24 D)-
24 7
102)
103) sin θ = 1
6, sec θ < 0 Find cos θ and tan θ.
A) cos θ = 35
6 , tan θ = 35
35 B) cos θ = -
35
6 , tan θ = - 35 35
C) cos θ = 35
6 , tan θ = - 35
35 D) cos θ = -
35
6 , tan θ = 35 35
Solve the problem. 104) If sin θ = 1
3, find csc θ.
A)- 1
3 B) 3 C)
2
3 D) undefined
104)
The point P on the unit circle that corresponds to a real number t is given. Find the indicated trigonometric function.
105) 3
8, 55
8 Find sin t.
A) 55
3 B)
55
8 C)
3 55
55 D)
3 8
105)
106) - 55
8 , 3
8 Find cot t.
A) 3
8 B)-
55
3 C)
55
8 D)-
8 3
106)
107) - 7
4 , - 3
4 Find cot t.
A)- 7
3 B)
7
3 C) -
3 7
7 D)
7 4
107)
108) 3
7, - 2 10
7 Find csc t.
A) 7
3 B)-
7 10
20 C) -
10
6 D)
3 7
108)
The point P on the circle x2 + y2 = r2 that is also on the terminal side of an angle θ in standard position is given. Find the indicated trigonometric function.
109) (-3, 4) Find cos θ.
A)- 4
5 B)-
3
5 C)
4
5 D)
3 5
109)
110) (-3, 2) Find cot θ.
A)- 2
3 B)
13
3 C) -
13
3 D)-
3 2
110)
111) (-3, -1) Find sec θ.
A)- 10 B)- 10
3 C) -
3 10
10 D)
10 3
Solve the problem.
112) For what numbers θ is f(θ) = sec θ not defined?
A) multiples of π (180°) B) all real numbers
C) odd multiples of π
2 (90°) D) odd multiples of π (180°)
112)
113) What is the range of the cosine function?
A) all real numbers greater than or equal to 1 or less than or equal to -1 B) all real numbers from -1 to 1, inclusive
C) all real numbers
D) all real numbers greater than or equal to 0
113)
114) What is the range of the secant function?
A) all real numbers greater than or equal to 1 or less than or equal to -1 B) all real numbers from -1 to 1, inclusive
C) all real numbers, except odd multiples of π
2(90)° D) all real numbers
114)
Use the fact that the trigonometric functions are periodic to find the exact value of the expression. Do not use a calculator.
115) sin 405°
A) 1
2 B)-
2
2 C) -
1
2 D)
2 2
115)
116) csc 660°
A)- 2 B)- 1
2 C) -
2 3
3 D)- 3
116)
117) tan 900°
A) 3
3 B) 0 C) -1 D) undefined
117)
118) sin 16π 3
A)- 3
2 B)-
1
2 C) -1 D)
3 2
118)
Find the exact value of the expression. Do not use a calculator. 119) cos (-3π) + sin 3π
2
A) 2 B)-2 C) -1 D) 0
119)
120) csc 7π
2 - sec
-8π 3
-
Use the even-odd properties to find the exact value of the expression. Do not use a calculator. 121) cos (-60°)
A)- 3
2 B)
3
2 C) -
1
2 D)
1 2
121)
122) cos (-30°)
A) 1
2 B)
-3
2 C)
3
2 D)-
1 2
122)
123) sin (-120°)
A)- 3
2 B)
1
2 C)
-1
2 D)
3 2
123)
124) csc - π 3
A)-2 B) 2 3
3 C)
-2 3
3 D) 2
124)
125) cos (-π)
A) 0 B) 1 C) -1 D) undefined
