Project 0 Radians and degrees
ITESM Campus Aguascalientes
MA3002 Advanced Mathematics
January-May 2017
Dr. Juan-Manuel CAMPOS-SANDOVAL
Name___________________________________
MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question.
Convert the degree measure to radians. Leave answer as a multiple of π.
1) 30°
π
π
π
A)
B)
C)
8
5
7
1)
D)
π
6
2) -45°
2)
π
A) - 4
π
B) - 6
π
C) - 3
π
D) - 5
11π
B)
12
11π
C)
6
11π
D)
3
8π
B)
5
4π
C)
5
9π
D)
5
3) 330°
3)
11π
A)
5
4) 288°
4)
16π
A)
5
5) 650°
A) 5)
65π
9
B) 65π
18
C) 65π
36
D) 29π
18
Convert the radian measure to degrees. Round to the nearest hundredth if necessary.
π
6)
4
A) 0.785°
7) - C)
π
°
4
D) 45π°
π
5
A) -36π°
8)
B) 45°
6)
7)
B) -36°
C) -0.63°
π
D) - °
5
10π
3
A) 601°
8)
B) 600.5°
C) 599.5°
1
D) 600°
9) -15π
A) -2880°
10)
9)
B) -2700°
C) -5400°
D) -1350°
5π
12
10)
A) 150°
B) 432π°
C) 75°
D) 144°
Convert the degree measure to radians, correct to four decimal places. Use 3.1416 for π.
11) 350°46′
A) 6.102
B) 6.122
C) 6.112
D) 6.092
12) -22°27′
A) -0.3918
B) -0.3818
C) -0.3618
D) -0.3718
13) 19°10′
A) 0.2345
B) 0.6345
C) 0.5345
D) 0.3345
14) 21.8431°
A) 0.2812
B) 0.4812
C) 0.3812
D) 0.5812
15) 85.8839°
A) 1.5990
B) 1.4990
C) 1.7990
D) 1.6990
11)
12)
13)
14)
15)
Convert the radian measure to degrees. Give answer using decimal degrees to the nearest hundredth. Use 3.1416 for π.
16) 0.2521
16)
A) 14.44°
B) 15.44°
C) 13.74°
D) 14.94°
17) 1
17)
A) 57.40°
18) -5.7
A) -326.59°
B) 57.30°
C) 114.50°
D) 114.60°
B) -326.99°
C) -652.78°
D) -653.18°
18)
Find the exact value without using a calculator.
2π
19) cos 3
A) - 20) sin 1
2
19)
C) - B) undefined
3
2
D)
3
2
3π
4
A) - 20)
2
2
B) - 1
2
C)
2
1
2
D)
2
2
21) sin -2π
3
A) -1
21)
B) - 1
2
3
2
C) - D)
3
2
22)
22) cos 2π
1
B)
2
A) 1
23) tan -5π
6
A)
24) tan 3
3
3
B)
3
2
3
3
D) - 3
24)
B) -1
C)
3
D) 1
25)
2 3
3
B) - 3
C) - 1
2
D) - 2
-5π
6
26)
3
3
A) - 3
B) - 27) cot π
A) undefined
B) -1
28) sec C)
4π
3
A) - 26) cot 23)
-7π
4
A)
25) csc D) -1
C) 0
C)
3
3
D)
3
27)
C) 0
D) 1
-5π
4
A)
2
2
28)
B) - 2 3
3
C) -2
D) - 2
Find the length of an arc intercepted by a central angle θ in a circle of radius r. Round your answer to 1 decimal place.
π
29) r = 38.81 ft; θ = radians
29)
3
A) 121.9 ft
B) 40.6 ft
C) 20.3 ft
D) 81.3 ft
5
30) r = 15.64 cm.; θ = π radians
4
A) 30.7 cm
30)
B) 122.8 cm
C) 19.6 cm
3
D) 61.4 cm
31) r = 31.31 in.; θ = 92°
A) 16.0 in.
31)
B) 100.5 in.
C) 50.3 in.
D) 25.1 in.
Assume that the cities lie on the same north -south line and that the radius of the earth is 6400 km.
32) Find the distance between City A, 60° N and City B, 35° N. (Round to the nearest kilometer.)
A) 2828 km
B) 2733 km
C) 2888 km
D) 2793 km
32)
33) Find the distance between City E, 20° N and City F, 58° S. (Round to the nearest kilometer.)
A) 4245 km
B) 8721 km
C) 8713 km
D) 4237 km
33)
Find the area of a sector of a circle having radius r and central angle θ. Express the answer to the nearest tenth.
π
34) r = 67.4 cm, θ = radians
34)
7
A) 15.1 cm 2
35) r = 20.0 m, θ = 20°
A) 139.6 m 2
B) 324.5 cm 2
C) 2038.8 cm 2
D) 1019.4 cm 2
B) 0.6 m 2
C) 69.8 m 2
D) 3.5 m 2
35)
Assume that the cities lie on the same north -south line and that the radius of the earth is 6400 km.
36) Find the latitude of Winnipeg, Canada if Winnipeg and Austin, TX, 30 °N, are 2234 km apart.
A) 70 °N
B) 50 °N
C) 60 °N
D) 20 °N
36)
Solve the problem. Round answer to 2 decimal places.
37) Find the radius of a circle in which a central angle of 67 square meters.
A) 13.06 m
B) 170.61 m
π
radian determines a sector of area
4
C) 18.47 m
37)
D) 9.24 m
38) What is the difference in area covered by a single 10-inch windshield wiper operating with a
central angle of 126° compared to a pair of 3-inch wipers operating together each having a central
angle of 106°?
A) 126.61 in. 2
B) 98.31 in.2
C) 93.31 in. 2
D) 101.63 in.2
38)
39) A sensor light installed on the edge of a home can detect motion for a distance of 51 ft. in front and
with a range of motion of 204°. Over what area will the sensor detect motion and become
illuminated?
A) 9260.89 ft 2
B) 4630.29 ft 2
C) 4630.39 ft 2
D) 9260.79 ft 2
39)
SHORT ANSWER. Write the word or phrase that best completes each statement or answers the question.
Provide an appropriate response.
40) If the radius of a circle is doubled, how is the length of the arc intercepted by a fixed
central angle changed?
4
40)
Answer Key
Testname: PROJECT_0_MA3002
1) D
2) A
3) C
4) B
5) B
6) B
7) B
8) D
9) B
10) C
11) B
12) A
13) D
14) C
15) B
16) A
17) B
18) A
19) A
20) D
21) C
22) A
23) C
24) D
25) A
26) D
27) A
28) D
29) B
30) D
31) C
32) D
33) C
34) D
35) C
36) B
37) A
38) C
39) C
40) s = rθ , so if r is doubled then s (the length of the arc) is doubled too.
5