ANSWER: 4-2 Degrees and Radians
120°
Write each degree measure in radians as a
multiple of π and each radian measure in
degrees.
10. 30°
SOLUTION: Identify all angles that are coterminal with the
given angle. Then find and draw one positive
and one negative angle coterminal with the
given angle.
20. 225°
SOLUTION: To convert a degree measure to radians, multiply by
All angles measuring
with a
angle. are coterminal
Sample answer: Let n = 1 and −1.
ANSWER: 14. SOLUTION: To convert a radian measure to degrees, multiply by
ANSWER: 225° + 360n°; Sample answer: 585°, −135°
ANSWER: 120°
Identify all angles that are coterminal with the
given angle. Then find and draw one positive
and one negative angle coterminal with the
given angle.
20. 225°
24. SOLUTION: All angles measuring
are coterminal with
SOLUTION: All angles measuring
with a
angle. Sample answer: Let n = 1 and −1.
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are coterminal
a
angle. Sample answer: Let n = 1 and −1.
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4-2 Degrees and Radians
Find the length of the intercepted arc with the
given central angle measure in a circle with the
given radius. Round to the nearest tenth.
24. SOLUTION: All angles measuring
29. , r = 4 yd
are coterminal with
SOLUTION: a
angle. Sample answer: Let n = 1 and −1.
ANSWER: 5.2 yd
30. 105°, r = 18.2 cm
SOLUTION: Method 1 Convert 105° to radian measure, and then use s = rθ
to find the arc length.
Substitute r = 18.2 and θ = .
ANSWER: Method 2 Use s =
to find the arc length.
Find the length of the intercepted arc with the
given central angle measure in a circle with the
given radius. Round to the nearest tenth.
29. , r = 4 yd
SOLUTION: eSolutions Manual - Powered by Cognero
ANSWER: 33.4 cm
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Find the rotation in revolutions per minute
given the angular speed and the radius given
ANSWER: ANSWER: 4-2 5.2
Degrees
and Radians
yd
33.4 cm
30. 105°, r = 18.2 cm
SOLUTION: Method 1 Convert 105° to radian measure, and then use s = rθ
to find the arc length.
Find the rotation in revolutions per minute
given the angular speed and the radius given
the linear speed and the rate of rotation.
36. = 104π rad/min
SOLUTION: The angular speed is 104π radians per minute.
Substitute r = 18.2 and θ = .
Each revolution measures 2π radians 104π ÷ 2π = 52
The angle of rotation is 52 revolutions per minute.
ANSWER: 52 rev/min
Method 2 Use s =
to find the arc length.
37. v = 82.3 m/s, 131 rev/min
SOLUTION: 131 × 2π = 262π The linear speed is 82.3 meters per second with an
angle of rotation of 262π radians per minute.
Use the linear speed equation to find the radius, r.
ANSWER: 33.4 cm
Find the rotation in revolutions per minute
given the angular speed and the radius given
the linear speed and the rate of rotation.
36. = 104π rad/min
SOLUTION: The angular speed is 104π radians per minute.
The radius is about 6 m.
Each revolution measures 2π radians ANSWER: 6m
104π ÷ 2π = 52
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The angle of rotation is 52 revolutions per minute.
Find the area of each sector.
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square feet.
The radius is about 6 m.
ANSWER: 4-2 ANSWER: Degrees and Radians
500.5 ft
6m
2
Find the area of each sector.
48. 47. SOLUTION: SOLUTION: The measure of the sector’s central angle θ is The measure of the sector’s central angle θ is 177°
and the radius is 18 feet. Convert the central angle
measure to radians.
Use the central angle and the radius to find the area
of the sector.
and the radius is 43.5 centimeters.
Therefore, the area of the sector is about 247.7
square centimeters.
ANSWER: 247.7 cm
2
49. GAMES The dart board shown is divided into Therefore, the area of the sector is about 500.5
square feet.
twenty equal sectors. If the diameter of the board is
18 inches, what area of the board does each sector
cover?
ANSWER: 500.5 ft
2
SOLUTION: 48. SOLUTION: The measure of the sector’s central angle θ is and the radius is 43.5 centimeters.
360° ÷ 20 or 18°
If the board is divided into 20 equal sectors, then the
central angle of each sector has a measure of 18°. So, the measure of a sector’s central angle is 18°
and the radius is 9 inches.
Convert the central angle measure to radians.
Therefore, the area of the sector is about 247.7
square centimeters.
Use the central angle and the radius to find the area
of a sector.
ANSWER: 2
247.7
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49. GAMES The dart board shown is divided into twenty equal sectors. If the diameter of the board is
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Therefore, the area of the sector is about 247.7
square centimeters.
ANSWER: 4-2 Degrees
2 and Radians
247.7 cm
49. GAMES The dart board shown is divided into twenty equal sectors. If the diameter of the board is
18 inches, what area of the board does each sector
cover?
SOLUTION: 360° ÷ 20 or 18°
If the board is divided into 20 equal sectors, then the
central angle of each sector has a measure of 18°. So, the measure of a sector’s central angle is 18°
and the radius is 9 inches.
Convert the central angle measure to radians.
Use the central angle and the radius to find the area
of a sector.
Therefore, each sector covers an area of about 12.7
square inches.
ANSWER: 2
12.7 in
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