Therefore, 87° 53′ 10″ can be written as about
87.886°.
4-2 Degrees and Radians
Write each decimal degree measure in DMS
form and each DMS measure in decimal degree
form to the nearest thousandth.
1. 11.773°
7. 45° 21′ 25″
SOLUTION: Each minute is
of a degree and each second is SOLUTION: First, convert 0. 773° into minutes and seconds.
of a minute, so each second is of a degree.
Next, convert 0.38' into seconds.
Therefore, 45° 21′ 25″ can be written as about
45.357°.
Therefore, 11.773° can be written as 11° 46′ 23″.
9. NAVIGATION A sailing enthusiast uses a sextant,
3. 141.549°
SOLUTION: First, convert 0. 549° into minutes and seconds.
an instrument that can measure the angle between
two objects with a precision to the nearest 10
seconds, to measure the angle between his sailboat
and a lighthouse. He will be able to use this angle
measure to calculate his distance from shore. If his
reading is 17° 37′ 50″, what is the measure in
decimal degree form to the nearest hundredth?
Next, convert 0.94' into seconds.
Therefore, 141.549° can be written as 141° 32′ 56″.
SOLUTION: Convert 17° 37′ 50″ to decimal degree form. Each
5. 87° 53′ 10″
minute is
of a degree and each second is of
SOLUTION: Each minute is
of a degree and each second is of a minute, so each second is a minute, so each second is
of a degree.
of a degree.
Therefore, 17° 37′ 50″ can be written as about
17.63°.
Therefore, 87° 53′ 10″ can be written as about
87.886°.
7. 45° 21′ 25″
SOLUTION: SOLUTION: Each minute is
Write each degree measure in radians as a
multiple of π and each radian measure in
degrees.
11. 225°
To convert a degree measure to radians, multiply by
of a degree and each second is eSolutions Manual - Powered by Cognero
of a minute, so each second is Page 1
of a 50″ can be written as about
4-2 Therefore, 17° 37′
Degrees and Radians
17.63°.
Write each degree measure in radians as a
multiple of π and each radian measure in
degrees.
11. 225°
SOLUTION: 17. SOLUTION: To convert a radian measure to degrees, multiply by
To convert a degree measure to radians, multiply by
13. –45°
SOLUTION: To convert a degree measure to radians, multiply by
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.
19. –75°
SOLUTION: All angles measuring
with a
angle. are coterminal
Sample answer: Let n = 1 and −1.
15. SOLUTION: To convert a radian measure to degrees, multiply by
17. SOLUTION: To convert a radian measure to degrees, multiply by
21. –150°
SOLUTION: All angles measuring
with a
angle. eSolutions Manual - Powered by Cognero
Sample answer: Let n = 1 and −1.
are coterminal
Page 2
4-2 Degrees and Radians
21. –150°
23. SOLUTION: All angles measuring
with a
angle. SOLUTION: are coterminal
All angles measuring
Sample answer: Let n = 1 and −1.
a
are coterminal with
angle. Sample answer: Let n = 1 and −1.
23. SOLUTION: All angles measuring
a
are coterminal with
angle. Sample answer: Let n = 1 and −1.
25. SOLUTION: All angles measuring
are coterminal with a
angle. Sample answer: Let n = 1 and −1.
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Page 3
4-2 Degrees and Radians
Find the rotation in revolutions per minute
given the angular speed and the radius given
the linear speed and the rate of rotation.
35. = 135π rad/h
25. SOLUTION: All angles measuring
are coterminal with a
SOLUTION: The angular speed is 135π radians per hour.
angle. Sample answer: Let n = 1 and −1.
Each revolution measures 2π radians.
2.25π ÷ 2π = 1.125
The angle of rotation is 1.125 revolutions per minute.
Find the rotation in revolutions per minute
given the angular speed and the radius given
the linear speed and the rate of rotation.
35. = 135π rad/h
SOLUTION: The angular speed is 135π radians per hour.
eSolutions Manual - Powered by Cognero
Each revolution measures 2π radians.
Page 4