Section 7.1

Angles and Their Measure

Copyright © 2012 Pearson Education, Inc. Publishing as Prentice Hall.

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(a) Convert 40°12’5” to a decimal in degrees. Round the answer to four decimal places.

(b) Convert 78.562° to the D°M’S” form. Round the answer to the nearest second.

1 1 1(a) 40 + 12 + 5 = 40 + 12 + 5

60 60 60

1 1 11 and 1 =

60 60 60

= 40 + 0.2 + 0.0014 40.2014

(b) 78 0.562 78 0.562 60 78 33.72 78 33 0.72

78 33 0.72 60 78 33 43.2 78 33 43

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Radians

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Find the length of the arc of a circle of radius 4 meters subtended by a central angle of 0.5 radian.

4 0.5 2 meterss

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(a) 30° (b) 120° (c) – 60° (d) 270° (e) 104 °

0 radian30 radians

180(a)

6

0 radian 2

0 radians180 3

(b) 12

0 radian0 radians

180 3(c) 6

0 radian 30 radians

180 2(d) 27

0 radian1.815 radians

180(e) 104

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5(a) radian (b) radian (c) radians (d) 5 radians

3 2 6

180(a) 60

3

180(b) 90

2

5 180(c) 150

6

180(d) 5 286.48

Converting from radians to degrees