Section 6.1Angles and Their Measure

(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

Radians

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

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

0 radian30 radians180

(a) 6

0 radian 20 radians

180 3(b) 12

0 radian0 radians180 3

(c) 6

0 radian 30 radians180 2

(d) 27

0 radian 1.815 radians180

(e) 104

5(a) radian (b) radian (c) radians (d) 5 radians3 2 6

180(a) 603

180(b) 90

2

5 180(c) 1506

180(d) 5 286.48

In order to use must be in radians.s r

Figure 13 (a)Figure 13 (b)

Find the area of the sector of a circle of radius 5 feet formed by an angle of 60°. Round the answer to two decimal places.

In order to use the equation for the area of a sector, must be in radians.

60180 3

21 255 13.09 square feet2 3 6

A

Linear Speed

Angular Speed

A child is spinning a rock at the end of a 3-foot rope at the rate of 160 revolutions per minute (rpm). Find the linear speed of the rock when it is released.

3

160 revolutions 2 radians radians3201 minute 1 revolution minute

v r 3 feet 320

radiansminute

3016feet

minute

v 3016

feetminute

1 mile

5280 feet60 minutes

1 hour34.3 mph