Section 6.1
Angles 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 
1     and 1 =    
 60 
 60 60 
 1 
 1 1 
(a) 40 + 12 + 5 = 40 + 12    + 5     = 40 + 0.2 + 0.0014
 60 
 60 60 
 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.
s   4 0.5  2 meters
(a) 30°
104 °
(b) 120°
(c) – 60°
  radian  
(a) 300 
  radians
 180  6

  radian 
(c)  600 


radians

3
 180 
(d) 270°
(e)
  radian  2
(b) 1200 
radians

 180  3
  radian  3
(d) 2700 
radians

 180  2
  radian 
(e) 1040 
  1.815 radians
 180 
(a)

3
radian
(b) 

2
radian
5
(c)
radians
6
(d) 5 radians
  180 
(a)

  60
3   
  180 
(b) 

  90
2   
5  180 
(c)

  150
6   
 180 
(d) 5 
  286.48
  
In order to use s  r  must be in radians.
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.
   

 180  3
  60 
1 2    25
A   5   
 13.09 square feet
2
6
3
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
radians


 320
1 minute
1 revolution
minute
radians
feet
v  r  3 feet  320
 3016
minute
minute
feet
1 mile 60 minutes
v  3016


 34.3 mph
minute 5280 feet
1 hour