Converting Degree Measure to Radian Measure
One half a rotation is 1800 or π rad
1
Convert to radian measure:

0

a) 210 180

or 1 
180
b) -
3150

180
Exact radian
7

4
≈ 3.67
Approximate radian
 5.50
Math 30-1


7

6
To convert from degrees
to radians, multiply by
180

180 
1
Converting Radian Measure to Degree Measure
1
Convert to degree measure:
a) 2  180

3

180
b) 

12
= 1200
c) 1.68 
or 1 
rad 
180

180

= -150
To convert from radians
to degrees, multiply by
180 
180


= 96.260
Math 30-1
2
Benchmark Conversions
Degrees
00
900
Radians
0

2
Degrees
300
450
Radians

6

4
1800

600

3
2700
3
2
7200
4
3600
2
1 radian  57.3 degrees
McGraw
Hill DVD Teacher Resources 4.1_178_IA
Math 30-1
3
Determining the Sector Angle or the Arc Length
Determine the measure of the sector angle:
5 cm

6.1 cm
a
 =
r
6.1
 =
5
  1.22
Determine the arc length.
8 cm
700
Convert 700 to radians:

7
70

180
18
θ is measured
in radians
a

r
7 a

18 8
a = 9.77
Math 30-1
The arc length is 9.77 cm.4
Determine the length of the arc of the peacock’s feathers.
a

r
θ is measured
in radians
a

Convert
to rads
r

17
a
255

180
12 24
17

a  106.8 in
12
2550
If the length of the arc of the parachute is 31.9 feet, how long
is the outside cord?
a

r
31.9
1.45 
r
r  22 feet
Math 30-1
5
Problem Solving
Determine the value of a.
Determine the length of the
radius to the nearest whole
number.
One rotation is 2π radians
a 17

 2
15 15
a

r
17 34

15
r
a 17 30


15 15
15
a 13

15 15
r  30
a  13
Math 30-1
6
Conversion between Radians and Degrees
Using Formula
a

r
Page 175
2a,c,d, 3a,c,f, 4a,c,e,f
5b,c, 12a, 13a,c,d, 15, 16, 18
Math 30-1
7