Name______________________________________
Algebra 2
Worksheet on Radians
When a central angle intercepts an arc that has the same length as a radius of the circle, the measure of this
angle is defined to be one radian.
6
The circumference of a circle is 2  r, where r is the
length of a radius. There are 2  radians in one
complete revolution about a point and one complete
revolution equals 360o.
4
arc length
=r
2
1 radian
-10
r
-5
5
10
2  radians = 360o
-2
-4
This gives us the important result:
-6
 radians = 180o
From this we can convert:
radians → degrees
R 
180

 D
Convert each degree measure to radian measure.
a. 120o
and
D

𝜋
𝜋
2
Quadrant II if
2
<𝜃<𝜋
Quadrant III if 𝜋 < 𝜃 <
Quadrant IV if
3𝜋
2
3𝜋
2
0,2

< 𝜃 < 2𝜋
3
2
In which quadrant or on which axis does the terminal side of the angle lie?
4
5
9
a.
b. 
c.
3
2
4
1 minute (1’) = (
1 o
)
60

180
R
Convert each radian measure to degree measure.

3
a.
radians
b. 
radians
3
4
b. -245o
Quadrant I if 0 < 𝜃 < 2
degrees → radians.
1 second (1”) = (
1
1 o
)’ or (
)
60
3600
Convert each angle measure as indicated.
a. 12.464o to degrees, minutes and seconds, to the nearest second.
Name______________________________________
Algebra 2
Worksheet on Radians
b. 23o42’45” to decimal degrees, to the nearest tenth.
In which quadrant, or on which axis, does the terminal side of the each angle lie?
1. 150o
2. 210o
3. -60o
4. 180o
5. -240o
6. 540o
7. 2 
8.

3
12.
10
3
9.
3
4
10.
7
3
Convert each degree measure to radian measure.
13. 150o
14. 210o
11.
5
4
15. 45o
16. 240o
Convert each radian measure to degree measure.
17.

6
18.

4
19.
5
6
20.
7
6
Convert to degrees, minutes, and seconds, to the nearest second.
21. 23.42o
22. 15.27o
23. 48.35o
24. 62.73o
Convert to decimal degrees, to the nearest tenth of a degree.
25. 14o33’45”
26. 38o24’36”
27. 35o45’10”
28. 28o32’20”
Name______________________________________
Algebra 2
Worksheet on Radians
More practice on conversions! 
Convert from radians to degrees: (multiply by
1)
7
10
5) 
9)
6
11
11
2
180

)
2)
15
22
3)
6)
2
3
7) 
10) 7 
Convert from degrees to radians. (multiply by
11) 

180

3
2
5
19
15
12)
4)
19
45
8)
5
11

25
and reduce the fractions!)
13) 500
14) 800
15) –2100
16) 1000
17) 900
18) -1800
19) -12000
20) –450
21) 5600
22) 170
23) 3600
24) 1300
Convert to degrees, minutes, and seconds, to the nearest second.
25) 2.478o
26) 15.129o
27) 78.3o
28) 26.708o
Convert to decimal degrees, to the nearest tenth of a degree.
29) 11o23’4”
30) 33o27’46”
31) 73o15’1”
32) 88o3’29”
Name______________________________________
Algebra 2
Worksheet on Radians
1 – 9: Determine the quadrant in which the angle lies. (The angle is given in radian measure.)
1.
4.

2.
5
8
3
5.
11
4
3.
-
7
4
6.
17
6
-
11
9
Hint: these angles are in radian, but 𝜋 is already included in the decimal! 
7.
3.5
8.
2.25
9.
5.63
Determine two coterminal angles in radian measure (one positive and one negative) for the given angle. Justify
your answers.
10.
2
3
11.
11
6
12.
-
2
15
Find, if possible, the complement and supplement of the angle in radian measure. You should recall
complement and supplement rules from Geometry, in degrees. It works the same for radians! Try it!
Name______________________________________
13.
3
4
C:
15.
14.
16.
12
S:
Worksheet on Radians
5
8
C:
S:

C:
Algebra 2
S:
2
9
C:
S: