1.4 Radians, Arc Length and Angular Speed Solutions
On the given unit circle mark the points determined by the given real numbers.

3
3
11
17
1. A)
B)
C)
D) 
E)
F)
4
2
4
4
4
11
3
4
4

4
17
4

3
2
2. A)

6
B)
2
3
2
3
C)
7
6
D)
10
6
E)
14
6
F)
14
6

6
7
6
23
6
10
6
23
6
Find a positive and a negative angle that are coterminal with the given angle.

7
2
3.
4.
5. 
6
4
3

4

4
9
4
 2 
 2  
7
4
7
19
 2 
6
6

2
4
 2 
3
3
7
5
 2  
6
6

2
8
 2  
3
3
Find the complement and supplement of each given angle.

3
6.
7.
8
3
complement
complement

2


3


3 2 


6
6
6
2

3


6 
5
 
2 12 12 12 12
supplement
3 4 3 



8
8
8
8
supplement
supplement



12
complement
8.
6 2 4
2



6
6
6
3

3 8 3 5



8
8
8
8




12


12 
11
 
12 12
12
Convert to radian measure. Leave the answers in terms of 
9. 750
750 x

180
11.  1800
10. 2000
0

5
12
2000 x

180
0

10
9
 1800 x
12.  3400

180
0
Convert to radian measure. Round your answer to 2 decimal places
13. 2400
14.  600
15. 117.80
16. 3450
 
 3400 x

180
0
 
17
9
17. 950
You need to use your calculator here to get the approximation. For each problem just enter the degree measure
in your calculator and then multiply by  and divide by 180.
13. 4.19 radians
14. -1.05 radians
15. 2.06 radians
16. 6.02 radians
17. 1.66 radians
Convert to degree measure. Round your answer to 2 decimal places
3
5
2
18. 
19. 8
20. 1
21. 2.347
22.
23.
4
4
7
You need to use your calculator here to get the approximation. For each problem just enter the degree measure
in your calculator and then multiply by180 and divide by  .
18. 1350
19. 14400
20. 57.300
21. 134.47 0
22. 2250
23. 51.430
24. A flywheel with a 15cm diameter is rotating at a rate of 7 radians/sec. What is the linear speed of a point
on its rim in centimeters per minute?
v  r
Since the diameter is given as 15 cm we know that the radius will be 7.5 cm.
 7
radians
radians 60sec
radians
7
x
 420
sec
sec
1min
min
radians 
cm

v  r   7.5cm   420
  3150
min 
min

25. The earth has a radius of about 4000 miles and rotates one revolution every 24 hours. What is the linear
speed of a point on the equator in miles per hour?
v  r
1 revolution = 2 radians
r  4000mi


t

2 radians  radians

24hrs
12 hr
mi
  radians  1000 mi
v  r   4000mi  
 1047.2

3 hr
hr
 12 hr 