Precalculus Unit 4 Day 9
Worksheet Unit Circle & Reference Angles #1(2013)
Name
Date
2-19-13
 It is recommended that you complete this worksheet by “visualizing” the unit circle and making a quick sketch.
 It is not recommended that you complete these problems by “staring” at the unit circle provided to you in class.
 You SHOULD however check your answers using the unit circle and/or your calculator for decimal approximations.
Read the recommendations above, then write the ordered pair associated with each given unit circle angle measure.
(Use exact simplified values.)
1. 
6.
3
2
2.
0
3.
2
3
4.
–
5.
4
3
7.

2
8.
7
4
9.
3
4
10.
7
6
Re-read the recommendations at the top of the page, then without a calculator, find the exact simplified values.
11.
 
sin  
3
16.
sin 
21.
cos 
 5 

 6 
13.
cos 
14.
sin 
cos 
  

 3 
18.
sin   
19.
sin  2 
23.
cos 
24.
12.
cos 
 3 

 4 
17.
 5 

 4 
22.


 5 

 6 
 3 

 4 
 4 

 3 
3 

 2 
15.
sin 
cos 
 2 

 3 
20.
cos 
 
cos   
2
25.
sin 


 11 

 6 
 7 

 6 
Precalculus Unit 4 Day 9
Worksheet Unit Circle & Reference Angles #2(2013)
Name
Date
2-19-13
 It is recommended that you complete this worksheet by “visualizing” the unit circle and making a quick sketch.
 It is not recommended that you complete these problems by “staring” at the unit circle provided to you in class.
 You SHOULD however check your answers using the unit circle and/or your calculator for decimal approximations.
In which quadrant does the terminal side lie? Determine the reference angle, β.
Sketch the angle in standard position to support your response.
1. 5
2.
35
6
3.
11
2
4.
10
3
5.
Write the ordered pair for each angle measure on the unit circle. Give exact value(s).
Use a coterminal angle and/or reference angle if the given angle is not between 0 and 2π.
Sketch the angle in standard position to support your response.
13
20
23
9
6.
7.
8.
9.
10.
2
3
6
4
201
4
15
6
Evaluate each trigonometric function without a calculator. Give exact simplified values.
Use a coterminal angle and/or reference angle if the given angle is not between 0 and 2π.
Sketch the angle in standard position to support your response.
11.
 
csc  
6
12.
 2 
cot 

 3 
13.
 4 
tan 

 3 
14.
tan  
15.
 7 
sec 

 6 
16.
csc   
17.
 5 
cot   
 3 
18.
 3 
sec  
 2 
19.
 
csc  
3
20.
 5 
tan   
 6 