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Precalculus Unit 2: Trigonometric Functions of Real Numbers
Review – Unit Circle and Trig Values
State whether the given points are on the unit circle, and show why algebraically.
 31 5 3 

,
2. 

9
9


5 2 6

1.  ,

7
7


Find the missing coordinate of P, using the fact that P lies on the unit circle in the given
quadrant.

2 10 
 Quadrant III
4. P x,

11


 2 
3. P  , y  Quadrant II
 5 
Find the terminal point Px, y  on the unit circle determined by the given value of t.
5. t 
8. t 

2
2
3
6. t 
11
6
7. t  3
9. t 
43
6
10. t  
3
4
Find the reference number for each value of t.
5
4
11. t 
17
3
12. t  
14. t 
7
6
15. t  3.92
13. t 
28
15
Find the exact value of the trigonometric function at the given real number.
16. sin
11
6
17. cos
29
6
 7 
21. sin  

 4 
20. cos
5
3
18. tan 3 
22. tan

3
 7 
19. tan 

 12 
 5 
23. tan  
 6 
 9 40 
Given the terminal point P ,  as determined by the real number t, find:
 41 41 
24. sin t
25. cos t
26. tan t
Find the sign of the given expression if the terminal point determined by t is in the given
quadrant.
27. sin t Quad III
28. sin t Quad II
29. cos t Quad II
30. cos t Quad IV
31. tan t Quad IV
32. tan t Quad III
35
and the terminal point is in Quadrant II, find the value of the other
37
five trigonometric functions.
33. Given sin t 
Answer Key
49
 1 Point is on circle
49
106
 1 Point is not on circle
2.
81
21
3. y 
25
9
4. x  
11
1.
5.
0,1
 3 1
, 
6. 
2
2

7.  1,0
 1 3

8.   ,

2
2



3 1
, 
9.  
2
2


2
2

,
10.  

2
2



11.
3

12.
4
2
13.
15

14.
6
15. 0.78
16. 
1
2
1
2
18. 0
19. undefined
3
20. 
2
17.
21.
2
2
22.
3
23. 
3
3
40
41
9
25.
41
24.
26.
40
9
27. negative
28. negative
29. negative
30. positive
31. positive
32. positive
35
37
12
cos t = 
37
35
tan t = 
12
33. sin t =
37
35
37
sec t = 
12
12
cot t = 
35
csc t =