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4-3 Part I
NAME:__________________________
Review
DATE:_______
Find the RATIO of the trig function indicated. Do NOT find the actual measure of the angle!
1.
2.
3.
4.
Use the given point on the terminal side of the angle  to find the trigonometric function indicated.
5.
6.
7.
Draw the reference triangle. Find the EXACT value of the trig ratio for .
8. sin  for �2, √5�
9. csc  for (−4, 3)
10. sec  for �2√3, −2�
Let  be an angle in standard position. In which quadrant or quadrants can  lie under the given conditions?
11. csc  is negative
12. sin  > 0
13. cos  and sin  have the same sign
14. cos  is negative and tan  is positive
Draw the reference triangle. Find the EXACT value of the trig ratio for .
12
5

15. Given cot  = − 5 in quadrant II.
16. Given csc  = 4 where 2 <  < .
Find sin .
Find tan .
17. Given cos  =
Find sin .
√3
4
where
3
2
<  < 2.
18. Given sec  = −
Find tan .
15
9
where  <  <
3
2
.
ANSWERS TO 4-3 Part I CORRECTIVE ASSIGNMENTS
1. √2
5.
9.
√11
− 6
5
3
13. I and III
17. −
4
2.
√13
4
7
6. − 12
10.
2√3
11. III and IV
3
12
9
65
7. −2
15.
14. III
18.
22√5
3.
3
4
=3
5
13
4.
8.
13√22
44
√5
3
12. I and II
4
16. − 3
4-3 Part II
NAME:__________________________
Review
DATE:_______
Find the reference angle.
1. 321°
2. 288°
3. −137°
4. 125°
5. −214°
6. −308°
7. 248°
8. 172°
Find the exact value.
9. sin 30°
10. cos 60°
11. tan 135°
12. sin 150°
13. cos 225°
14. tan 150°
15. sin(−330)°
16. cos(−135) °
17. tan(−315)°
18. csc(−270)°
19. sec 180°
20. cot 90 °
Find the exact value.

21. sin 4
22. cos 6
25. cos 
26. tan
29. tan(−
3
4
)

23. tan
√3
2
3
4
27. sin(−

31. sec 2
32. cot
35. tan  = √3
36. sin  =
39. tan  = −1
40. sin  = − 2
43. csc  = − 1
44. sec  = undefined
4
30. csc 2
2
41. cos  =
24. sin
3
7
If ° ≤  ≤ °, then find 
1
√2
34. cos  = 2
33. sin  =
37. sin  = 0
2
38. cos  = −
42. cot  = 1
√2
2
5
)
3
28. cos(−
11
6
)
3
4
√3
2
1
45. Find all six trig functions. Fill in the table.
radians


 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
46. Find all six trig functions. Fill in the table.
radians

−

47. Find all six trig functions. Fill in the table.
radians


ANSWERS TO CORRECTIVE ASSIGNMENT 4-3 Part II
1. 39°
2. 72°
3. 43°
4. 55°
5. 34°
17. 1
18. 1
19. −1
20. 0
21.
9.
1
10.
2
25. −1
33. 45°, 135°
1
26. −1
37. 0°/360°, 180°
41. 30°, 330°
45.
sin cos tan
csc
−
√3
2
1
2
−√3
11. −1
2
−
2√3
3
27. −
12.
√3
2
28.
34. 60°, 300°
38. 135°, 225°
42. 45°, 225°
46.
sec cot
sin
2
−
√3
3
−
√2
2
1
13. −
2
√3
2
√2
2
6. 52°
√2
2
14.
22.
29. 1
√3
3
√3
2
35. 60°, 240°
cos
tan
csc
sec
cot
√2
2
−1
−√2
√2
−1
8. 8°
23. −√3
24.
15.
30.undefined
39. 135°, 315°
43. 270°
7. 68°
1
16. −
2
31. 1
36. 60°, 120°
47.
sin
1
2
cos
−
√3
2
32. −1
40. 210°, 330°
44. 90°, 270°
tan
−
√3
3
csc
2
sec
−
√2
2
√2
2
2√3
3
cot
−√3
4-3 Part III
NAME:__________________________
Review
DATE:_______
EXACT VALUE = TABLE
Use the table to find the EXACT value.
3
1. csc 210°
2. sin
3. cot �−
4
5
5. sin 330°
6. sin
9. csc −120°
10. cos −1260°
5
6
�
4. sec(−180°)
25
7. tan 1125°
8. cot −
11. sec −1050°
12. tan
Use the table to find the angle where ° ≤  ≤ °.
√3
14. csc  = √2
13. cos  = −
15. sec  = undefined
16. sin  =
17. csc  = −1
18. csc  =
19. cos  = 0
20. cot  = √3
21. csc  = −2
22. sec  = −
23. tan  = −√3
24. cot  =
4
2
2√3
3
2√3
3
6
3
2
√2
2
√3
3
APPROXIMATE VALUE = CALCULATOR
Round to the nearest hundredth!
Use the calculator to find the APPROXIMATE value of each.
25. csc 70°
26. cot −115°
27. sec 140°
5
29. sin 18

33. csc 11
7
28. sin 56°
4
30. tan − 12
31. cot
23
32. cot
34. sec −214°
35. csc
5
36. sin 4°
25
7
5
Use the calculator to find each angle where ° ≤  ≤ °. Round to the nearest hundredth.
37. cos  = −0.788
38. sec  = 1.236
39. tan  = 0.487732
40. sec  = −1.13257
41. cot  = −0.9004
42. csc  = 1.28
43. sin  = −0.35
44. tan  = −1.81
45. csc  = −1.92
ANSWERS TO 4-3 Part III CORRECTIVE ASSIGNMENT
1. −2
6. −
11.
√2
2
2√3
3
16. 45°, 135°
21. 210°, 330°
26. 0.47
31. −3.89
36. 0.07
41. 132°, 312°
√2
2
2.
7. 1
12. undefined
17.
22.
27.
32.
37.
42.
270°
150°, 210°
−1.31
−1.38
142°, 218°
51.38°, 128.62°
3. √3
4. −1
13. 150°, 210°
14. 45°, 135°
8. −√3
18.
23.
28.
33.
60°, 120°
120°, 300°
0.83
3.55
9. −
2√3
3
19. 90°, 270°
24. 60°, 240°
29. 1.06
1
5. − 2
10. −1
15. 90°, 270°
20. 30°, 210°
25. 1.06
30. 3.73
35. 1.28
34. −1.21
38. 36°, 324°
39. 26°, 206°
40. 152°, 208°
43. 200.49°, 339.51° 44. 118.92°, 298.92° 45. 211.39°, 328.61°

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