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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 𝜃 to find the trigonometric function indicated.
5.
6.
7.
Draw the reference triangle. Find the EXACT value of the trig ratio for 𝜽.
8. sin 𝜃 for �2, √5�
9. csc 𝜃 for (−4, 3)
10. sec 𝜃 for �2√3, −2�
Let 𝜽 be an angle in standard position. In which quadrant or quadrants can 𝜽 lie under the given conditions?
11. csc 𝜃 is negative
12. sin 𝜃 > 0
13. cos 𝜃 and sin 𝜃 have the same sign
14. cos 𝜃 is negative and tan 𝜃 is positive
Draw the reference triangle. Find the EXACT value of the trig ratio for 𝜽.
12
5
𝜋
15. Given cot 𝜃 = − 5 in quadrant II.
16. Given csc 𝜃 = 4 where 2 < 𝜃 < 𝜋.
Find sin 𝜃.
Find tan 𝜃.
17. Given cos 𝜃 =
Find sin 𝜃.
√3
4
where
3𝜋
2
< 𝜃 < 2𝜋.
18. Given sec 𝜃 = −
Find tan 𝜃.
15
9
where 𝜋 < 𝜃 <
3𝜋
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.
𝜋
21. sin 4
22. cos 6
25. cos 𝜋
26. tan
29. tan(−
3𝜋
4
)
𝜋
23. tan
√3
2
3𝜋
4
27. sin(−
𝜋
31. sec 2𝜋
32. cot
35. tan 𝜃 = √3
36. sin 𝜃 =
39. tan 𝜃 = −1
40. sin 𝜃 = − 2
43. csc 𝜃 = − 1
44. sec 𝜃 = undefined
4
30. csc 2
2
41. cos 𝜃 =
24. sin
3
7𝜋
If 𝟎° ≤ 𝜽 ≤ 𝟑𝟑𝟑°, then find 𝜽
1
√2
34. cos 𝜃 = 2
33. sin 𝜃 =
37. sin 𝜃 = 0
2𝜋
38. cos 𝜃 = −
42. cot 𝜃 = 1
√2
2
5𝜋
)
3
28. cos(−
11𝜋
6
)
3𝜋
4
√3
2
1
45. Find all six trig functions. Fill in the table.
radians
𝟓𝟓
𝟑
𝐬𝐬𝐬 𝜽
𝐜𝐜𝐜 𝜽
𝐭𝐭𝐭 𝜽
𝐜𝐜𝐜 𝜽
𝐬𝐬𝐬 𝜽
𝐜𝐜𝐜 𝜽
𝐬𝐬𝐬 𝜽
𝐜𝐜𝐜 𝜽
𝐭𝐭𝐭 𝜽
𝐜𝐜𝐜 𝜽
𝐬𝐬𝐬 𝜽
𝐜𝐜𝐜 𝜽
𝐬𝐬𝐬 𝜽
𝐜𝐜𝐜 𝜽
𝐭𝐭𝐭 𝜽
𝐜𝐜𝐜 𝜽
𝐬𝐬𝐬 𝜽
𝐜𝐜𝐜 𝜽
46. Find all six trig functions. Fill in the table.
radians
𝝅
−
𝟒
47. Find all six trig functions. Fill in the table.
radians
𝟓𝟓
𝟔
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.
3𝜋
1. csc 210°
2. sin
3. cot �−
4
5𝜋
5. sin 330°
6. sin
9. csc −120°
10. cos −1260°
5𝜋
6
�
4. sec(−180°)
25𝜋
7. tan 1125°
8. cot −
11. sec −1050°
12. tan
Use the table to find the angle where 𝟎° ≤ 𝜽 ≤ 𝟑𝟑𝟑°.
√3
14. csc 𝜃 = √2
13. cos 𝜃 = −
15. sec 𝜃 = undefined
16. sin 𝜃 =
17. csc 𝜃 = −1
18. csc 𝜃 =
19. cos 𝜃 = 0
20. cot 𝜃 = √3
21. csc 𝜃 = −2
22. sec 𝜃 = −
23. tan 𝜃 = −√3
24. cot 𝜃 =
4
2
2√3
3
2√3
3
6
3𝜋
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°
5𝜋
29. sin 18
𝜋
33. csc 11
7𝜋
28. sin 56°
4𝜋
30. tan − 12
31. cot
23𝜋
32. cot
34. sec −214°
35. csc
5𝜋
36. sin 4°
25
7
5
Use the calculator to find each angle where 𝟎° ≤ 𝜽 ≤ 𝟑𝟑𝟑°. Round to the nearest hundredth.
37. cos 𝜃 = −0.788
38. sec 𝜃 = 1.236
39. tan 𝜃 = 0.487732
40. sec 𝜃 = −1.13257
41. cot 𝜃 = −0.9004
42. csc 𝜃 = 1.28
43. sin 𝜃 = −0.35
44. tan 𝜃 = −1.81
45. csc 𝜃 = −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°