Radians and the
Unit Circle
Algebra 2 Honors
Trig Homework
Homework Packet
Name the quadrant of 𝜽.
1. sin 𝜃 < 0, cos 𝜃 > 0
Name__________________
Assignment: F4
2.
sin 𝜃 < 0, cos 𝜃 < 0
3.
sin 𝜃 > 0, cos 𝜃 > 0
6.
csc 𝜃 < 0, cos 𝜃 < 0
4.
sin 𝜃 > 0, cos 𝜃 < 0
5.
sec 𝜃 > 0, tan 𝜃 < 0
7.
cos 𝜃 < 0, 180° < 𝜃 < 360°
8.
tan 𝜃 > 0, 90° < 𝜃 < 270°
Express each degree measure in radians. Leave your answer in terms of 𝝅.
9. 45°
10. 30°
11. 60°
12. 270°
13. −120°
16. 495°
14. 135°
15. −330°
Express each degree measure in radians. Give answers to the nearest hundredth of a radian.
17. 10°
18. −50°
19. 300°
20. −174°
Express each radian measure in degrees. Leave your answers in terms of 𝝅 when appropriate.
𝜋
4𝜋
7𝜋
−7𝜋
21. − 2
22. 3
23. − 6
24. 2
25.
3𝜋
26. 4
27. -2
1
28. − 2
Express each radian measure in degrees. Give answers to the nearest tenth of a degree.
29. 3
30. 0.4
31. -1.6
32. -1.5
Find the exact value of all six trigonometric functions at each quadrantal value.
𝜋
33. 0𝜋
34. 2
𝜋
35. – 𝜋
36. − 2
Find the measure of the reference angle 𝜽′ of the given angle 𝜽.
37. 𝜃 = 233°
38. 𝜃 = −205°
39. 𝜃 = 134.7°
41. 𝜃 =
7𝜋
4
42. 𝜃 = −
5𝜋
6
43. 𝜃 =
18𝜋
5
40. 𝜃 = −184.1°
44. 𝜃 = −
Write each of the following as a function of an acute angle.
45. cos 216°
46. sec(−106° )
47. cot 287.1°
11𝜋
3
48. cos(−221.9° )
First, give the quadrant of angle 𝜽. Then find the five other trigonometric functions of 𝜽. Give answers
involving radicals in simplest radical form.
8
13
49. cos 𝜃 = − , 0° < 𝜃 < 180°
50. sec 𝜃 = , sin 𝜃 < 0
17
5
Find the exact value of the trig function.
𝜋
3𝜋
51. cos 3
52. cot − 4
53. sin 4
54. sec
55. cos 330°
57. tan 135°
58. sin −60°
59. csc
11𝜋
6
63. sec 315°
𝜋
56. csc 240°
60. tan
8𝜋
3
61. cot −
64. sin 300°
5𝜋
6
65. tan −150°
62. cos
3𝜋
4
15𝜋
4
66. csc 480°
For some number s, the point P is s units from A(1, 0) along the unit circle 𝒙𝟐 + 𝒚𝟐 = 𝟏. Find the exact
values of the six trigonometric functions of s.
5
12
67. (− 13 , 13)
√7
3
68. ( 4 , 4)
Verify the identify 𝐬𝐢𝐧𝟐 𝜽 + 𝐜𝐨𝐬 𝟐 𝜽 = 𝟏 for the given value of 𝜽.
3𝜋
7𝜋
70. 4
71. 6
2
69. (− 5 , −
72. 0.7
√21
)
5
Answers
1. Q4
2.
Q3
3.
Q1
4.
Q2
5.
Q4
Q3
9.
𝜋
4
10.
𝜋
6
14.
3𝜋
4
15. −
6.
Q3
7.
Q3
8.
11.
𝜋
3
12.
3𝜋
2
13. −
16.
11𝜋
4
17. 0.17
18. -0.87
19. 5.24
20. -3.04
22. 240°
23. −210°
24. −630°
25. 540°
29. 171.9°
30. 22.9°
21. −90°
26.
720°
𝜋
360°
𝜋
27. −
31. −91.7°
28. −
2𝜋
3
90°
𝜋
11𝜋
6
32. −85.9°
33. sin(0𝜋) = 0, cos(0𝜋) = 1, tan(0𝜋) = 0, csc(0𝜋) = 𝑢𝑛𝑑𝑒𝑓., sec(0𝜋) = 1, cot(0𝜋) = 𝑢𝑛𝑑𝑒𝑓.
𝜋
2
𝜋
2
𝜋
2
𝜋
2
𝜋
2
𝜋
2
34. sin ( ) = 1, cos ( ) = 0, tan ( ) = 𝑢𝑛𝑑𝑒𝑓., csc ( ) = 1, sec ( ) = 𝑢𝑛𝑑𝑒𝑓, cot ( ) = 0
35. sin(−𝜋) = 0, cos(−𝜋) = −1, tan(−𝜋) = 0, csc(−𝜋) = 𝑢𝑛𝑑𝑒𝑓., sec(−𝜋) = −1, cot(−𝜋) = 𝑢𝑛𝑑𝑒𝑓.
𝜋
𝜋
𝜋
𝜋
𝜋
𝜋
36. sin (− 2 ) = −1, cos (− 2 ) = 0, tan (− 2 ) = 𝑢𝑛𝑑𝑒𝑓., csc (− 2 ) = −1, sec (− 2 ) = 𝑢𝑛𝑑𝑒𝑓, cot (− 2 ) = 0
37. 53°
42.
38. 25°
𝜋
6
43.
47. − cot 72.9°
39. 45.3°
2𝜋
5
44.
𝜋
3
15
,
17
tan 𝜃 = −
12
15
,
8
17
csc 𝜃 = 15 , sec 𝜃 = −
5
50. 𝑄𝑢𝑎𝑑𝑟𝑎𝑡𝑛𝑡 4: sin 𝜃 = − 13 , cos 𝜃 = 13 , tan 𝜃 = −
1
2
56. −
2√3
3
53.
57. −1
58. −
√3
2
62.
66.
2√3
3
67. sin 𝜃 = 13 , cos 𝜃 = − 13 , tan 𝜃 = −
63.
12
68. sin 𝜃 = 4 , cos 𝜃 =
√21
,
5
46. − sec 74°
√7
,
4
tan 𝜃 =
2
3√7
,
7
√2
2
csc 𝜃 = 3 , sec 𝜃 =
21
cos 𝜃 = − 5 , tan 𝜃 = √2 , csc 𝜃 = −
=−
8
15
5
12
,
5
55.
59. −2
60. −√3
√3
2
65.
13
csc 𝜃 = 12 , sec 𝜃 = −
4√7
, cot 𝜃
7
5√21
,
21
√3
2
54. −√2
64. −
5
4
17
, cot 𝜃
8
13
√3
3
69. sin 𝜃 = −
45. − cos 36°
csc 𝜃 = − 12 , cot 𝜃 = − 12
√2
2
52. 1
√2
2
12
,
5
61.
3
41.
48. − cos 41.9°
49. 𝑄𝑢𝑎𝑑𝑟𝑎𝑡𝑛𝑡 2: sin 𝜃 =
51.
𝜋
4
40. 4.1°
=
√7
3
5
sec 𝜃 = − 2 , cot 𝜃 =
2√21
21
√3
3
13
, cot 𝜃
5
5
= − 12