9.2 Reference and Special Angles
Write your
questions here!
NOTES
Reference Anglessin 40°
sin 140°
sin 220°
sin 320°
Find the Reference Angle
23𝜋
12
−100°
SPECIAL ANGLES
FIND THE EXACT VALUE!
cos 120° =
tan 315° =
sin 210° =
sec 180° =
5𝜋
=
4
𝜋
cot =
4
sin
2𝜋
�=
3
3𝜋
sec
=
2
cos �−
Find all 6 trig functions
degrees
𝟑𝟑°
degrees
radians
𝐬𝐬𝐬 𝜽
𝐜𝐜𝐜 𝜽
𝐭𝐭𝐭 𝜽
𝐜𝐜𝐜 𝜽
𝐬𝐬𝐬 𝜽
𝐜𝐜𝐜 𝜽
- degree
- radian
radians
𝝅
𝟐
𝐬𝐬𝐬 𝜽
𝐜𝐜𝐜 𝜽
𝐭𝐭𝐭 𝜽
𝐜𝐜𝐜 𝜽
𝐬𝐬𝐬 𝜽
𝐜𝐜𝐜 𝜽
- degree
- radian
If 𝟎° ≤ 𝜽 ≤ 𝟑𝟑𝟑°, then find 𝜽
1
a. sin 𝜃 = 2
1
b. cos 𝜃 = 2
c. tan 𝜃 = −1
d. sin 𝜃 =
√3
2
e. cos 𝜃 = 0
f. cot 𝜃 = undefined
SUMMARY:
Now,
summarize
your notes
here!
PRACTICE
9.2 Reference and Special Angles
Find the reference angle.
1.
2.
3.
5. −130°
6. 230°
7. −
9. sin 90° =
10. cos 120° =
11. tan 45° =
15. sin 330° =
16. tan 315° =
17. cos 240° =
4.
13𝜋
8.
9
Find the exact value.
12. tan 120° =
18. sin(−225°) =
21. sec (180°) =
Find the exact value.
𝜋
30. sin
33. tan
4𝜋
3
5𝜋
4
7𝜋
4
19. cos (−240°) =
22. csc (−270°) =
𝜋
24. sin 2 =
27. cos
13. cos 225° =
=
=
=
𝜋
36. cos �− 3 � =
25. tan 4 =
𝜋
28. cos 6 =
31. cos
5𝜋
3
=
34. sin(−𝜋) =
𝜋
37. sec �− 2 � =
14. sin 135° =
20. tan (− 300°) =
23. cot (−315°) =
26. cos
3𝜋
32. sin
5𝜋
=
2
29. tan 𝜋 =
6
=
35. tan �−
38. sin �−
3𝜋
2
5𝜋
4
�=
�=
3𝜋
4
If 𝟎° ≤ 𝜽 ≤ 𝟑𝟑𝟑°, then find 𝜽
1
39. sin 𝜃 = 2
42. sin 𝜃 =
40. cos 𝜃
√2
2
43. cos 𝜃 = −
45. csc 𝜃 = 2
If 𝟎𝟎 ≤ 𝜽 ≤ 𝟐𝟐, then find 𝜽
√3
= 2
√3
=2
41. tan 𝜃 = −√3
√2
2
44. tan 𝜃 = −
46. sec 𝜃 = −2
√3
3
47. cot 𝜃 = undefined
If you like pictures of circles,
you can draw one here!
√2
=2
49. tan 𝜃 = 1
50. cos 𝜃
51. cos 𝜃 = − 2
52. tan 𝜃 = √3
53. cos 𝜃 = 0
54. csc 𝜃 = undefined
55. cot 𝜃 = − 1
56. sin 𝜃 = − 2
48. sin 𝜃
1
If you like pictures of circles,
you can draw one here!
1
57. Fill in the table below.
degrees
radians
𝟐𝟐𝟐°
𝐬𝐬𝐬 𝜽
𝐜𝐜𝐜 𝜽
𝐭𝐭𝐭 𝜽
𝐜𝐜𝐜 𝜽
𝐬𝐬𝐬 𝜽
𝐜𝐜𝐜 𝜽
- degree
- radian
𝐬𝐬𝐬 𝜽
𝐜𝐜𝐜 𝜽
𝐭𝐭𝐭 𝜽
𝐜𝐜𝐜 𝜽
𝐬𝐬𝐬 𝜽
𝐜𝐜𝐜 𝜽
- degree
- radian
58. Fill in the table below.
degrees
radians
−
𝟑𝟑
𝟒
59. Fill in the table below.
degrees
radians
𝐬𝐬𝐬 𝜽
−
1
2
𝐜𝐜𝐜 𝜽
√3
2
𝐭𝐭𝐭 𝜽
𝐜𝐜𝐜 𝜽
𝐬𝐬𝐬 𝜽
𝐜𝐜𝐜 𝜽
- degree
- radian
Skillz Review! Let’s put some Trig in our Algebra!
COMPLEX FRACTION aka FRACTION IN A FRACTION
2
 
3 =
6
 
5
secθ
=
tan θ
 1 


 cos x  =
 1 


 sin x 
ADD/SUBTRACT FRACTIONS
2 4
+ =
5 7
1
1
+ =
sin x 3
9.2 Reference and Special Angles
1. Find the reference angle.
tan θ − secθ =
APPLICATION
2. Find the exact value.
cos
7𝜋
=
6
3. Mr. Brust wants a table including every single special angle in a unit circle, but he is really lazy. On the back of
the page he filled in a table for quadrant I and then took a nap. Use his info to fill in the rest of the table and
quadrants II, III, and IV on the Unit Circle. Don’t do any math! Just use your knowledge of reference angles to
complete the table. You will need this table for the next section, so take your time and make it look pretty!
(+, +)
𝐬𝐬𝐬 𝜽
𝐜𝐜𝐜 𝜽
𝐭𝐭𝐭 𝜽
𝐜𝐜𝐜 𝜽
𝐬𝐬𝐬 𝜽
6
1
2
3
2
3
3
2
2 3
3
π
4
2
2
2
2
1
3
2
1
2
1
0
degrees
radians
0° / 360°
0π / 2π
30°
π
45°
60°
90°
π
3
π
2
0
1
0
3
Und
und
2
1
2
𝐜𝐜𝐜 𝜽
und
- degree
- radian
− 0° / − 360°
− 0π / − 2π
3
-330°
−
11π
6
1
-315°
−
7π
4
2 3
3
2
3
3
-300°
−
1
Und
0
-270°
−
5π
3
3π
2