Unit Circle Flashcards: 16 Angles, Radians & Exact Coordinates
Master 16 standard unit-circle positions with 64 two-way cards for degrees, radians, and exact (cos θ, sin θ) coordinates.
Par šo kavu
Unit Circle Flashcards
Master the 16 unique standard positions in 0 ≤ θ < 2π with 64 exact-answer cards. Every card uses the single tag unit-circle.
What the cards practice
- 16 degree-to-radian cards convert each standard degree measure to its exact radian measure.
- 16 radian-to-degree cards retrieve the reverse conversion.
- 16 angle-to-coordinate cards show degrees and radians together and ask for the exact ordered pair (cos θ, sin θ).
- 16 coordinate-to-angle cards ask for the unique radian angle in [0, 2π) and give the equivalent degree measure as brief reference context.
Learning sequence
The fixed sequence has four deterministic passes. The first pass moves progressively from 0° through 330°. The next three passes interleave quadrants, axes, and reference-angle families to avoid long predictable numerical runs. In both coordinate-bearing passes, sign variants from the same absolute-coordinate family recur every four positions and are never adjacent. Direct degree/radian reverse pairs are 24–40 positions apart; direct angle/coordinate reverse pairs are 17–45 positions apart.
Scope and exclusions
The endpoint at 360° = 2π is excluded because it repeats the coordinates of 0; omitting it keeps coordinate-to-angle recall unique in [0, 2π). Reverse single-function prompts such as “which angle has cosine 1/2?” are excluded because sine and cosine values repeat at multiple standard angles. Nonstandard angles are excluded because they require calculation rather than recall of the standard unit-circle positions.
The deck also excludes tangent, cotangent, secant, cosecant, negative and coterminal angles, proofs, generic definitions, calculator approximations, and decimal coordinates. Cards use exact Unicode math in ordinary Markdown instead of renderer-specific syntax or images, so every client and indexed text surface can read them directly.
Related guides
- How to use flashcards for math
- How to use flashcards for AP Calculus AB and BC
- How to use interleaving with flashcards
- How to make better flashcards
Source and license
Authoritative source: OpenStax, Algebra and Trigonometry, first edition, revision AT-2015-002(03/17)-BW, by Jay Abramson, §7.3 Unit Circle, printed pages 604–616 (PDF pages 622–634); original publication year 2015.
© 2017 Rice University. Download for free at https://openstax.org/details/books/algebra-and-trigonometry.
The textbook source is licensed under CC BY 4.0. This deck restates standard mathematical facts as original flashcard prompts and answers; every value was independently computed and verified, and no OpenStax prose, figure, or media was copied. This adapted deck, its metadata, and its original cover are also licensed under CC BY 4.0. Flashcards Open Source App is not affiliated with or endorsed by OpenStax, Study.com, Pearson, or Buffalo State University.
Kartītes šajā kavā
1. kartīte
Jautājums
Convert 0° to radians in [0, 2π).
Atbilde
0
2. kartīte
Jautājums
Convert 30° to radians in [0, 2π).
Atbilde
π/6
3. kartīte
Jautājums
Convert 45° to radians in [0, 2π).
Atbilde
π/4
4. kartīte
Jautājums
Convert 60° to radians in [0, 2π).
Atbilde
π/3
5. kartīte
Jautājums
Convert 90° to radians in [0, 2π).
Atbilde
π/2
6. kartīte
Jautājums
Convert 120° to radians in [0, 2π).
Atbilde
2π/3
7. kartīte
Jautājums
Convert 135° to radians in [0, 2π).
Atbilde
3π/4
8. kartīte
Jautājums
Convert 150° to radians in [0, 2π).
Atbilde
5π/6
9. kartīte
Jautājums
Convert 180° to radians in [0, 2π).
Atbilde
π
10. kartīte
Jautājums
Convert 210° to radians in [0, 2π).
Atbilde
7π/6
11. kartīte
Jautājums
Convert 225° to radians in [0, 2π).
Atbilde
5π/4
12. kartīte
Jautājums
Convert 240° to radians in [0, 2π).
Atbilde
4π/3
13. kartīte
Jautājums
Convert 270° to radians in [0, 2π).
Atbilde
3π/2
14. kartīte
Jautājums
Convert 300° to radians in [0, 2π).
Atbilde
5π/3
15. kartīte
Jautājums
Convert 315° to radians in [0, 2π).
Atbilde
7π/4
16. kartīte
Jautājums
Convert 330° to radians in [0, 2π).
Atbilde
11π/6
17. kartīte
Jautājums
For the unit-circle position 30° = π/6, give the exact ordered pair (cos θ, sin θ).
Atbilde
(√3/2, 1/2)
18. kartīte
Jautājums
For the unit-circle position 225° = 5π/4, give the exact ordered pair (cos θ, sin θ).
Atbilde
(−√2/2, −√2/2)
19. kartīte
Jautājums
For the unit-circle position 120° = 2π/3, give the exact ordered pair (cos θ, sin θ).
Atbilde
(−1/2, √3/2)
20. kartīte
Jautājums
For the unit-circle position 270° = 3π/2, give the exact ordered pair (cos θ, sin θ).
Atbilde
(0, −1)
21. kartīte
Jautājums
For the unit-circle position 150° = 5π/6, give the exact ordered pair (cos θ, sin θ).
Atbilde
(−√3/2, 1/2)
22. kartīte
Jautājums
For the unit-circle position 315° = 7π/4, give the exact ordered pair (cos θ, sin θ).
Atbilde
(√2/2, −√2/2)
23. kartīte
Jautājums
For the unit-circle position 240° = 4π/3, give the exact ordered pair (cos θ, sin θ).
Atbilde
(−1/2, −√3/2)
24. kartīte
Jautājums
For the unit-circle position 0° = 0, give the exact ordered pair (cos θ, sin θ).
Atbilde
(1, 0)
25. kartīte
Jautājums
For the unit-circle position 210° = 7π/6, give the exact ordered pair (cos θ, sin θ).
Atbilde
(−√3/2, −1/2)
26. kartīte
Jautājums
For the unit-circle position 45° = π/4, give the exact ordered pair (cos θ, sin θ).
Atbilde
(√2/2, √2/2)
27. kartīte
Jautājums
For the unit-circle position 300° = 5π/3, give the exact ordered pair (cos θ, sin θ).
Atbilde
(1/2, −√3/2)
28. kartīte
Jautājums
For the unit-circle position 90° = π/2, give the exact ordered pair (cos θ, sin θ).
Atbilde
(0, 1)
29. kartīte
Jautājums
For the unit-circle position 330° = 11π/6, give the exact ordered pair (cos θ, sin θ).
Atbilde
(√3/2, −1/2)
30. kartīte
Jautājums
For the unit-circle position 135° = 3π/4, give the exact ordered pair (cos θ, sin θ).
Atbilde
(−√2/2, √2/2)
31. kartīte
Jautājums
For the unit-circle position 60° = π/3, give the exact ordered pair (cos θ, sin θ).
Atbilde
(1/2, √3/2)
32. kartīte
Jautājums
For the unit-circle position 180° = π, give the exact ordered pair (cos θ, sin θ).
Atbilde
(−1, 0)
33. kartīte
Jautājums
Convert π/2 radians to degrees in [0°, 360°).
Atbilde
90°
34. kartīte
Jautājums
Convert 7π/6 radians to degrees in [0°, 360°).
Atbilde
210°
35. kartīte
Jautājums
Convert π/4 radians to degrees in [0°, 360°).
Atbilde
45°
36. kartīte
Jautājums
Convert 2π/3 radians to degrees in [0°, 360°).
Atbilde
120°
37. kartīte
Jautājums
Convert 3π/2 radians to degrees in [0°, 360°).
Atbilde
270°
38. kartīte
Jautājums
Convert π/6 radians to degrees in [0°, 360°).
Atbilde
30°
39. kartīte
Jautājums
Convert 5π/4 radians to degrees in [0°, 360°).
Atbilde
225°
40. kartīte
Jautājums
Convert 5π/3 radians to degrees in [0°, 360°).
Atbilde
300°
41. kartīte
Jautājums
Convert 0 radians to degrees in [0°, 360°).
Atbilde
0°
42. kartīte
Jautājums
Convert 5π/6 radians to degrees in [0°, 360°).
Atbilde
150°
43. kartīte
Jautājums
Convert 7π/4 radians to degrees in [0°, 360°).
Atbilde
315°
44. kartīte
Jautājums
Convert π/3 radians to degrees in [0°, 360°).
Atbilde
60°
45. kartīte
Jautājums
Convert π radians to degrees in [0°, 360°).
Atbilde
180°
46. kartīte
Jautājums
Convert 11π/6 radians to degrees in [0°, 360°).
Atbilde
330°
47. kartīte
Jautājums
Convert 3π/4 radians to degrees in [0°, 360°).
Atbilde
135°
48. kartīte
Jautājums
Convert 4π/3 radians to degrees in [0°, 360°).
Atbilde
240°
49. kartīte
Jautājums
In [0, 2π), which unit-circle angle has exact coordinates (cos θ, sin θ) = (−1, 0)?
Atbilde
π
Equivalent degree measure: 180°.
50. kartīte
Jautājums
In [0, 2π), which unit-circle angle has exact coordinates (cos θ, sin θ) = (√3/2, 1/2)?
Atbilde
π/6
Equivalent degree measure: 30°.
51. kartīte
Jautājums
In [0, 2π), which unit-circle angle has exact coordinates (cos θ, sin θ) = (√2/2, −√2/2)?
Atbilde
7π/4
Equivalent degree measure: 315°.
52. kartīte
Jautājums
In [0, 2π), which unit-circle angle has exact coordinates (cos θ, sin θ) = (−1/2, √3/2)?
Atbilde
2π/3
Equivalent degree measure: 120°.
53. kartīte
Jautājums
In [0, 2π), which unit-circle angle has exact coordinates (cos θ, sin θ) = (1, 0)?
Atbilde
0
Equivalent degree measure: 0°.
54. kartīte
Jautājums
In [0, 2π), which unit-circle angle has exact coordinates (cos θ, sin θ) = (−√3/2, −1/2)?
Atbilde
7π/6
Equivalent degree measure: 210°.
55. kartīte
Jautājums
In [0, 2π), which unit-circle angle has exact coordinates (cos θ, sin θ) = (−√2/2, √2/2)?
Atbilde
3π/4
Equivalent degree measure: 135°.
56. kartīte
Jautājums
In [0, 2π), which unit-circle angle has exact coordinates (cos θ, sin θ) = (1/2, −√3/2)?
Atbilde
5π/3
Equivalent degree measure: 300°.
57. kartīte
Jautājums
In [0, 2π), which unit-circle angle has exact coordinates (cos θ, sin θ) = (0, −1)?
Atbilde
3π/2
Equivalent degree measure: 270°.
58. kartīte
Jautājums
In [0, 2π), which unit-circle angle has exact coordinates (cos θ, sin θ) = (−√3/2, 1/2)?
Atbilde
5π/6
Equivalent degree measure: 150°.
59. kartīte
Jautājums
In [0, 2π), which unit-circle angle has exact coordinates (cos θ, sin θ) = (√2/2, √2/2)?
Atbilde
π/4
Equivalent degree measure: 45°.
60. kartīte
Jautājums
In [0, 2π), which unit-circle angle has exact coordinates (cos θ, sin θ) = (−1/2, −√3/2)?
Atbilde
4π/3
Equivalent degree measure: 240°.
61. kartīte
Jautājums
In [0, 2π), which unit-circle angle has exact coordinates (cos θ, sin θ) = (0, 1)?
Atbilde
π/2
Equivalent degree measure: 90°.
62. kartīte
Jautājums
In [0, 2π), which unit-circle angle has exact coordinates (cos θ, sin θ) = (√3/2, −1/2)?
Atbilde
11π/6
Equivalent degree measure: 330°.
63. kartīte
Jautājums
In [0, 2π), which unit-circle angle has exact coordinates (cos θ, sin θ) = (−√2/2, −√2/2)?
Atbilde
5π/4
Equivalent degree measure: 225°.
64. kartīte
Jautājums
In [0, 2π), which unit-circle angle has exact coordinates (cos θ, sin θ) = (1/2, √3/2)?
Atbilde
π/3
Equivalent degree measure: 60°.
64 kartītes
Unit Circle Flashcards: 16 Angles, Radians & Exact Coordinates
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