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.
A pakliról
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.
Kártyák ebben a pakliban
1. kártya
Kérdés
Convert 0° to radians in [0, 2π).
Válasz
0
2. kártya
Kérdés
Convert 30° to radians in [0, 2π).
Válasz
π/6
3. kártya
Kérdés
Convert 45° to radians in [0, 2π).
Válasz
π/4
4. kártya
Kérdés
Convert 60° to radians in [0, 2π).
Válasz
π/3
5. kártya
Kérdés
Convert 90° to radians in [0, 2π).
Válasz
π/2
6. kártya
Kérdés
Convert 120° to radians in [0, 2π).
Válasz
2π/3
7. kártya
Kérdés
Convert 135° to radians in [0, 2π).
Válasz
3π/4
8. kártya
Kérdés
Convert 150° to radians in [0, 2π).
Válasz
5π/6
9. kártya
Kérdés
Convert 180° to radians in [0, 2π).
Válasz
π
10. kártya
Kérdés
Convert 210° to radians in [0, 2π).
Válasz
7π/6
11. kártya
Kérdés
Convert 225° to radians in [0, 2π).
Válasz
5π/4
12. kártya
Kérdés
Convert 240° to radians in [0, 2π).
Válasz
4π/3
13. kártya
Kérdés
Convert 270° to radians in [0, 2π).
Válasz
3π/2
14. kártya
Kérdés
Convert 300° to radians in [0, 2π).
Válasz
5π/3
15. kártya
Kérdés
Convert 315° to radians in [0, 2π).
Válasz
7π/4
16. kártya
Kérdés
Convert 330° to radians in [0, 2π).
Válasz
11π/6
17. kártya
Kérdés
For the unit-circle position 30° = π/6, give the exact ordered pair (cos θ, sin θ).
Válasz
(√3/2, 1/2)
18. kártya
Kérdés
For the unit-circle position 225° = 5π/4, give the exact ordered pair (cos θ, sin θ).
Válasz
(−√2/2, −√2/2)
19. kártya
Kérdés
For the unit-circle position 120° = 2π/3, give the exact ordered pair (cos θ, sin θ).
Válasz
(−1/2, √3/2)
20. kártya
Kérdés
For the unit-circle position 270° = 3π/2, give the exact ordered pair (cos θ, sin θ).
Válasz
(0, −1)
21. kártya
Kérdés
For the unit-circle position 150° = 5π/6, give the exact ordered pair (cos θ, sin θ).
Válasz
(−√3/2, 1/2)
22. kártya
Kérdés
For the unit-circle position 315° = 7π/4, give the exact ordered pair (cos θ, sin θ).
Válasz
(√2/2, −√2/2)
23. kártya
Kérdés
For the unit-circle position 240° = 4π/3, give the exact ordered pair (cos θ, sin θ).
Válasz
(−1/2, −√3/2)
24. kártya
Kérdés
For the unit-circle position 0° = 0, give the exact ordered pair (cos θ, sin θ).
Válasz
(1, 0)
25. kártya
Kérdés
For the unit-circle position 210° = 7π/6, give the exact ordered pair (cos θ, sin θ).
Válasz
(−√3/2, −1/2)
26. kártya
Kérdés
For the unit-circle position 45° = π/4, give the exact ordered pair (cos θ, sin θ).
Válasz
(√2/2, √2/2)
27. kártya
Kérdés
For the unit-circle position 300° = 5π/3, give the exact ordered pair (cos θ, sin θ).
Válasz
(1/2, −√3/2)
28. kártya
Kérdés
For the unit-circle position 90° = π/2, give the exact ordered pair (cos θ, sin θ).
Válasz
(0, 1)
29. kártya
Kérdés
For the unit-circle position 330° = 11π/6, give the exact ordered pair (cos θ, sin θ).
Válasz
(√3/2, −1/2)
30. kártya
Kérdés
For the unit-circle position 135° = 3π/4, give the exact ordered pair (cos θ, sin θ).
Válasz
(−√2/2, √2/2)
31. kártya
Kérdés
For the unit-circle position 60° = π/3, give the exact ordered pair (cos θ, sin θ).
Válasz
(1/2, √3/2)
32. kártya
Kérdés
For the unit-circle position 180° = π, give the exact ordered pair (cos θ, sin θ).
Válasz
(−1, 0)
33. kártya
Kérdés
Convert π/2 radians to degrees in [0°, 360°).
Válasz
90°
34. kártya
Kérdés
Convert 7π/6 radians to degrees in [0°, 360°).
Válasz
210°
35. kártya
Kérdés
Convert π/4 radians to degrees in [0°, 360°).
Válasz
45°
36. kártya
Kérdés
Convert 2π/3 radians to degrees in [0°, 360°).
Válasz
120°
37. kártya
Kérdés
Convert 3π/2 radians to degrees in [0°, 360°).
Válasz
270°
38. kártya
Kérdés
Convert π/6 radians to degrees in [0°, 360°).
Válasz
30°
39. kártya
Kérdés
Convert 5π/4 radians to degrees in [0°, 360°).
Válasz
225°
40. kártya
Kérdés
Convert 5π/3 radians to degrees in [0°, 360°).
Válasz
300°
41. kártya
Kérdés
Convert 0 radians to degrees in [0°, 360°).
Válasz
0°
42. kártya
Kérdés
Convert 5π/6 radians to degrees in [0°, 360°).
Válasz
150°
43. kártya
Kérdés
Convert 7π/4 radians to degrees in [0°, 360°).
Válasz
315°
44. kártya
Kérdés
Convert π/3 radians to degrees in [0°, 360°).
Válasz
60°
45. kártya
Kérdés
Convert π radians to degrees in [0°, 360°).
Válasz
180°
46. kártya
Kérdés
Convert 11π/6 radians to degrees in [0°, 360°).
Válasz
330°
47. kártya
Kérdés
Convert 3π/4 radians to degrees in [0°, 360°).
Válasz
135°
48. kártya
Kérdés
Convert 4π/3 radians to degrees in [0°, 360°).
Válasz
240°
49. kártya
Kérdés
In [0, 2π), which unit-circle angle has exact coordinates (cos θ, sin θ) = (−1, 0)?
Válasz
π
Equivalent degree measure: 180°.
50. kártya
Kérdés
In [0, 2π), which unit-circle angle has exact coordinates (cos θ, sin θ) = (√3/2, 1/2)?
Válasz
π/6
Equivalent degree measure: 30°.
51. kártya
Kérdés
In [0, 2π), which unit-circle angle has exact coordinates (cos θ, sin θ) = (√2/2, −√2/2)?
Válasz
7π/4
Equivalent degree measure: 315°.
52. kártya
Kérdés
In [0, 2π), which unit-circle angle has exact coordinates (cos θ, sin θ) = (−1/2, √3/2)?
Válasz
2π/3
Equivalent degree measure: 120°.
53. kártya
Kérdés
In [0, 2π), which unit-circle angle has exact coordinates (cos θ, sin θ) = (1, 0)?
Válasz
0
Equivalent degree measure: 0°.
54. kártya
Kérdés
In [0, 2π), which unit-circle angle has exact coordinates (cos θ, sin θ) = (−√3/2, −1/2)?
Válasz
7π/6
Equivalent degree measure: 210°.
55. kártya
Kérdés
In [0, 2π), which unit-circle angle has exact coordinates (cos θ, sin θ) = (−√2/2, √2/2)?
Válasz
3π/4
Equivalent degree measure: 135°.
56. kártya
Kérdés
In [0, 2π), which unit-circle angle has exact coordinates (cos θ, sin θ) = (1/2, −√3/2)?
Válasz
5π/3
Equivalent degree measure: 300°.
57. kártya
Kérdés
In [0, 2π), which unit-circle angle has exact coordinates (cos θ, sin θ) = (0, −1)?
Válasz
3π/2
Equivalent degree measure: 270°.
58. kártya
Kérdés
In [0, 2π), which unit-circle angle has exact coordinates (cos θ, sin θ) = (−√3/2, 1/2)?
Válasz
5π/6
Equivalent degree measure: 150°.
59. kártya
Kérdés
In [0, 2π), which unit-circle angle has exact coordinates (cos θ, sin θ) = (√2/2, √2/2)?
Válasz
π/4
Equivalent degree measure: 45°.
60. kártya
Kérdés
In [0, 2π), which unit-circle angle has exact coordinates (cos θ, sin θ) = (−1/2, −√3/2)?
Válasz
4π/3
Equivalent degree measure: 240°.
61. kártya
Kérdés
In [0, 2π), which unit-circle angle has exact coordinates (cos θ, sin θ) = (0, 1)?
Válasz
π/2
Equivalent degree measure: 90°.
62. kártya
Kérdés
In [0, 2π), which unit-circle angle has exact coordinates (cos θ, sin θ) = (√3/2, −1/2)?
Válasz
11π/6
Equivalent degree measure: 330°.
63. kártya
Kérdés
In [0, 2π), which unit-circle angle has exact coordinates (cos θ, sin θ) = (−√2/2, −√2/2)?
Válasz
5π/4
Equivalent degree measure: 225°.
64. kártya
Kérdés
In [0, 2π), which unit-circle angle has exact coordinates (cos θ, sin θ) = (1/2, √3/2)?
Válasz
π/3
Equivalent degree measure: 60°.
64 kártya
Unit Circle Flashcards: 16 Angles, Radians & Exact Coordinates
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