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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.

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À propos de ce paquet

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

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.

Cartes de ce paquet

  1. Carte 1

    Question

    Convert 0° to radians in [0, 2π).

    Réponse

    0

  2. Carte 2

    Question

    Convert 30° to radians in [0, 2π).

    Réponse

    π/6

  3. Carte 3

    Question

    Convert 45° to radians in [0, 2π).

    Réponse

    π/4

  4. Carte 4

    Question

    Convert 60° to radians in [0, 2π).

    Réponse

    π/3

  5. Carte 5

    Question

    Convert 90° to radians in [0, 2π).

    Réponse

    π/2

  6. Carte 6

    Question

    Convert 120° to radians in [0, 2π).

    Réponse

    2π/3

  7. Carte 7

    Question

    Convert 135° to radians in [0, 2π).

    Réponse

    3π/4

  8. Carte 8

    Question

    Convert 150° to radians in [0, 2π).

    Réponse

    5π/6

  9. Carte 9

    Question

    Convert 180° to radians in [0, 2π).

    Réponse

    π

  10. Carte 10

    Question

    Convert 210° to radians in [0, 2π).

    Réponse

    7π/6

  11. Carte 11

    Question

    Convert 225° to radians in [0, 2π).

    Réponse

    5π/4

  12. Carte 12

    Question

    Convert 240° to radians in [0, 2π).

    Réponse

    4π/3

  13. Carte 13

    Question

    Convert 270° to radians in [0, 2π).

    Réponse

    3π/2

  14. Carte 14

    Question

    Convert 300° to radians in [0, 2π).

    Réponse

    5π/3

  15. Carte 15

    Question

    Convert 315° to radians in [0, 2π).

    Réponse

    7π/4

  16. Carte 16

    Question

    Convert 330° to radians in [0, 2π).

    Réponse

    11π/6

  17. Carte 17

    Question

    For the unit-circle position 30° = π/6, give the exact ordered pair (cos θ, sin θ).

    Réponse

    (√3/2, 1/2)

  18. Carte 18

    Question

    For the unit-circle position 225° = 5π/4, give the exact ordered pair (cos θ, sin θ).

    Réponse

    (−√2/2, −√2/2)

  19. Carte 19

    Question

    For the unit-circle position 120° = 2π/3, give the exact ordered pair (cos θ, sin θ).

    Réponse

    (−1/2, √3/2)

  20. Carte 20

    Question

    For the unit-circle position 270° = 3π/2, give the exact ordered pair (cos θ, sin θ).

    Réponse

    (0, −1)

  21. Carte 21

    Question

    For the unit-circle position 150° = 5π/6, give the exact ordered pair (cos θ, sin θ).

    Réponse

    (−√3/2, 1/2)

  22. Carte 22

    Question

    For the unit-circle position 315° = 7π/4, give the exact ordered pair (cos θ, sin θ).

    Réponse

    (√2/2, −√2/2)

  23. Carte 23

    Question

    For the unit-circle position 240° = 4π/3, give the exact ordered pair (cos θ, sin θ).

    Réponse

    (−1/2, −√3/2)

  24. Carte 24

    Question

    For the unit-circle position 0° = 0, give the exact ordered pair (cos θ, sin θ).

    Réponse

    (1, 0)

  25. Carte 25

    Question

    For the unit-circle position 210° = 7π/6, give the exact ordered pair (cos θ, sin θ).

    Réponse

    (−√3/2, −1/2)

  26. Carte 26

    Question

    For the unit-circle position 45° = π/4, give the exact ordered pair (cos θ, sin θ).

    Réponse

    (√2/2, √2/2)

  27. Carte 27

    Question

    For the unit-circle position 300° = 5π/3, give the exact ordered pair (cos θ, sin θ).

    Réponse

    (1/2, −√3/2)

  28. Carte 28

    Question

    For the unit-circle position 90° = π/2, give the exact ordered pair (cos θ, sin θ).

    Réponse

    (0, 1)

  29. Carte 29

    Question

    For the unit-circle position 330° = 11π/6, give the exact ordered pair (cos θ, sin θ).

    Réponse

    (√3/2, −1/2)

  30. Carte 30

    Question

    For the unit-circle position 135° = 3π/4, give the exact ordered pair (cos θ, sin θ).

    Réponse

    (−√2/2, √2/2)

  31. Carte 31

    Question

    For the unit-circle position 60° = π/3, give the exact ordered pair (cos θ, sin θ).

    Réponse

    (1/2, √3/2)

  32. Carte 32

    Question

    For the unit-circle position 180° = π, give the exact ordered pair (cos θ, sin θ).

    Réponse

    (−1, 0)

  33. Carte 33

    Question

    Convert π/2 radians to degrees in [0°, 360°).

    Réponse

    90°

  34. Carte 34

    Question

    Convert 7π/6 radians to degrees in [0°, 360°).

    Réponse

    210°

  35. Carte 35

    Question

    Convert π/4 radians to degrees in [0°, 360°).

    Réponse

    45°

  36. Carte 36

    Question

    Convert 2π/3 radians to degrees in [0°, 360°).

    Réponse

    120°

  37. Carte 37

    Question

    Convert 3π/2 radians to degrees in [0°, 360°).

    Réponse

    270°

  38. Carte 38

    Question

    Convert π/6 radians to degrees in [0°, 360°).

    Réponse

    30°

  39. Carte 39

    Question

    Convert 5π/4 radians to degrees in [0°, 360°).

    Réponse

    225°

  40. Carte 40

    Question

    Convert 5π/3 radians to degrees in [0°, 360°).

    Réponse

    300°

  41. Carte 41

    Question

    Convert 0 radians to degrees in [0°, 360°).

    Réponse

    0°

  42. Carte 42

    Question

    Convert 5π/6 radians to degrees in [0°, 360°).

    Réponse

    150°

  43. Carte 43

    Question

    Convert 7π/4 radians to degrees in [0°, 360°).

    Réponse

    315°

  44. Carte 44

    Question

    Convert π/3 radians to degrees in [0°, 360°).

    Réponse

    60°

  45. Carte 45

    Question

    Convert π radians to degrees in [0°, 360°).

    Réponse

    180°

  46. Carte 46

    Question

    Convert 11π/6 radians to degrees in [0°, 360°).

    Réponse

    330°

  47. Carte 47

    Question

    Convert 3π/4 radians to degrees in [0°, 360°).

    Réponse

    135°

  48. Carte 48

    Question

    Convert 4π/3 radians to degrees in [0°, 360°).

    Réponse

    240°

  49. Carte 49

    Question

    In [0, 2π), which unit-circle angle has exact coordinates (cos θ, sin θ) = (−1, 0)?

    Réponse

    π

    Equivalent degree measure: 180°.

  50. Carte 50

    Question

    In [0, 2π), which unit-circle angle has exact coordinates (cos θ, sin θ) = (√3/2, 1/2)?

    Réponse

    π/6

    Equivalent degree measure: 30°.

  51. Carte 51

    Question

    In [0, 2π), which unit-circle angle has exact coordinates (cos θ, sin θ) = (√2/2, −√2/2)?

    Réponse

    7π/4

    Equivalent degree measure: 315°.

  52. Carte 52

    Question

    In [0, 2π), which unit-circle angle has exact coordinates (cos θ, sin θ) = (−1/2, √3/2)?

    Réponse

    2π/3

    Equivalent degree measure: 120°.

  53. Carte 53

    Question

    In [0, 2π), which unit-circle angle has exact coordinates (cos θ, sin θ) = (1, 0)?

    Réponse

    0

    Equivalent degree measure: 0°.

  54. Carte 54

    Question

    In [0, 2π), which unit-circle angle has exact coordinates (cos θ, sin θ) = (−√3/2, −1/2)?

    Réponse

    7π/6

    Equivalent degree measure: 210°.

  55. Carte 55

    Question

    In [0, 2π), which unit-circle angle has exact coordinates (cos θ, sin θ) = (−√2/2, √2/2)?

    Réponse

    3π/4

    Equivalent degree measure: 135°.

  56. Carte 56

    Question

    In [0, 2π), which unit-circle angle has exact coordinates (cos θ, sin θ) = (1/2, −√3/2)?

    Réponse

    5π/3

    Equivalent degree measure: 300°.

  57. Carte 57

    Question

    In [0, 2π), which unit-circle angle has exact coordinates (cos θ, sin θ) = (0, −1)?

    Réponse

    3π/2

    Equivalent degree measure: 270°.

  58. Carte 58

    Question

    In [0, 2π), which unit-circle angle has exact coordinates (cos θ, sin θ) = (−√3/2, 1/2)?

    Réponse

    5π/6

    Equivalent degree measure: 150°.

  59. Carte 59

    Question

    In [0, 2π), which unit-circle angle has exact coordinates (cos θ, sin θ) = (√2/2, √2/2)?

    Réponse

    π/4

    Equivalent degree measure: 45°.

  60. Carte 60

    Question

    In [0, 2π), which unit-circle angle has exact coordinates (cos θ, sin θ) = (−1/2, −√3/2)?

    Réponse

    4π/3

    Equivalent degree measure: 240°.

  61. Carte 61

    Question

    In [0, 2π), which unit-circle angle has exact coordinates (cos θ, sin θ) = (0, 1)?

    Réponse

    π/2

    Equivalent degree measure: 90°.

  62. Carte 62

    Question

    In [0, 2π), which unit-circle angle has exact coordinates (cos θ, sin θ) = (√3/2, −1/2)?

    Réponse

    11π/6

    Equivalent degree measure: 330°.

  63. Carte 63

    Question

    In [0, 2π), which unit-circle angle has exact coordinates (cos θ, sin θ) = (−√2/2, −√2/2)?

    Réponse

    5π/4

    Equivalent degree measure: 225°.

  64. Carte 64

    Question

    In [0, 2π), which unit-circle angle has exact coordinates (cos θ, sin θ) = (1/2, √3/2)?

    Réponse

    π/3

    Equivalent degree measure: 60°.

A centered unit-circle geometry with coordinate axes and radial guide lines on a dark blue background.

64 cartes

Unit Circle Flashcards: 16 Angles, Radians & Exact Coordinates

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