math56 cardsHigh school

Unit circle flashcards

56 free flashcards for the unit circle: the 16 standard angles in degrees and radians, the sine and cosine of each, and the signs in each quadrant.

Every card checked against the sources below.

Download .txt

What’s in the deck

  • Degrees to radians for the 16 standard angles, 0° to 330°.
  • The cosine and sine of each angle, the x and y of its point on the circle.
  • The signs: which of sine and cosine is positive in each quadrant.

Tip: Cosine is the x-coordinate and sine is the y-coordinate. Once that sticks, most cards are a reference angle plus a sign.

How to study it

  • First quadrant first: 0°, 30°, 45°, 60° and 90° give every value on the circle; the other quadrants only change the sign.
  • Short sessions on spaced days beat cramming the night before a test. The guide to memorizing the unit circle has the hand trick and the three patterns behind all 48 values.

All 56 cards, with answers

  1. 1
    On the unit circle, which coordinate represents cos(θ)?
    The x-coordinate
  2. 2
    On the unit circle, which coordinate represents sin(θ)?
    The y-coordinate
  3. 3
    In Quadrant II of the unit circle, cosine is _____ and sine is positive.
    negative
  4. 4
    In Quadrant II of the unit circle, cosine is negative and sine is _____.
    positive
  5. 5
    In Quadrant III of the unit circle, cosine is _____ and sine is negative.
    negative
  6. 6
    In Quadrant III of the unit circle, cosine is negative and sine is _____.
    negative
  7. 7
    In Quadrant IV of the unit circle, cosine is _____ and sine is negative.
    positive
  8. 8
    In Quadrant IV of the unit circle, cosine is positive and sine is _____.
    negative
  9. 9
    What is 0° in radians?
    0 rad
  10. 10
    What is cos(0)?
    1
  11. 11
    What is sin(0)?
    0
  12. 12
    What is 30° in radians?
    π/6
  13. 13
    What is cos(π/6) (or cos(30°))?
    √3/2
  14. 14
    What is sin(π/6) (or sin(30°))?
    1/2
  15. 15
    What is 45° in radians?
    π/4
  16. 16
    What is cos(π/4) (or cos(45°))?
    √2/2
  17. 17
    What is sin(π/4) (or sin(45°))?
    √2/2
  18. 18
    What is 60° in radians?
    π/3
  19. 19
    What is cos(π/3) (or cos(60°))?
    1/2
  20. 20
    What is sin(π/3) (or sin(60°))?
    √3/2
  21. 21
    What is 90° in radians?
    π/2
  22. 22
    What is cos(π/2) (or cos(90°))?
    0
  23. 23
    What is sin(π/2) (or sin(90°))?
    1
  24. 24
    What is 120° in radians?
    2π/3
  25. 25
    What is cos(2π/3) (or cos(120°))?
    −1/2
  26. 26
    What is sin(2π/3) (or sin(120°))?
    √3/2
  27. 27
    What is 135° in radians?
    3π/4
  28. 28
    What is cos(3π/4) (or cos(135°))?
    −√2/2
  29. 29
    What is sin(3π/4) (or sin(135°))?
    √2/2
  30. 30
    What is 150° in radians?
    5π/6
  31. 31
    What is cos(5π/6) (or cos(150°))?
    −√3/2
  32. 32
    What is sin(5π/6) (or sin(150°))?
    1/2
  33. 33
    What is 180° in radians?
    π
  34. 34
    What is cos(π) (or cos(180°))?
    −1
  35. 35
    What is sin(π) (or sin(180°))?
    0
  36. 36
    What is 210° in radians?
    7π/6
  37. 37
    What is cos(7π/6) (or cos(210°))?
    −√3/2
  38. 38
    What is sin(7π/6) (or sin(210°))?
    −1/2
  39. 39
    What is 225° in radians?
    5π/4
  40. 40
    What is cos(5π/4) (or cos(225°))?
    −√2/2
  41. 41
    What is sin(5π/4) (or sin(225°))?
    −√2/2
  42. 42
    What is 240° in radians?
    4π/3
  43. 43
    What is cos(4π/3) (or cos(240°))?
    −1/2
  44. 44
    What is sin(4π/3) (or sin(240°))?
    −√3/2
  45. 45
    What is 270° in radians?
    3π/2
  46. 46
    What is cos(3π/2) (or cos(270°))?
    0
  47. 47
    What is sin(3π/2) (or sin(270°))?
    −1
  48. 48
    What is 300° in radians?
    5π/3
  49. 49
    What is cos(5π/3) (or cos(300°))?
    1/2
  50. 50
    What is sin(5π/3) (or sin(300°))?
    −√3/2
  51. 51
    What is 315° in radians?
    7π/4
  52. 52
    What is cos(7π/4) (or cos(315°))?
    √2/2
  53. 53
    What is sin(7π/4) (or sin(315°))?
    −√2/2
  54. 54
    What is 330° in radians?
    11π/6
  55. 55
    What is cos(11π/6) (or cos(330°))?
    √3/2
  56. 56
    What is sin(11π/6) (or sin(330°))?
    −1/2

Studying in Anki or Quizlet?

  1. Copy all the cards, or download the .txt.
  2. Quizlet: paste them into its import box. It reads Tab between term and definition.
  3. Anki: File, then Import, and pick the .txt file.

learn it before you drill it

The guide behind this deck: the full list, the tricks that make it stick and a schedule.

memorize it

How to memorize the unit circle (it's really only three numbers)

Memorize the unit circle with three patterns instead of 48 values: the square-root count, reference angles and the quadrant signs, plus the hand trick and a deck.

56 flashcards5 min

Checked against

  1. Precalculus 2e, 5.2 Unit Circle: Sine and Cosine Functions, OpenStax
  2. Precalculus 2e, 5.3 The Other Trigonometric Functions, OpenStax
  3. Learn the Unit Circle (PDF), University of Houston
  4. Evaluating the Unit Circle: Left Hand Trick (PDF), Los Angeles Mission College
  5. Unit Circle, Mathwords
  6. Assessment Framework for the Digital SAT Suite (PDF), College Board
  7. AP Precalculus Course and Exam Description (PDF), College Board
  8. AP Calculus AB Exam, College Board
  9. What's on the MCAT Exam? (PDF), AAMC
  10. Algebra and Trigonometry 2e, 7.3 Unit Circle, OpenStax
  11. Distributed Practice in Verbal Recall Tasks (Cepeda et al., 2006), Psychological Bulletin
  12. Improving Students' Learning With Effective Learning Techniques (Dunlosky et al., 2013), Psychological Science in the Public Interest

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