• 48 values
  • Checked September 2026

Unit Circle Quiz

Fill in the unit circle one box at a time: degrees, radians, then each point.

Unit Circle Quiz

Name Date

What goes in the lit box?

1 of 7

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48
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Write the name of each numbered value.Answer key

  1. 0°
  2. 90°
  3. 180°
  4. 270°
  5. 30°
  6. 45°
  7. 60°
  8. 120°
  9. 135°
  10. 150°
  11. 210°
  12. 225°
  13. 240°
  14. 300°
  15. 315°
  16. 330°
  17. 0
  18. π/2
  19. π
  20. 3π/2
  21. π/6
  22. π/4
  23. π/3
  24. 2π/3
  25. 3π/4
  26. 5π/6
  27. 7π/6
  28. 5π/4
  29. 4π/3
  30. 5π/3
  31. 7π/4
  32. 11π/6
  33. (1, 0)
  34. (0, 1)
  35. (−1, 0)
  36. (0, −1)
  37. (√3/2, 1/2)
  38. (√2/2, √2/2)
  39. (1/2, √3/2)
  40. (−1/2, √3/2)
  41. (−√2/2, √2/2)
  42. (−√3/2, 1/2)
  43. (−√3/2, −1/2)
  44. (−√2/2, −√2/2)
  45. (−1/2, −√3/2)
  46. (1/2, −√3/2)
  47. (√2/2, −√2/2)
  48. (√3/2, −1/2)

Drawn for this site by script from the table of 16 angles, 2026-09-23. Licence: own work.

Each value is a button. Use the arrow keys to move between them and Enter to choose. Names are read out in Study, and once a value is answered.

Next step Every math and classroom diagram

All 48 values on the diagram

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Degrees 16

  1. 0° The starting side, on the positive x-axis.
  2. 90° A quarter of a turn, on an axis.
  3. 180° Half a turn, on an axis.
  4. 270° Three quarters of a turn, on an axis.
  5. 30° Quadrant I, reference angle 30°.
  6. 45° Quadrant I, reference angle 45°.
  7. 60° Quadrant I, reference angle 60°.
  8. 120° Quadrant II, reference angle 60°.
  9. 135° Quadrant II, reference angle 45°.
  10. 150° Quadrant II, reference angle 30°.
  11. 210° Quadrant III, reference angle 30°.
  12. 225° Quadrant III, reference angle 45°.
  13. 240° Quadrant III, reference angle 60°.
  14. 300° Quadrant IV, reference angle 60°.
  15. 315° Quadrant IV, reference angle 45°.
  16. 330° Quadrant IV, reference angle 30°.

Radians 16

  1. 0 0° × π/180 = 0.
  2. π/2 90° × π/180 = π/2.
  3. π 180° × π/180 = π.
  4. 3π/2 270° × π/180 = 3π/2.
  5. π/6 30° × π/180 = π/6.
  6. π/4 45° × π/180 = π/4.
  7. π/3 60° × π/180 = π/3.
  8. 2π/3 120° × π/180 = 2π/3.
  9. 3π/4 135° × π/180 = 3π/4.
  10. 5π/6 150° × π/180 = 5π/6.
  11. 7π/6 210° × π/180 = 7π/6.
  12. 5π/4 225° × π/180 = 5π/4.
  13. 4π/3 240° × π/180 = 4π/3.
  14. 5π/3 300° × π/180 = 5π/3.
  15. 7π/4 315° × π/180 = 7π/4.
  16. 11π/6 330° × π/180 = 11π/6.

Coordinates 16

  1. (1, 0) cos 0° = 1, sin 0° = 0.
  2. (0, 1) cos 90° = 0, sin 90° = 1.
  3. (−1, 0) cos 180° = −1, sin 180° = 0.
  4. (0, −1) cos 270° = 0, sin 270° = −1.
  5. (√3/2, 1/2) cos 30° = √3/2, sin 30° = 1/2.
  6. (√2/2, √2/2) cos 45° = √2/2, sin 45° = √2/2.
  7. (1/2, √3/2) cos 60° = 1/2, sin 60° = √3/2.
  8. (−1/2, √3/2) cos 120° = −1/2, sin 120° = √3/2.
  9. (−√2/2, √2/2) cos 135° = −√2/2, sin 135° = √2/2.
  10. (−√3/2, 1/2) cos 150° = −√3/2, sin 150° = 1/2.
  11. (−√3/2, −1/2) cos 210° = −√3/2, sin 210° = −1/2.
  12. (−√2/2, −√2/2) cos 225° = −√2/2, sin 225° = −√2/2.
  13. (−1/2, −√3/2) cos 240° = −1/2, sin 240° = −√3/2.
  14. (1/2, −√3/2) cos 300° = 1/2, sin 300° = −√3/2.
  15. (√2/2, −√2/2) cos 315° = √2/2, sin 315° = −√2/2.
  16. (√3/2, −1/2) cos 330° = √3/2, sin 330° = −1/2.

How this list was compiled: The definition x = cos t, y = sin t for the point where an angle meets the unit circle, the degree and radian names of 30°, 45° and 60° and their sine and cosine values (Table 1), and the four quadrants: OpenStax, Precalculus 2e, section 5.2 Unit Circle: Sine and Cosine Functions, https://openstax.org/books/precalculus-2e/pages/5-2-unit-circle-sine-and-cosine-functions, read 2026-09-23 (facts only; nothing copied). Every one of the 16 angles was then worked out by the script that draws the circle: each radian label is checked to equal the angle × π/180, and each exact coordinate is checked against the computed cosine and sine, so the drawing and the key cannot disagree. Licence: own work

The drawing: Drawn for this site by script from the table of 16 angles, 2026-09-23. Licence: own work

How it works

This unit circle quiz lights one blank box and you pick what goes in it: the angle in degrees, the angle in radians, or the point (cos θ, sin θ). The three 0° boxes are filled in as the example.

Read the full guide

Degrees, then radians, then points

Each ring of boxes is asked in two rounds. Degrees sit inside the circle, radians just outside it, and the points on the outer ring. Every round reaches round the whole circle: the axes, 30°, 45° and 60°, and the other three quadrants. A wrong pick writes the right value in the box.

A blank unit circle printable

After a round you can print the unit circle worksheet blank, with numbered boxes and lines to fill in, or labeled as a cheat sheet with all 48 values.

  • Learn the first quadrant only. Every other point is the same pair with one or both signs flipped.

Questions and answers

How do I get from degrees to radians?

Multiply by π/180: 30° is π/6, 45° is π/4, 120° is 2π/3 and 180° is π. For a unit circle radians quiz, choose Radians under Start from.

Why is the point (cos θ, sin θ)?

The circle has radius 1, so the point where the angle's side meets it is x = cos θ and y = sin θ. At 30° that is (√3/2, 1/2), and at 60° the two numbers swap places.

Where does tan fit on the unit circle?

Tan θ is sin θ divided by cos θ, the y of the point over its x. At 45° both are √2/2, so tan 45° = 1. At 90° and 270° x is 0, so tan is undefined.

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