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