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