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