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