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