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