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