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