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