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