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