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