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