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