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