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