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