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