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