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