# Unit Circle Flashcards: 16 Angles, Radians & Exact Coordinates ![A centered unit\-circle geometry with coordinate axes and radial guide lines on a dark blue background\.]() Master 16 standard unit\-circle positions with 64 two\-way cards for degrees, radians, and exact \(cos θ, sin θ\) coordinates\. Von [Flashcards Open Source App]() [Mit diesem Lernkartenset kostenlos lernen]() Nibomo wird geöffnet, damit du mit dem Lernen beginnen kannst\. ## Details zum Lernkartenset - Karten: 64 Karten - Version: 1 - Veröffentlicht: 16. August 2026 - Zuletzt aktualisiert: 10. September 2026 - Lizenz: OpenStax source and adapted deck, metadata, and original cover: CC BY 4\.0 \(https://creativecommons\.org/licenses/by/4\.0/\)\. - Zielgruppensprachen: [en]() - Fach: Mathematics - Tags: unit\-circle ## Über dieses Lernkartenset ### 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](/de/blog/how-to-use-flashcards-for-math/) * [How to use flashcards for AP Calculus AB and BC](/de/blog/how-to-use-flashcards-for-ap-calculus-ab-bc/) * [How to use interleaving with flashcards](/de/blog/how-to-use-interleaving-with-flashcards/) * [How to make better flashcards](/de/blog/how-to-make-better-flashcards/) #### Source and license Authoritative source: [OpenStax, *Algebra and Trigonometry*, first edition, revision AT-2015-002(03/17)-BW](https://assets.openstax.org/oscms-prodcms/media/documents/AlgebraAndTrigonometry-OP_1tE6R5r.pdf), 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 . The textbook source is licensed under [CC BY 4.0](https://creativecommons.org/licenses/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. ## Ähnliche Lernkartensets - [Circle of Fifths Flashcards: Keys, Signatures & Relative Minors]() - [AP Physics 1 Flashcards: Complete 8\-Unit Course Review]() - [AP Statistics Flashcards: Complete 5\-Unit Course Review]() - [Squared and Cubed Unit Conversion Flashcards]() - [AP Chemistry Flashcards: Complete 9\-Unit Course Review]() - [AP Biology Flashcards: Complete 8\-Unit Course Review]() ## Karten in diesem Lernkartenset ### Karte 1 **Frage** Convert 0° to radians in \[0, 2π). **Antwort** 0 ### Karte 2 **Frage** Convert 30° to radians in \[0, 2π). **Antwort** π/6 ### Karte 3 **Frage** Convert 45° to radians in \[0, 2π). **Antwort** π/4 ### Karte 4 **Frage** Convert 60° to radians in \[0, 2π). **Antwort** π/3 ### Karte 5 **Frage** Convert 90° to radians in \[0, 2π). **Antwort** π/2 ### Karte 6 **Frage** Convert 120° to radians in \[0, 2π). **Antwort** 2π/3 ### Karte 7 **Frage** Convert 135° to radians in \[0, 2π). **Antwort** 3π/4 ### Karte 8 **Frage** Convert 150° to radians in \[0, 2π). **Antwort** 5π/6 ### Karte 9 **Frage** Convert 180° to radians in \[0, 2π). **Antwort** π ### Karte 10 **Frage** Convert 210° to radians in \[0, 2π). **Antwort** 7π/6 ### Karte 11 **Frage** Convert 225° to radians in \[0, 2π). **Antwort** 5π/4 ### Karte 12 **Frage** Convert 240° to radians in \[0, 2π). **Antwort** 4π/3 ### Karte 13 **Frage** Convert 270° to radians in \[0, 2π). **Antwort** 3π/2 ### Karte 14 **Frage** Convert 300° to radians in \[0, 2π). **Antwort** 5π/3 ### Karte 15 **Frage** Convert 315° to radians in \[0, 2π). **Antwort** 7π/4 ### Karte 16 **Frage** Convert 330° to radians in \[0, 2π). **Antwort** 11π/6 ### Karte 17 **Frage** For the unit-circle position 30° = π/6, give the exact ordered pair (cos θ, sin θ). **Antwort** (√3/2, 1/2) ### Karte 18 **Frage** For the unit-circle position 225° = 5π/4, give the exact ordered pair (cos θ, sin θ). **Antwort** (−√2/2, −√2/2) ### Karte 19 **Frage** For the unit-circle position 120° = 2π/3, give the exact ordered pair (cos θ, sin θ). **Antwort** (−1/2, √3/2) ### Karte 20 **Frage** For the unit-circle position 270° = 3π/2, give the exact ordered pair (cos θ, sin θ). **Antwort** (0, −1) ### Karte 21 **Frage** For the unit-circle position 150° = 5π/6, give the exact ordered pair (cos θ, sin θ). **Antwort** (−√3/2, 1/2) ### Karte 22 **Frage** For the unit-circle position 315° = 7π/4, give the exact ordered pair (cos θ, sin θ). **Antwort** (√2/2, −√2/2) ### Karte 23 **Frage** For the unit-circle position 240° = 4π/3, give the exact ordered pair (cos θ, sin θ). **Antwort** (−1/2, −√3/2) ### Karte 24 **Frage** For the unit-circle position 0° = 0, give the exact ordered pair (cos θ, sin θ). **Antwort** (1, 0) ### Karte 25 **Frage** For the unit-circle position 210° = 7π/6, give the exact ordered pair (cos θ, sin θ). **Antwort** (−√3/2, −1/2) ### Karte 26 **Frage** For the unit-circle position 45° = π/4, give the exact ordered pair (cos θ, sin θ). **Antwort** (√2/2, √2/2) ### Karte 27 **Frage** For the unit-circle position 300° = 5π/3, give the exact ordered pair (cos θ, sin θ). **Antwort** (1/2, −√3/2) ### Karte 28 **Frage** For the unit-circle position 90° = π/2, give the exact ordered pair (cos θ, sin θ). **Antwort** (0, 1) ### Karte 29 **Frage** For the unit-circle position 330° = 11π/6, give the exact ordered pair (cos θ, sin θ). **Antwort** (√3/2, −1/2) ### Karte 30 **Frage** For the unit-circle position 135° = 3π/4, give the exact ordered pair (cos θ, sin θ). **Antwort** (−√2/2, √2/2) ### Karte 31 **Frage** For the unit-circle position 60° = π/3, give the exact ordered pair (cos θ, sin θ). **Antwort** (1/2, √3/2) ### Karte 32 **Frage** For the unit-circle position 180° = π, give the exact ordered pair (cos θ, sin θ). **Antwort** (−1, 0) ### Karte 33 **Frage** Convert π/2 radians to degrees in \[0°, 360°). **Antwort** 90° ### Karte 34 **Frage** Convert 7π/6 radians to degrees in \[0°, 360°). **Antwort** 210° ### Karte 35 **Frage** Convert π/4 radians to degrees in \[0°, 360°). **Antwort** 45° ### Karte 36 **Frage** Convert 2π/3 radians to degrees in \[0°, 360°). **Antwort** 120° ### Karte 37 **Frage** Convert 3π/2 radians to degrees in \[0°, 360°). **Antwort** 270° ### Karte 38 **Frage** Convert π/6 radians to degrees in \[0°, 360°). **Antwort** 30° ### Karte 39 **Frage** Convert 5π/4 radians to degrees in \[0°, 360°). **Antwort** 225° ### Karte 40 **Frage** Convert 5π/3 radians to degrees in \[0°, 360°). **Antwort** 300° ### Karte 41 **Frage** Convert 0 radians to degrees in \[0°, 360°). **Antwort** 0° ### Karte 42 **Frage** Convert 5π/6 radians to degrees in \[0°, 360°). **Antwort** 150° ### Karte 43 **Frage** Convert 7π/4 radians to degrees in \[0°, 360°). **Antwort** 315° ### Karte 44 **Frage** Convert π/3 radians to degrees in \[0°, 360°). **Antwort** 60° ### Karte 45 **Frage** Convert π radians to degrees in \[0°, 360°). **Antwort** 180° ### Karte 46 **Frage** Convert 11π/6 radians to degrees in \[0°, 360°). **Antwort** 330° ### Karte 47 **Frage** Convert 3π/4 radians to degrees in \[0°, 360°). **Antwort** 135° ### Karte 48 **Frage** Convert 4π/3 radians to degrees in \[0°, 360°). **Antwort** 240° ### Karte 49 **Frage** In \[0, 2π), which unit-circle angle has exact coordinates (cos θ, sin θ) = (−1, 0)? **Antwort** π Equivalent degree measure: 180°. ### Karte 50 **Frage** In \[0, 2π), which unit-circle angle has exact coordinates (cos θ, sin θ) = (√3/2, 1/2)? **Antwort** π/6 Equivalent degree measure: 30°. ### Karte 51 **Frage** In \[0, 2π), which unit-circle angle has exact coordinates (cos θ, sin θ) = (√2/2, −√2/2)? **Antwort** 7π/4 Equivalent degree measure: 315°. ### Karte 52 **Frage** In \[0, 2π), which unit-circle angle has exact coordinates (cos θ, sin θ) = (−1/2, √3/2)? **Antwort** 2π/3 Equivalent degree measure: 120°. ### Karte 53 **Frage** In \[0, 2π), which unit-circle angle has exact coordinates (cos θ, sin θ) = (1, 0)? **Antwort** 0 Equivalent degree measure: 0°. ### Karte 54 **Frage** In \[0, 2π), which unit-circle angle has exact coordinates (cos θ, sin θ) = (−√3/2, −1/2)? **Antwort** 7π/6 Equivalent degree measure: 210°. ### Karte 55 **Frage** In \[0, 2π), which unit-circle angle has exact coordinates (cos θ, sin θ) = (−√2/2, √2/2)? **Antwort** 3π/4 Equivalent degree measure: 135°. ### Karte 56 **Frage** In \[0, 2π), which unit-circle angle has exact coordinates (cos θ, sin θ) = (1/2, −√3/2)? **Antwort** 5π/3 Equivalent degree measure: 300°. ### Karte 57 **Frage** In \[0, 2π), which unit-circle angle has exact coordinates (cos θ, sin θ) = (0, −1)? **Antwort** 3π/2 Equivalent degree measure: 270°. ### Karte 58 **Frage** In \[0, 2π), which unit-circle angle has exact coordinates (cos θ, sin θ) = (−√3/2, 1/2)? **Antwort** 5π/6 Equivalent degree measure: 150°. ### Karte 59 **Frage** In \[0, 2π), which unit-circle angle has exact coordinates (cos θ, sin θ) = (√2/2, √2/2)? **Antwort** π/4 Equivalent degree measure: 45°. ### Karte 60 **Frage** In \[0, 2π), which unit-circle angle has exact coordinates (cos θ, sin θ) = (−1/2, −√3/2)? **Antwort** 4π/3 Equivalent degree measure: 240°. ### Karte 61 **Frage** In \[0, 2π), which unit-circle angle has exact coordinates (cos θ, sin θ) = (0, 1)? **Antwort** π/2 Equivalent degree measure: 90°. ### Karte 62 **Frage** In \[0, 2π), which unit-circle angle has exact coordinates (cos θ, sin θ) = (√3/2, −1/2)? **Antwort** 11π/6 Equivalent degree measure: 330°. ### Karte 63 **Frage** In \[0, 2π), which unit-circle angle has exact coordinates (cos θ, sin θ) = (−√2/2, −√2/2)? **Antwort** 5π/4 Equivalent degree measure: 225°. ### Karte 64 **Frage** In \[0, 2π), which unit-circle angle has exact coordinates (cos θ, sin θ) = (1/2, √3/2)? **Antwort** π/3 Equivalent degree measure: 60°. --- *[Die gestaltete HTML\-Version dieser Seite ansehen]()* *KI-Agenten können in diesem Dienst ein Benutzerkonto anlegen, beginnend mit `GET 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