MAKE IT YOURS

A world for every learner

Choose a grade to discover its colours and creative world.

Grade 12 Radians & the Unit Circle Worksheet with Answers

Grade 12 (US) · Year 13 (UK) · Class 12 (India) · Math

Unit 1: TrigonometryThe Unit CircleCCSS F-TF.A.2

Converting degrees and radians and finding exact sine, cosine and tangent values on the unit circle. This free high school worksheet has 12 questions and a full answer key. Print it or save it as a PDF — every answer is checked by code, not guessed.

Save to PinterestJump to answer key
  • Answer keys checked by code
  • No ads, ever
  • No student accounts needed
  • Safety & privacy
Practice Sheetaethelsystems.com

Radians & the Unit Circle

Grade 12 · Math

Score___ / 12

Name

Class

Date

Learning goal: The Unit Circle · CCSS F-TF.A.2

Directions: Use the pictures to help you. Solve each problem. Show your work, then write your answer in the box.

Example

Convert π/4 radians to degrees.

Answer: 45°

RememberUnit circle and trig laws

(1, 0)30° (√3/2, ½)45° (√2/2, √2/2)60° (½, √3/2)(0, 1)(−1, 0)(0, −1)Point on the circle = (cos θ, sin θ)tan θ = sin θ ÷ cos θ180° = π radianssin² θ + cos² θ = 1Law of sines: a/sin A = b/sin BLaw of cosines: c² = a² + b² − 2ab cos C
  1. 1

    Find the exact value of tan(180°).

    180°0°90°180°270°
    Answer
  2. 2

    Convert 11π/6 radians to degrees.

    11π/60°90°180°270°
    Answer
  3. 3

    In which quadrant does a 150° angle in standard position lie?

    Answer
  4. 4

    Find the exact value of cos(180°).

    180°0°90°180°270°
    Answer
  5. 5

    Find the exact value of cos(45°).

    45°0°90°180°270°
    Answer
  6. 6

    Convert 4π/3 radians to degrees.

    4π/30°90°180°270°
    Answer
  7. 7

    Convert 0° to radians.

    0°0°90°180°270°
    Answer
  8. 8

    Find the exact value of tan(120°).

    120°0°90°180°270°
    Answer
  9. 9

    Convert 45° to radians.

    45°0°90°180°270°
    Answer
  10. 10

    In which quadrant does a 210° angle in standard position lie?

    Answer
  11. 11

    Find the exact value of cos(150°).

    150°0°90°180°270°
    Answer
  12. 12

    Find the exact value of sin(300°).

    300°0°90°180°270°
    Answer

★ Challenge corner for fast finishers

On a grid, you walk from the bottom-left corner to a point 2 blocks right and 2 blocks up, moving only right or up. How many different shortest paths are there?

How did I do?

Teacher's comments

Free printable worksheets with answer keys · aethelsystems.com/worksheets/math/12/unit_circle

Answer key (click to show)
  1. 1.0
  2. 2.330°
  3. 3.Quadrant II
  4. 4.-1
  5. 5.√2/2
  6. 6.240°
  7. 7.0
  8. 8.-√3
  9. 9.π/4
  10. 10.Quadrant III
  11. 11.-√3/2
  12. 12.-√3/2
  13. ★6 (challenge corner)

Need another Radians & the Unit Circle worksheet?

Generate unlimited fresh versions at easy, medium or hard difficulty, each with its own answer key. Free during our launch — no card needed.

Create a free account

How to use this worksheet

  • Use it for revision before a test, as homework, or as a timed practice set.
  • Students can self-mark with the answer key and note which question types they got wrong.
  • Generate several versions of the same topic for spaced practice in the weeks before an exam.

Related worksheets

Radians & the Unit Circle at other grades

Grade 10Grade 11

More Grade 12 Math worksheets

Grade 12 Trigonometric RatiosGrade 12 Trig Identities & EquationsGrade 12 Law of Sines & Law of CosinesGrade 12 VectorsGrade 12 Matrix OperationsGrade 12 Function Operations & CompositionGrade 12 Inverse FunctionsGrade 12 Properties of Logarithms

Can't find what you need? Tell us which worksheet to make next.

Frequently asked questions

Does this Grade 12 Radians & the Unit Circle worksheet come with answers?

Yes. The full answer key is on this page, and it prints on its own page after the questions. Every answer is calculated or checked by code rather than written by an AI model, so the key is always correct.

How do I print it or save it as a PDF?

Click "Download PDF" to save a ready-to-print PDF with the answer key on the last page, or click "Print" to send the worksheet and answer key straight to your printer.

Can I get a different Radians & the Unit Circle worksheet?

Yes. Create a free account to generate as many fresh Grade 12 Radians & the Unit Circle worksheets as you like, at easy, medium or hard difficulty, each with its own answer key.

Is this worksheet free?

Yes. This worksheet is free to print, and Practice Sheet is free to use during our launch with no card needed.