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Grade 11 Radians & the Unit Circle Worksheet with Answers

Grade 11 (US) · Year 12 (UK) · Class 11 (India) · Math

Unit 6: Sequences, Series & TrigonometryTrigonometric FunctionsCCSS 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.

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Radians & the Unit Circle

Grade 11 · Math

Score___ / 12

Name

Class

Date

Learning goal: Trigonometric Functions · 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/3 radians to degrees.

Answer: 60°

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

    Convert 45° to radians.

    45°0°90°180°270°
    Answer
  2. 2

    Convert 315° to radians.

    315°0°90°180°270°
    Answer
  3. 3

    Convert 3π/2 radians to degrees.

    3π/20°90°180°270°
    Answer
  4. 4

    In which quadrant does a 135° angle in standard position lie?

    Answer
  5. 5

    In which quadrant does a 30° angle in standard position lie?

    Answer
  6. 6

    Convert 5π/6 radians to degrees.

    5π/60°90°180°270°
    Answer
  7. 7

    In which quadrant does a 60° angle in standard position lie?

    Answer
  8. 8

    Convert π/6 radians to degrees.

    π/60°90°180°270°
    Answer
  9. 9

    Find the exact value of tan(210°).

    210°0°90°180°270°
    Answer
  10. 10

    Convert 90° to radians.

    90°0°90°180°270°
    Answer
  11. 11

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

    Answer
  12. 12

    Convert 135° to radians.

    135°0°90°180°270°
    Answer

★ Challenge corner for fast finishers

The sum of 8 consecutive integers is 188. What is the largest of them?

How did I do?

Teacher's comments

Free printable worksheets with answer keys · aethelsystems.com/worksheets/math/11/unit_circle

Answer key (click to show)
  1. 1.π/4
  2. 2.7π/4
  3. 3.270°
  4. 4.Quadrant II
  5. 5.Quadrant I
  6. 6.150°
  7. 7.Quadrant I
  8. 8.30°
  9. 9.√3/3
  10. 10.π/2
  11. 11.Quadrant III
  12. 12.3π/4
  13. ★27 (challenge corner)

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