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Grade 10 Radians & the Unit Circle Worksheet with Answers

Grade 10 (US) · Year 11 (UK) · Class 10 (India) · Math

Unit 8: Going FurtherAdvanced: Precalculus PreviewCCSS F-TF.A.2Advanced

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 10 · Math

Score___ / 12

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Class

Date

Learning goal: Advanced: Precalculus Preview · 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/6 radians to degrees.

Answer: 30°

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 π radians to degrees.

    π0°90°180°270°
    Answer
  2. 2

    Convert 5π/3 radians to degrees.

    5π/30°90°180°270°
    Answer
  3. 3

    Convert 30° to radians.

    30°0°90°180°270°
    Answer
  4. 4

    Find the exact value of sin(225°).

    225°0°90°180°270°
    Answer
  5. 5

    In which quadrant does a 315° angle in standard position lie?

    Answer
  6. 6

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

    Answer
  7. 7

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

    Answer
  8. 8

    Convert 45° to radians.

    45°0°90°180°270°
    Answer
  9. 9

    In which quadrant does a 330° angle in standard position lie?

    Answer
  10. 10

    Convert 300° to radians.

    300°0°90°180°270°
    Answer
  11. 11

    Find the exact value of cos(270°).

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

    In which quadrant does a 120° angle in standard position lie?

    Answer

★ Challenge corner for fast finishers

How many different ways can the letters of the word CODE be arranged? (all letters are different)

How did I do?

Teacher's comments

Free printable worksheets with answer keys · aethelsystems.com/worksheets/math/10/unit_circle

Answer key (click to show)
  1. 1.180°
  2. 2.300°
  3. 3.π/6
  4. 4.-√2/2
  5. 5.Quadrant IV
  6. 6.Quadrant II
  7. 7.Quadrant I
  8. 8.π/4
  9. 9.Quadrant IV
  10. 10.5π/3
  11. 11.0
  12. 12.Quadrant II
  13. ★24 (challenge corner)

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