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Read exact coordinates on the unit circle

11th grade (Year 12 in England) Β· 16 questions Β· Common Core: HSF.TF.A.2, HSF.TF.A.3 Β· England: A-level Pure Mathematics

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  1. Question 1

    Find the exact value of cos(Ο€/3).

    • A. √3/2
    • B. βˆ’1/2
    • C. βˆ’βˆš3/2
    • D. 1/2

  2. Question 2

    What are the coordinates of the point on the unit circle at an angle of 300Β°?

    • A. (βˆ’1/2, βˆ’βˆš3/2)
    • B. (1/2, βˆ’βˆš3/2)
    • C. (1/2, √3/2)
    • D. (βˆ’βˆš3/2, 1/2)

  3. Question 3

    Find the exact value of sin(7Ο€/6).

    • A. √2/2
    • B. βˆ’βˆš2/2
    • C. βˆ’1/2
    • D. √3/2

  4. Question 4

    What are the coordinates of the point on the unit circle at an angle of 270Β°?

    • A. (0, βˆ’1)
    • B. (0, 1)
    • C. (βˆ’1, 0)

  5. Question 5

    Find the exact value of sin(4Ο€/3).

    • A. √3/2
    • B. βˆ’βˆš3/2
    • C. βˆ’βˆš2/2
    • D. 1/2

  6. Question 6

    What are the coordinates of the point on the unit circle at an angle of 240Β°?

    • A. (βˆ’1/2, √3/2)
    • B. (βˆ’1/2, βˆ’βˆš3/2)
    • C. (1/2, βˆ’βˆš3/2)
    • D. (βˆ’βˆš3/2, βˆ’1/2)

  7. Question 7

    Find the exact value of cos(Ο€/4).

    • A. βˆ’βˆš3/2
    • B. βˆ’1/2
    • C. √2/2
    • D. 1/2

  8. Question 8

    What are the coordinates of the point on the unit circle at an angle of 330Β°?

    • A. (√3/2, 1/2)
    • B. (√3/2, βˆ’1/2)
    • C. (βˆ’βˆš3/2, βˆ’1/2)
    • D. (βˆ’1/2, √3/2)

  9. Question 9

    Find the exact value of cos(Ο€/4).

    • A. √2/2
    • B. 1/2
    • C. √3/2
    • D. βˆ’βˆš2/2

  10. Question 10

    What are the coordinates of the point on the unit circle at an angle of 330Β°?

    • A. (βˆ’βˆš3/2, βˆ’1/2)
    • B. (√3/2, βˆ’1/2)
    • C. (βˆ’1/2, √3/2)
    • D. (√3/2, 1/2)

  11. Question 11

    Find the exact value of sin(2Ο€/3).

    • A. βˆ’βˆš2/2
    • B. βˆ’βˆš3/2
    • C. √3/2
    • D. √2/2

  12. Question 12

    What are the coordinates of the point on the unit circle at an angle of 315Β°?

    • A. (√2/2, βˆ’βˆš2/2)
    • B. (√2/2, √2/2)
    • C. (βˆ’βˆš2/2, √2/2)
    • D. (βˆ’βˆš2/2, βˆ’βˆš2/2)

  13. Question 13

    Find the exact value of sin(11Ο€/6).

    • A. βˆ’βˆš2/2
    • B. √2/2
    • C. βˆ’1/2
    • D. √3/2

  14. Question 14

    What are the coordinates of the point on the unit circle at an angle of 120Β°?

    • A. (βˆ’1/2, √3/2)
    • B. (√3/2, βˆ’1/2)
    • C. (1/2, √3/2)
    • D. (βˆ’1/2, βˆ’βˆš3/2)

  15. Question 15

    Find the exact value of cos(5Ο€/4).

    • A. βˆ’βˆš3/2
    • B. βˆ’1/2
    • C. βˆ’βˆš2/2
    • D. 1/2

  16. Question 16

    What are the coordinates of the point on the unit circle at an angle of 60Β°?

    • A. (√3/2, 1/2)
    • B. (1/2, βˆ’βˆš3/2)
    • C. (1/2, √3/2)
    • D. (βˆ’1/2, √3/2)

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  1. 1/2
  2. (1/2, βˆ’βˆš3/2)
  3. βˆ’1/2
  4. (0, βˆ’1)
  5. βˆ’βˆš3/2
  6. (βˆ’1/2, βˆ’βˆš3/2)
  7. √2/2
  8. (√3/2, βˆ’1/2)
  9. √2/2
  10. (√3/2, βˆ’1/2)
  11. √3/2
  12. (√2/2, βˆ’βˆš2/2)
  13. βˆ’1/2
  14. (βˆ’1/2, √3/2)
  15. βˆ’βˆš2/2
  16. (1/2, √3/2)