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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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Score/ 16

  1. Question 1

    What are the coordinates of the point on the unit circle at an angle of 45Β°?

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

  2. Question 2

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

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

  3. Question 3

    What are the coordinates of the point on the unit circle at an angle of 45Β°?

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

  4. Question 4

    Find the exact value of sin(5Ο€/3).

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

  5. Question 5

    What are the coordinates of the point on the unit circle at an angle of 225Β°?

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

  6. Question 6

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

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

  7. Question 7

    What are the coordinates of the point on the unit circle at an angle of 135Β°?

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

  8. Question 8

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

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

  9. Question 9

    What are the coordinates of the point on the unit circle at an angle of 90Β°?

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

  10. Question 10

    Find the exact value of sin(5Ο€/3).

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

  11. Question 11

    What are the coordinates of the point on the unit circle at an angle of 30Β°?

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

  12. Question 12

    Find the exact value of cos(5Ο€/6).

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

  13. Question 13

    What are the coordinates of the point on the unit circle at an angle of 30Β°?

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

  14. Question 14

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

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

  15. Question 15

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

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

  16. Question 16

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

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

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Answer key: Read exact coordinates on the unit circle

  1. 1. A. (√2/2, √2/2)

  2. 2. D. βˆ’βˆš3/2

  3. 3. C. (√2/2, √2/2)

  4. 4. A. βˆ’βˆš3/2

  5. 5. B. (βˆ’βˆš2/2, βˆ’βˆš2/2)

  6. 6. D. √2/2

  7. 7. A. (βˆ’βˆš2/2, √2/2)

  8. 8. D. 1/2

  9. 9. A. (0, 1)

  10. 10. A. βˆ’βˆš3/2

  11. 11. D. (√3/2, 1/2)

  12. 12. B. βˆ’βˆš3/2

  13. 13. D. (√3/2, 1/2)

  14. 14. D. √3/2

  15. 15. D. (√3/2, βˆ’1/2)

  16. 16. D. √3/2