6.7 Be able to use the definitions sin θ, cos θ and tan θ, for any positive angle up to 360°(measured in degrees only) Quiz: AQA Further Maths, Unit 6

The 20 questions

1. On a unit circle, which coordinate represents sin θ for an angle θ?

   • x-coordinate
   • Reciprocal of x
   • Gradient of radius
   • y-coordinate

2. On a unit circle, which coordinate represents cos θ for an angle θ?

   • Gradient of radius
   • x-coordinate
   • y-coordinate
   • Arc length

3. In terms of the coordinates (x, y) of a point on the unit circle, what is tan θ?

   • x + y
   • y ÷ x
   • y × x
   • x ÷ y

4. In standard mathematical convention, in which direction are positive angles measured from the positive x-axis?

   • Clockwise
   • Downwards
   • Vertically
   • Anticlockwise

5. In which quadrant is sin θ positive and cos θ negative?

   • Third quadrant
   • First quadrant
   • Second quadrant
   • Fourth quadrant

6. In which quadrant are sin θ, cos θ and tan θ all positive?

   • First quadrant
   • Second quadrant
   • Fourth quadrant
   • Third quadrant

7. What is the value of tan 45°?

   • √2
   • √3
   • 0
   • 1

8. What is the value of cos 90°?

   • 0
   • −1
   • 1
   • 0.5

9. What is the exact value of sin 120°?

   • √3/2
   • −√3/2
   • 1/2
   • −1/2

10. A point on the unit circle has x-coordinate −0.6 and a positive y-coordinate. What is sin θ for this point?

    • 0.8
    • −0.6
    • 0.6
    • −0.8

11. For 0° ≤ θ < 360°, which angle has tan θ = −1 and cos θ negative?

    • 315°
    • 45°
    • 135°
    • 225°

12. What are the coordinates of the point on the unit circle at 210°?

    • (√3/2, 1/2)
    • (−1/2, −√3/2)
    • (−√3/2, −1/2)
    • (1/2, −√3/2)

13. In which quadrant does an angle of 300° lie?

    • First
    • Second
    • Fourth
    • Third

14. If sin θ = 0.6 and cos θ is negative, what is cos θ?

    • −0.6
    • 0.6
    • 0.8
    • −0.8

15. Point P has coordinates (3, −4) relative to the origin O. Using r = OP, what is sin θ for the direction of OP?

    • 0.8
    • −0.6
    • −0.8
    • 0.75

16. Which angle between 0° and 360° has the same sine as 40° but lies in the second quadrant?

    • 220°
    • 320°
    • 140°
    • 50°

17. For 0° ≤ θ < 360°, sin θ = −0.5 and tan θ is positive. What is θ?

    • 210°
    • 150°
    • 30°
    • 330°

18. If tan θ = 2 and sin θ is negative, with 0° ≤ θ < 360°, what is sin θ exactly?

    • 1/2
    • −2/√5 (about −0.894)
    • −1/√5 (about −0.447)
    • 2/√5 (about 0.894)

19. What is the relationship between sin 100° and sin 80°?

    • sin 100° is negative
    • sin 100° is larger
    • sin 80° is larger
    • They are equal

20. A point on the unit circle has x-coordinate −0.6 and a negative y-coordinate. What is tan θ?

    • 3/4
    • 4/3
    • −4/3
    • −3/4

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