6.6 Sketch and use graphs of y = sin x, y = cos x and y = tan x for angles of any size Quiz: AQA Further Maths, Unit 6

The 20 questions

1. What is the period of y = sin x, in degrees?

   • 270°
   • 90°
   • 180°
   • 360°

2. What is the period of y = tan x, in degrees?

   • 180°
   • 360°
   • 90°
   • 45°

3. What is the maximum value of y = cos x?

   • 0
   • 360
   • 2
   • 1

4. For x ≥ 0°, at which angle does y = sin x first reach its maximum value of 1?

   • 90°
   • 180°
   • 0°
   • 270°

5. What is the value of cos 0° read from the graph of y = cos x?

   • 0
   • −1
   • 1
   • 0.5

6. Between 0° and 360°, at which angles does y = tan x have vertical asymptotes?

   • 90° and 270°
   • 60° and 300°
   • 45° and 225°
   • 0° and 180°

7. Which of these graphs is symmetric about the y-axis?

   • y = tan x
   • y = sin x
   • y = cos x
   • y = sin 2x

8. Where does the graph of y = sin x cross the y-axis?

   • At (0, 1)
   • At (0, −1)
   • At the origin (0, 0)
   • At (90°, 0)

9. On the graph of y = sin x for 0° ≤ x ≤ 360°, at which angle is the minimum value of −1 reached?

   • 360°
   • 270°
   • 90°
   • 180°

10. At which angle between 0° and 360° does y = cos x reach its minimum value?

    • 90°
    • 180°
    • 270°
    • 0°

11. How many points does the graph of y = sin x have on the x-axis for 0° ≤ x ≤ 360°?

    • 1
    • 2
    • 4
    • 3

12. The graph of y = 3 sin x is drawn. What is its amplitude?

    • 3
    • 2
    • 1
    • 6

13. What is the range of y = cos x + 2?

    • −1 ≤ y ≤ 1
    • 0 ≤ y ≤ 2
    • 2 ≤ y ≤ 4
    • 1 ≤ y ≤ 3

14. What is the value of sin 450°?

    • 1
    • 0
    • −1
    • 0.5

15. What is the value of tan 135°?

    • −1
    • 1
    • 0
    • −√3

16. Which transformation maps the graph of y = sin x onto y = sin(x − 90°)?

    • Translation 90° up
    • Translation 90° down
    • Translation 90° left
    • Translation 90° right

17. How many solutions does cos x = 0.5 have for 0° ≤ x < 720°?

    • 2
    • 3
    • 4
    • 6

18. At which angles between 0° and 360° is y = tan x undefined?

    • 180° and 360°
    • 90° and 270°
    • 0° and 180°
    • 45° and 225°

19. How many values of x between 0° and 360° satisfy 2 sin x = 1?

    • 4
    • 3
    • 2
    • 1

20. What is the amplitude of y = sin x + cos x?

    • 1
    • 2
    • √2
    • 2√2

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