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Grade 10 · Functions & Graphs
Trigonometric Graphs (Grade 10)
MEMORANDUM
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  / 16

Answer all questions. Show all your working — marks are awarded for method as well as the final answer. Teacher copy: accept any correct equivalent method.

  1. 1
    Write down the amplitude of y = 2 sin x.
    (2)
    90°180°270°360°-2-112xyy = sin xy = 2 sin x
    2✓✓ (2)
  2. 2
    Write down the period of y = sin x.
    (2)
    90°180°270°360°-11xyy = sin xy = cos x
    360°✓✓ (2)
  3. 3
    Write down the range of y = 2 sin x + 1.
    (2)
    −1 ≤ y ≤ 3✓✓ (2)
  4. 4
    Describe the transformation from y = cos x to y = cos x + 1.
    (2)
    90°180°270°360°-2-112xyy = cos xy = cos x + 1
    A shift of 1 unit upwards✓✓ (2)
  5. 5
    Write down the equations of the asymptotes of y = tan x for x ∈ [0° ; 360°].
    (2)
    90°180°270°360°-4-224xyy = tan x
    x = 90° and x = 270°✓✓ (2)
  6. 6
    Write down the maximum value of y = 3 cos x − 1.
    (2)
    3 − 1 = 2✓✓ (2)
  7. 7
    For what value of x in [0° ; 360°] does y = sin x reach its minimum?
    (2)
    90°180°270°360°-11xyy = sin xy = cos x
    x = 270°✓✓ (2)
  8. 8
    What does a negative value of a do to y = a sin x?
    (2)
    It reflects the graph in the x-axis.✓✓ (2)
TOTAL: 16 marks
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