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4MA1/2H Jun 2024, Question 25: Trigonometric Graphs and Equations

Pearson Edexcel International GCSE Mathematics A 4MA1 · Paper 2H (Higher) · Calculator · 2 marks

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The question, in short

Using the sketched curve of y = 2sin(x + 60)°, work out the coordinates of the maximum point A and of the point B where the curve crosses the x-axis with positive gradient.

Summarised in our own words. Use the official paper for the exact wording and the diagram.

Part (i) · 1 mark

Work out the coordinates of A, the maximum point lying just to the right of the y-axis.

  1. 1The maximum value of sin occurs when the angle is 90°
  2. 2So x + 60 = 90
  3. 3x = 30
  4. 4y = 2sin(90) = 2 × 1 = 2
  5. 5(30, 2)

Answer(30, 2)

Part (ii) · 1 mark

Work out the coordinates of B, where the curve crosses the x-axis after its minimum.

  1. 1B is on the x-axis, so 2sin(x + 60)° = 0.
  2. 2After the minimum (x + 60 = 270), sin next rises through 0 at x + 60 = 360.
  3. 3x = 360 − 60 = 300, so B = (300, 0)

Answer(300, 0)

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