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4MA1/2HR Jun 2023, Question 26: Trigonometric Graphs and Equations

Pearson Edexcel International GCSE Mathematics A 4MA1 · Paper 2HR (Higher) · Calculator · 0 marks

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The question, in short

From a sketch of y = a cos bx° + c for −90 ≤ x ≤ 450, find the constants a, b and c.

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

Part (a) · 0 marks

Find the value of a from the sketched cosine curve.

  1. 1The maximum value of the curve is 3 and the minimum value is −1.
  2. 2The amplitude a is half the distance between the max and min: (3 − (−1)) / 2 = 4 / 2 = 2.

Answer2

Part (b) · 0 marks

Find the value of b from the sketched cosine curve.

  1. 1y = a cos bx° + c is at a maximum when cos bx° = 1
  2. 2cos 0° = 1, so the curve has a maximum at x = 0
  3. 3From the sketch the next maximum is at x = 120°
  4. 4So the period of the curve is 120 − 0 = 120°
  5. 5For y = a cos bx° + c the period is 360 ÷ b
  6. 6360 ÷ b = 120
  7. 7b = 360 ÷ 120 = 3

Answer3

Part (c) · 0 marks

Find the value of c from the sketched cosine curve.

  1. 1The midline of the graph is halfway between the max and min: (3 + (−1)) / 2 = 2 / 2 = 1.
  2. 2This midline is the value of c, the vertical shift.
  3. 3So c = 1.

Answer1

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