4MA1/2HR Jun 2025, Question 25: Trigonometric Graphs and Equations
Pearson Edexcel International GCSE Mathematics A 4MA1 · Paper 2HR (Higher) · Calculator · 3 marks
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The question, in short
A curve of the form y = a sin(x + b)° + c is shown for 0 ≤ x ≤ 360, with key points at (0, 3), (45, 4), (135, 1), (225, −2), (315, 1) and (360, 3). Determine values of a, b and c.
Summarised in our own words. Use the official paper for the exact wording and the diagram.
Solution · 3 marks
- 1Maximum 4, minimum −2
- 2c = (4 + (−2)) ÷ 2 = 1
- 3a = (4 − (−2)) ÷ 2 = 3
- 4The maximum of sin is at 90°; here it is at x = 45
- 5So x + b = 90 when x = 45, giving b = 45
- 6Check: 3 sin(0 + 45)° + 1 = 3.12… ≈ 3 at x = 0
Answera = 3, b = 45, c = 1
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