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4MA1/1H Jun 2018, Question 18: Trigonometric Graphs and Equations

Pearson Edexcel International GCSE Mathematics A 4MA1 · Paper 1H (Higher) · Calculator · 5 marks

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The question, in short

Use the given minimum point (−2, −1) of y = f(x) to find transformed minimum coordinates, then use a sine graph to determine a, b and c in y = a sin(x − b)° + c.

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

Part (ai) · 1 mark

State the coordinates of the minimum point of y = f(x − 5), given the original minimum is (−2, −1).

  1. 1x-coordinate shifts right by 5: −2 + 5 = 3
  2. 2y-coordinate remains unchanged: −1
  3. 3(3, −1)

Answer(3, −1)

Part (aii) · 1 mark

State the coordinates of the minimum point of y = (1/2)f(x), given the original minimum is (−2, −1).

  1. 1x-coordinate remains unchanged: −2
  2. 2y-coordinate scaled by 1/2: −1 × 0.5 = −0.5
  3. 3(−2, −0.5)

Answer(−2, −0.5)

Part (b) · 3 marks

From the drawn sine curve for −90 ≤ x ≤ 450, find the values of a, b and c.

  1. 1The greatest value is 3 and the least value is −1
  2. 2c = (3 + (−1)) ÷ 2 = 1 and a = (3 − (−1)) ÷ 2 = 2
  3. 3sin peaks at 90°, but this curve peaks at x = 180, so b = 180 − 90 = 90
  4. 4a = 2, b = 90, c = 1

Answera = 2, b = 90, c = 1

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