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WMA11/01 Jan 2022, Question 9: Trig Graphs: Shifts and Counting Solutions

Pearson Edexcel International AS Level Mathematics · Pure Mathematics 1 (WMA11) · Calculator · 4 marks

The question, in short

Using the graph of y = A cos(x − 30)° with minimum P at (30, −3), find the constant A and the coordinates of the maximum point Q.

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

Part (a) · 1 mark

State the value of the constant A from the given minimum point P.

  1. 1At x = 30, cos(0)° = 1, so y = A
  2. 2P(30, −3) gives A = −3

AnswerA = −3

Part (b) · 3 marks

Determine the coordinates of Q, the third maximum to the right of the y-axis.

  1. 1The maximum value is 3, so Q has y = 3
  2. 2The period is 360°; maxima are 180° after each minimum: x = 210, 570, 930, …
  3. 3Q is the third maximum: x = 30 + 180 + 2 × 360 = 930
  4. 4Q = (930, 3)

AnswerQ(930, 3)

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