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WMA11/01 Jan 2019, Question 5: Trig Graphs: Amplitude and Period

Pearson Edexcel International AS Level Mathematics · Pure Mathematics 1 (WMA11) · Calculator · 6 marks

The question, in short

Using the graph of y = cos 2x, identify the first minimum P, sketch y = sin x on the same axes, and count solutions of cos 2x = sin x over two large intervals.

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

Part (a) · 2 marks

Give the coordinates of the minimum point P on the curve y = cos 2x.

  1. 1cos 2x has its first minimum when 2x = π
  2. 2So x = π/2 and y = cos π = −1

Answer(π/2, −1)

Part (b) · 2 marks

On the provided copy of the graph, draw the curve y = sin x.

  1. 1y = sin x passes through O and has amplitude 1
  2. 2It reaches 1 at x = π/2 and −1 at x = 3π/2, with period 2π
  3. 3Draw it between x = −π/2 and x = 3π, crossing the x-axis at 0, π, 2π and 3π

AnswerSine curve through O with maximum 1 and minimum −1 and period 2π: crosses the x-axis at 0, π, 2π, 3π, maximum (π/2, 1) and (5π/2, 1), minimum (−π/2, −1) and (3π/2, −1)

Part (ci) · 1 mark

Find how many solutions of cos 2x = sin x lie between 0 and 20π inclusive.

  1. 1In 0 ≤ x ≤ 2π the curves meet 3 times (x = π/6, 5π/6, 3π/2)
  2. 2The pattern repeats every 2π, so in 0 ≤ x ≤ 20π there are 10 × 3 = 30 solutions

Answer30

Part (cii) · 1 mark

Find how many solutions of cos 2x = sin x lie between 0 and 21π inclusive.

  1. 1From 20π to 21π the pattern matches 0 to π
  2. 2In 0 ≤ x ≤ π there are 2 solutions (π/6 and 5π/6), so 30 + 2 = 32

Answer32

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Also searched as: WMA11 January 2019 · WMA11/01 · wma11 jan19 · IAS Maths Pure Mathematics 1 January 2019 · question 5.
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