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WMA11/01 Jan 2020, Question 7: Trig Graphs: Amplitude and Period

Pearson Edexcel International AS Level Mathematics · Pure Mathematics 1 (WMA11) · Calculator · 5 marks

The question, in short

Using the graph of y = 3 sin x in degrees, give coordinates of points P and Q, then handle a shifted curve y = 3 sin x + k with maximum 10 and locate its first minimum R.

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

Part (ai) · 2 marks

Give the coordinates of P, the first maximum on the graph of y = 3 sin x.

  1. 1sin x has its first maximum at x = 90°
  2. 2y = 3 sin 90° = 3, so P is (90°, 3)

AnswerP(90°, 3)

Part (aii) · 1 mark

Give the coordinates of Q, where the curve next crosses the positive x-axis after its second maximum.

  1. 1The curve crosses the x-axis at 0°, 180°, 360°, 540°, …
  2. 2Q is after the second maximum (at 450°), so Q is (540°, 0)

AnswerQ(540°, 0)

Part (b) · 2 marks

For y = 3 sin x + k with greatest value 10, find k and give coordinates of the earliest minimum R.

  1. 1Maximum of 3 sin x + k is 3 + k = 10, so k = 7
  2. 2Minimum value is −3 + 7 = 4, first reached at x = 270°
  3. 3R is (270°, 4)

AnswerR(270°, 4)

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Also searched as: WMA11 January 2020 · WMA11/01 · wma11 jan20 · IAS Maths Pure Mathematics 1 January 2020 · question 7.
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