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WMA11/01 Oct 2019, Question 9: Trig Graphs: Amplitude and Period

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

The question, in short

For the curve y = sin(x/12) in radians, find its period, the coordinates of minimum point M, and solutions related to sin(x/12) = k and cos(x/12) = k using α.

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

Part (a) · 1 mark

State the period of the curve C.

  1. 1The period of sin x is 2π; sin(x/12) is stretched by factor 12 in the x-direction
  2. 2Period = 12 × 2π = 24π

Answer24π

Part (b) · 1 mark

Give the coordinates of the minimum point M shown on the graph.

  1. 1The minimum of sin is −1, when x/12 = 3π/2
  2. 2x = 18π, so M = (18π, −1)

AnswerM = (18π, −1)

Part (ci) · 1 mark

Find the negative solution of sin(x/12) = k nearest zero, in terms of α.

  1. 1sin(x/12) = k has x/12 = α/12 or π − α/12 (plus multiples of 2π)
  2. 2Subtract 2π from π − α/12: x/12 = −π − α/12
  3. 3x = −12π − α, the negative solution closest to zero

Answer−12π − α

Part (cii) · 1 mark

Find the smallest positive solution of cos(x/12) = k, in terms of α.

  1. 1cos(x/12) = sin(π/2 − x/12), so cos(x/12) = k when π/2 − x/12 = α/12
  2. 2x/12 = π/2 − α/12
  3. 3x = 6π − α

Answer6π − α

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Also searched as: WMA11 October 2019 · WMA11/01 · wma11 oct19 · IAS Maths Pure Mathematics 1 October 2019 · question 9.
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