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WMA11/01 Oct 2023, Question 10: Trig Graphs: Amplitude and Period

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

The question, in short

Use the cosine curve y = 3cos(x/n)° with first positive x-intercept P(270, 0) to find n, the period, a minimum point Q, and constant k for a sine curve through R(a, 12/5) and S(−a, −3/5).

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

Part (ai) · 1 mark

Find the constant n in the equation of C₁ using the first positive x-axis crossing at P(270, 0).

  1. 1First zero of cos is at 90°, so 270/n = 90
  2. 2n = 3

Answern = 3

Part (aii) · 1 mark

State the period of the curve C₁.

  1. 1Period of cos(x/3) = 360 × 3
  2. 2= 1080°

Answer1080°

Part (b) · 2 marks

Give the coordinates of Q, the second minimum of C₁ to the right of the y-axis.

  1. 1Minimum value of 3cos is −3, when x/3 = 180, 540, …
  2. 2Q is the second minimum: x/3 = 540, so x = 1620
  3. 3Q = (1620, −3)

AnswerQ(1620, −3)

Part (c) · 2 marks

Using R(a, 12/5) and S(−a, −3/5) on y = 2sin x° + k with 0 < a < 90, find k.

  1. 1R: 2sin a + k = 12/5
  2. 2S: 2sin(−a) + k = −2sin a + k = −3/5
  3. 3Add: 2k = 12/5 − 3/5 = 9/5
  4. 4k = 9/10

Answerk = 9/10

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Also searched as: WMA11 October 2023 · WMA11/01 · wma11 oct23 · IAS Maths Pure Mathematics 1 October 2023 · question 10.
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