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WMA12/01 Jun 2024, Question 8: Harder Trig Equations

Pearson Edexcel International AS Level Mathematics · Pure Mathematics 2 (WMA12) · Calculator · 12 marks

The question, in short

Solve a trigonometric equation in radians to 3 s.f., then use a sinusoidal temperature model with given conditions to find k, the maximum temperature and when it occurs.

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

Part (i) · 5 marks

Solve 5 sin x tan x + 13 = cos x for 0 < x ≤ π, giving the answer in radians to 3 significant figures.

  1. 1tan x = sin x / cos x, so 5 sin²x / cos x + 13 = cos x
  2. 25 sin²x + 13 cos x = cos²x
  3. 35(1 − cos²x) + 13 cos x = cos²x, so 6cos²x − 13 cos x − 5 = 0
  4. 4(3 cos x + 1)(2 cos x − 5) = 0
  5. 5cos x = −1/3 (cos x = 5/2 is impossible)
  6. 6x = arccos(−1/3) = 1.91

Answerx = 1.91

Part (iia) · 4 marks

Given H = 20 at 6 am and 0 < k < 20, find all possible values of k to 2 decimal places.

  1. 1At 6 am, t = 6: 20 = 10 + 12 sin(6k + 18)°
  2. 2sin(6k + 18)° = 5/6
  3. 36k + 18 = 56.44° or 180 − 56.44 = 123.56°
  4. 4k = (56.44 − 18)/6 = 6.41 or k = (123.56 − 18)/6 = 17.59

Answerk = 6.41 or k = 17.59

Part (iib) · 1 mark

With 0 < k < 10, find the maximum temperature inside the greenhouse.

  1. 1The greatest value of sin is 1
  2. 2H max = 10 + 12 = 22 °C

Answer22 °C

Part (iic) · 2 marks

Find the time of day when the maximum temperature occurs, to the nearest minute.

  1. 1Maximum when 6.41t + 18 = 90
  2. 2t = 72/6.407… = 11.24 hours
  3. 30.24 hours ≈ 14 minutes, so the time is 11:14 am

Answer11:14 (11:14 am)

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Also searched as: WMA12 June 2024 · WMA12/01 · wma12 jun24 · IAS Maths Pure Mathematics 2 June 2024 · question 8.
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