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WMA12/01 Jan 2022, Question 7: Solving Trig Equations

Pearson Edexcel International AS Level Mathematics · Pure Mathematics 2 (WMA12) · Calculator · 8 marks

The question, in short

Solve two trigonometry equations showing full working, one in degrees over −90° < x < 90° and one in radians over 0 < θ < 2π, with specified accuracy.

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

Part (i) · 4 marks

Solve 3sin(2x − 15°) = cos(2x − 15°) for −90° < x < 90°, giving answers to one decimal place.

  1. 1Divide by cos(2x − 15°): tan(2x − 15°) = 1/3
  2. 22x − 15° = 18.43° or 18.43° − 180° = −161.57° (range −195° < 2x − 15° < 165°)
  3. 32x = 33.43° or −146.57°
  4. 4x = 16.7° or x = −73.3°

Answerx = 16.7°, x = −73.3°

Part (ii) · 4 marks

Solve 4sin²θ + 8cosθ = 3 for 0 < θ < 2π, giving answers to 3 significant figures.

  1. 14(1 − cos²θ) + 8cosθ = 3
  2. 24cos²θ − 8cosθ − 1 = 0
  3. 3cosθ = (8 ± √80)/8 = 1 ± √5/2; only 1 − √5/2 = −0.118 is valid
  4. 4θ = arccos(−0.118) = 1.689… or 2π − 1.689… = 4.594…
  5. 5θ = 1.69, 4.59

Answerθ = 1.69, θ = 4.59

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