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WMA12/01 Jun 2025, Question 8: Harder Trig Equations

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

The question, in short

Solve two trig equations showing full working: one in radians for 0 ≤ x < π, one in degrees for 0 ≤ θ < 360°, with specified answer forms.

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

Part (i) · 3 marks

Solve 3tan(2x + π/5) = √3 for 0 ≤ x < π, giving answers in radians as kπ with k rational.

  1. 1tan(2x + π/5) = √3/3, so 2x + π/5 = arctan(√3/3) = π/6 + nπ
  2. 22x + π/5 lies between π/5 and 2π + π/5, so 2x + π/5 = 7π/6 or 13π/6
  3. 32x = 7π/6 − π/5 = 29π/30 or 2x = 13π/6 − π/5 = 59π/30
  4. 4x = 29π/60 or x = 59π/60

Answerx = 29π/60, 59π/60

Part (ii) · 5 marks

Solve 5sinθ tanθ = cosθ + 4 for 0 ≤ θ < 360°, giving answers in degrees to one decimal place.

  1. 1tanθ = sinθ/cosθ, so 5sin²θ/cosθ = cosθ + 4
  2. 25sin²θ = cos²θ + 4cosθ, and sin²θ = 1 − cos²θ: 5 − 5cos²θ = cos²θ + 4cosθ
  3. 36cos²θ + 4cosθ − 5 = 0
  4. 4cosθ = (−4 ± √136)/12 = 0.63849… (the other root is below −1, so reject)
  5. 5θ = 50.3° or θ = 360° − 50.3° = 309.7°

Answerθ = 50.3°, 309.7°

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