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0606/22 May/Jun 2025, Question 9: Solving Trig Equations

Cambridge IGCSE Additional Mathematics 0606 · Paper 22 (Calculator) · Calculator · 10 marks

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The question, in short

Find all angle solutions within the stated degree and radian intervals for two trigonometric equations, one involving sec and cosec of 3x, the other a product of sine and cosine.

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

Part (a) · 5 marks

Determine every x between −120° and 120° satisfying 3 sec 3x = √3 cosec 3x.

  1. 13/cos 3x = √3/sin 3x
  2. 2tan 3x = √3/3 = 1/√3
  3. 3−360° ≤ 3x ≤ 360°: 3x = −330°, −150°, 30°, 210°
  4. 4x = −110°, −50°, 10°, 70°

Answerx = −110°, −50°, 10°, 70°

Part (b) · 5 marks

Determine every y with 0 ≤ y < 2π satisfying 2cos(y + π/3) sin(y + π/3) = sin(y + π/3).

  1. 1sin(y + π/3)(2cos(y + π/3) − 1) = 0
  2. 2sin(y + π/3) = 0 or cos(y + π/3) = 1/2
  3. 3π/3 ≤ y + π/3 < 7π/3
  4. 4sin = 0: y + π/3 = π, 2π, so y = 2π/3, 5π/3
  5. 5cos = 1/2: y + π/3 = π/3, 5π/3, so y = 0, 4π/3

Answery = 0, 2π/3, 4π/3, 5π/3

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Also searched as: 0606/22/M/J/25 · 0606_s25_qp_22 · 0606 s25 22 · question 9.
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