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0606/22 May/Jun 2026, Question 10: Solving Trig Equations

Cambridge IGCSE Additional Mathematics 0606 · Paper 22 (Calculator) · Calculator · 6 marks

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The question, in short

Solve tan(3x + 1) = 5 sin(3x + 1) for x in the interval −π/3 < x < π/3.

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Solution · 6 marks

  1. 1sin(3x + 1)/cos(3x + 1) = 5 sin(3x + 1)
  2. 2sin(3x + 1)(1 − 5 cos(3x + 1)) = 0
  3. 3sin(3x + 1) = 0 or cos(3x + 1) = 1/5
  4. 4−π + 1 < 3x + 1 < π + 1
  5. 5sin = 0: 3x + 1 = 0, π, so x = −1/3, (π − 1)/3 = 0.714
  6. 6cos = 1/5: 3x + 1 = ±1.3694, so x = 0.123, −0.790

Answerx = −1/3, 0.714, 0.123, −0.790

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Also searched as: 0606/22/M/J/26 · 0606_s26_qp_22 · 0606 s26 22 · question 10.
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