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0606/22 Oct/Nov 2025, Question 11: Solving Trig Equations

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

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The question, in short

Solve two trigonometric equations: one in tan 2x over 0° to 180°, and one in cosec(y + 1.2) with y in radians between −5 and 2.

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

Part (a) · 4 marks

Solve tan²2x − 4 tan 2x = 0 for x in the range 0° ≤ x ≤ 180°.

  1. 1tan 2x(tan 2x − 4) = 0
  2. 2tan 2x = 0: 2x = 0°, 180°, 360°, so x = 0°, 90°, 180°
  3. 3tan 2x = 4: 2x = 75.96°, 255.96°
  4. 4x = 37.98° ≈ 38.0°, 127.98° ≈ 128.0°
  5. 5x = 0°, 38.0°, 90°, 128.0°, 180°

Answerx = 0°, 38.0°, 90°, 128.0°, 180°

Part (b) · 6 marks

Solve cosec(y + 1.2) = 4 for y in radians, where −5 < y < 2.

  1. 1sin(y + 1.2) = 1/4
  2. 2Range for y + 1.2: −3.8 < y + 1.2 < 3.2
  3. 3y + 1.2 = 0.2526…, π − 0.2526… = 2.8889…, −π − 0.2526… = −3.3943…
  4. 4y = 0.2526… − 1.2 = −0.947
  5. 5y = 2.8889… − 1.2 = 1.69
  6. 6y = −3.3943… − 1.2 = −4.59

Answery = −4.59, −0.947, 1.69

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