Lemmara logoLemmaraWorked solution

0606/21 May/Jun 2025, Question 8: Solving Trig Equations

Cambridge IGCSE Additional Mathematics 0606 · Paper 21 (Calculator) · Calculator · 9 marks

اقرأ هذا الحل مشروحاً بالعربي ←

The question, in short

Solve two trigonometric equations: one with cot and cos over 0 < x ≤ π/2, and one with cosec and sin in radians for −1 ≤ θ ≤ 2.

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

Part (a) · 3 marks

Find x in 0 < x ≤ π/2 satisfying (2 − 3cot x)cos x = 0.

  1. 1cos x = 0 or 2 − 3cot x = 0
  2. 2cos x = 0 gives x = π/2
  3. 3cot x = 2/3, so tan x = 3/2
  4. 4x = tan⁻¹(1.5) = 0.983

Answerx = π/2, x = 0.983

Part (b) · 6 marks

Find θ in radians, −1 ≤ θ ≤ 2, satisfying 2cosec(2θ + 1) − 12sin(2θ + 1) = 5.

  1. 12/sin(2θ + 1) − 12sin(2θ + 1) = 5
  2. 212sin²(2θ + 1) + 5sin(2θ + 1) − 2 = 0
  3. 3(4sin(2θ + 1) − 1)(3sin(2θ + 1) + 2) = 0
  4. 4sin(2θ + 1) = 1/4: 2θ + 1 = 0.2527, 2.8889 (−1 ≤ 2θ + 1 ≤ 5)
  5. 5sin(2θ + 1) = −2/3: 2θ + 1 = −0.7297, 3.8713
  6. 6θ = −0.374, 0.944, −0.865, 1.44

Answerθ = −0.374, 0.944, −0.865, 1.44

Stuck on a step? Read the free lesson: Solving Trig Equations

Practise more solving trig equations questions

Real 0606 past-paper questions, marked on your working like the exam, with a worked solution for every part.

Practise free on Lemmara

More past-paper questions on solving trig equations

Also searched as: 0606/21/M/J/25 · 0606_s25_qp_21 · 0606 s25 21 · question 8.
Lemmara is an independent study tool, not affiliated with or endorsed by Cambridge International Education. The worked solutions are Lemmara’s own.