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0580/43 May/Jun 2026, Question 12: Trigonometric Graphs and Equations

Cambridge IGCSE Mathematics 0580 · Paper 43 (Extended) · Calculator · 5 marks

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The question, in short

Sketch y = cos x from 0° to 360° on given axes, then solve 3cos x + 1 = 0 over the same interval.

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

Part (a) · 2 marks

Draw the cosine curve for 0° ≤ x ≤ 360°, showing key points at 90°, 180°, 270°, 360° and values between −1 and 1.

  1. 1Start at (0°, 1)
  2. 2Cross the x-axis at 90° and 270°
  3. 3Minimum at (180°, −1)
  4. 4End at (360°, 1), smooth curve

AnswerCorrect sketch through (0, 1), (90, 0), (180, −1), (270, 0) and (360, 1)

Part (b) · 3 marks

Find all angles x in 0° ≤ x ≤ 360° satisfying 3cos x + 1 = 0.

  1. 13cos x = −1
  2. 2cos x = −1/3
  3. 3x = cos⁻¹(−1/3) = 109.47…° = 109.5°
  4. 4x = 360° − 109.47° = 250.5°

Answer109.5 and 250.5

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Also searched as: 0580/43/M/J/26 · 0580_s26_qp_43 · 0580 s26 43 · question 12.
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