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0580/22 Oct/Nov 2025, Question 21: Trigonometric Graphs and Equations

Cambridge IGCSE Mathematics 0580 · Paper 22 (Extended) · Non-calculator · 5 marks

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The question, in short

Sketch y = cos x on the given axes for 0° ≤ x ≤ 360°, then solve 2cos x + √3 = 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

On the diagram with x-axis marked 0°, 180°, 360° and y-axis marked 1 and −1, sketch the curve y = cos x for 0° ≤ x ≤ 360°.

  1. 1Start at (0, 1), fall through (90, 0) to the minimum (180, −1)
  2. 2Rise through (270, 0) back to (360, 1), drawing a smooth curve

AnswerCorrect sketch to go through (0, 1), (180, −1) and (360, 1)

Part (b) · 3 marks

Solve 2cos x + √3 = 0 for 0° ≤ x ≤ 360°, giving all values of x in the range.

  1. 1cos x = −√3/2
  2. 2cos⁻¹(√3/2) = 30°, and cos is negative in the 2nd and 3rd quadrants
  3. 3x = 180 − 30 = 150° and x = 180 + 30 = 210°

Answer150 and 210

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Also searched as: 0580/22/O/N/25 · 0580_w25_qp_22 · 0580 w25 22 · question 21.
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