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0580/23 Oct/Nov 2025, Question 17: Trigonometric Graphs and Equations

Cambridge IGCSE Mathematics 0580 · Paper 23 (Extended) · Non-calculator · 4 marks

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The question, in short

Draw the cosine curve over the interval 0° to 360° on the given axes, then use cos x° = 1/√2 with x reflex to work out x.

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

Part (a) · 2 marks

Plot y = cos x between 0° and 360°, showing the turning points and intercepts on the supplied grid.

  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) · 2 marks

Given cos x° = 1/√2 and that x is a reflex angle, determine x.

  1. 1cos⁻¹(1/√2) = 45°
  2. 2Cos is also positive in the 4th quadrant: x = 360 − 45 = 315 (a reflex angle)

Answer315

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