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0580/43 May/Jun 2025, Question 25: Trigonometric Graphs and Equations

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

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The question, in short

Sketch y = sin x between 0° and 360°, then solve 2 + 5 sin x = 1 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 sine curve for x from 0° to 360°, showing key features on axes marked at y = −1 and 1.

  1. 1Start at (0, 0), rise to a maximum of 1 at x = 90°
  2. 2Back to 0 at x = 180°, down to a minimum of −1 at x = 270°
  3. 3Back to 0 at x = 360°, drawn as a smooth curve

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

Part (b) · 3 marks

Find all values of x between 0° and 360° satisfying 2 + 5 sin x = 1.

  1. 15 sin x = 1 − 2 = −1
  2. 2sin x = −1/5 = −0.2
  3. 3sin⁻¹(0.2) = 11.54°
  4. 4x = 180 + 11.54 = 191.5° and x = 360 − 11.54 = 348.5°

Answer191.5, 348.5 and no others

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Also searched as: 0580/43/M/J/25 · 0580_s25_qp_43 · 0580 s25 43 · question 25.
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