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0580/22 May/Jun 2022, Question 17: Trigonometric Graphs and Equations

Cambridge IGCSE Mathematics 0580 · Paper 22 (Extended) · Calculator · 5 marks

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The question, in short

Sketch y = sin x from 0° to 360° on the given axes, then solve 3 sin 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 sine curve for 0° ≤ x ≤ 360°, showing correct intercepts and maximum and minimum values of 1 and −1.

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

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 3 sin x + 1 = 0.

  1. 13 sin x = −1, so sin x = −1/3
  2. 2sin⁻¹(1/3) = 19.47…°
  3. 3x = 180 + 19.47… = 199.47… ≈ 199.5°
  4. 4x = 360 − 19.47… = 340.52… ≈ 340.5°

Answer199.5 or 199.47… and 340.5 or 340.52 to 340.53…

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