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0580/21 May/Jun 2023, Question 19: Trigonometric Graphs and Equations

Cambridge IGCSE Mathematics 0580 · Paper 21 (Extended) · Calculator · 5 marks

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The question, in short

Sketch y = cos x between 0° and 360° on the given axes, then solve 5 cos 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

Draw the cosine curve for x from 0° to 360° on the axes, showing correct turning points and intercepts.

  1. 1Start at (0, 1), go down through (90, 0) to the minimum (180, −1)
  2. 2Go back up through (270, 0) to (360, 1), with a smooth wave shape

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

Part (b) · 3 marks

Find all values of x between 0° and 360° satisfying 5 cos x + 3 = 0.

  1. 15 cos x = −3, so cos x = −3/5 = −0.6
  2. 2x = cos⁻¹(−0.6) = 126.86…° ≈ 126.9°
  3. 3Second solution: 360 − 126.86… = 233.13…° ≈ 233.1°
  4. 4x = 126.9, 233.1

Answer126.9 or 126.86 to 126.87, 233.1 or 233.13 to 233.14

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