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0580/22 May/Jun 2024, Question 22: Trigonometric Graphs and Equations

Cambridge IGCSE Mathematics 0580 · Paper 22 (Extended) · Calculator · 7 marks

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The question, in short

Identify the function type for two sketched curves, then sketch y = sin x over 0° to 360° and solve sin x + 0.4 = 0 in that range.

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

Part (ai) · 1 mark

Choose which function type matches the first curve by ringing the correct option.

  1. 1The curve has the S-shape of y = x³, so it is cubic

Answercubic

Part (aii) · 1 mark

Choose which function type matches the second curve by ringing the correct option.

  1. 1Two separate branches that approach the axes but never meet them: reciprocal

Answerreciprocal

Part (bi) · 2 marks

Draw the graph of y = sin x on the grid for x from 0° to 360°.

  1. 1Start at (0, 0), rise to a maximum of 1 at 90°
  2. 2Fall through (180, 0) to a minimum of −1 at 270°
  3. 3Rise back to (360, 0) with a smooth wave shape

Answercorrect sine curve sketch through (0, 0), (180, 0) and (360, 0)

Part (bii) · 3 marks

Find the values of x between 0° and 360° satisfying sin x + 0.4 = 0.

  1. 1sin x = −0.4
  2. 2sin⁻¹(0.4) = 23.57…°
  3. 3x = 180 + 23.58 = 203.6° or x = 360 − 23.58 = 336.4°

Answer203.6 and 336.4

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