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0580/23 Oct/Nov 2022, Question 20: Trigonometric Graphs and Equations

Cambridge IGCSE Mathematics 0580 · Paper 23 (Extended) · Calculator · 5 marks

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The question, in short

Sketch y = sin x between 0° and 360° on the given axes, then solve 3 − 2 sin x = 13/4 for x in the same interval.

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

Part (a) · 2 marks

Draw the sine curve y = sin x over 0° to 360°, showing its key features on the axes.

  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), 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 from 0° to 360° satisfying 3 − 2 sin x = 13/4.

  1. 1−2 sin x = 13/4 − 3 = 1/4
  2. 2sin x = −1/8
  3. 3sin⁻¹(1/8) = 7.18°
  4. 4x = 180 + 7.18 = 187.2° or x = 360 − 7.18 = 352.8°
  5. 5x = 187.2 and 352.8

Answer187.2 and 352.8

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Also searched as: 0580/23/O/N/22 · 0580_w22_qp_23 · 0580 w22 23 · question 20.
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