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0580/23 May/Jun 2025, Question 23: Choosing the Right Trigonometric Ratio

Cambridge IGCSE Mathematics 0580 · Paper 23 (Extended) · Non-calculator · 6 marks

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The question, in short

State cos 90°, then use the diagram of two right-angled triangles sharing a side to express x in terms of n.

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

Part (a) · 1 mark

Write down the value of cos 90°.

  1. 1cos 90° = 0

Answer0

Part (b) · 5 marks

Using the diagram with side n and 30° angles, find x expressed in terms of n.

  1. 1Lower triangle: hypotenuse = n ÷ sin 30° = n ÷ 1/2 = 2n
  2. 2Upper triangle: cos 30° = 2n/x
  3. 3x = 2n ÷ cos 30° = 2n ÷ (√3/2)
  4. 4x = 4n/√3 = (4n√3)/3

Answer4n/√3 or (4n√3)/3

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Also searched as: 0580/23/M/J/25 · 0580_s25_qp_23 · 0580 s25 23 · question 23.
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