plumiTrigonometry with de Moivre: AQA A‑Level Further Maths questions
AQA A-Level Further Maths past-paper questions on B.7 Trigonometry with de Moivre, 2019–2025, with mark schemes and examiner’s reports where available. Add MadAsMaths questions to your practice, or browse them separately by topic and difficulty.
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All 5 questions on Trigonometry with de Moivre, as a list
- June 2024, Paper 1, Q13 (9 marks): (a) Use de Moivre’s theorem to show that cos3 θ = 4cos3 θ – 3cos θ [3 marks] 13 (b) Use de Moivre’s theorem to express sin3 θ in terms of sin θ [2 marks] 13 (c)
- June 2023, Paper 2, Q15 (10 marks): (a) Given that z = cos y + i siny , use de Moivre’s theorem to show that zn − z−n = 2i sin ny [2 marks] 15 (b) The series S is defined as S = siny + sin 3y + ::
- June 2022, Paper 1, Q12 (17 marks): The Argand diagram shows the solutions to the equation z5 = 1 Im Re z5 z2 z3 z4 z1 12 (a) Solve the equation z5 = 1 giving your answers in the form z = cosy + i
- November 2021, Paper 2, Q13 (16 marks): (a) Two of the solutions to the equation cos 6y = 0 are y = p 4 and y = 3p 4 Find the other solutions to the equation cos 6y = 0 for 0 × y × p [2 marks] 13 (b)
- June 2019, Paper 1, Q8 (10 marks): (a) If z = cos y + i sin y , use de Moivre’s theorem to prove that zn − 1 zn = 2i sinny [3 marks] 8 (b) Express sin5 y in terms of sin 5y, sin 3y and siny [4 ma
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