plumiTrigonometry with de Moivre: Edexcel A‑Level Further Maths questions
Edexcel A-Level Further Maths past-paper questions on 2.7 Trigonometry with de Moivre, 2018–2025, 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 6 questions on Trigonometry with de Moivre, as a list
- June 2025, Core Pure 1, Q10 (12 marks): (a) Given that, for n ∈ z z n n n 1 2cos θ z z n n n 1 2isin θ show that 8 4 4 2 3 4 sin cos cos θ θ θ (5) O y R x Figure 1 Figure 2 Figure 1 shows the central
- June 2024, Core Pure 1, Q4 (10 marks): The complex number z = e iθ, where θ is real. (a) Show that z n + 1 zn ≡2 cos nθ where n is a positive integer. (2) (b) Show that cos 5 θ = 1 16 (cos 5θ + 5 cos
- June 2022, Core Pure 1, Q8 (12 marks): (a) Given zn + 1 zn = 2 cos nθ n ∈ show that 32 cos6 θ ≡ cos 6θ + 6 cos 4θ + 15 cos 2θ + 10 (5) y x O x = –4 x = 4 R Figure 1 Figure 2 Figure 1 shows a solid
- November 2021, Core Pure 2, Q9 (8 marks): (a) Given that | z | < 1 , write down the sum of the infinite series 1 + z + z2 + z3 + … (1) (b) Given that z = 1 2 (cos θ + i sin θ) , (i) use the answer to pa
- November 2020, Core Pure 2, Q4 (10 marks): (a) Use de Moivre’s theorem to prove that sin 7θ = 7 sin θ − 56 sin3 θ + 112 sin5 θ − 64 sin7 θ (5) (b) Hence find the distinct roots of the equation 1 + 7x − 5
- June 2019, Core Pure 2, Q4 (8 marks): The infinite series C and S are defined by C = cos ș + 1 2 cos 5ș + 1 4 cos 9ș + 1 8 cos 13ș + … S = sin ș + 1 2 sin 5ș + 1 4 sin 9ș + 1 8 sin 13ș + … Given tha
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