plumiSolving trig equations: Edexcel A‑Level Maths questions
Edexcel A-Level Maths past-paper questions on 5.9 Solving trig equations, 2010–2025, 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 21 questions on Solving trig equations, as a list
- June 2025, Pure 1, Q14 (7 marks): In this question you must show all stages of your working. Solutions relying on calculator technology are not acceptable. (a) Show that sin(x + 30°) + 3 cos(x +
- June 2025, Pure 2, Q13 (3 marks): Given that for all values of k, where 0 < ½k½ < 1, the equation sin (nx) = k n ∈ has exactly 6 solutions in the interval 0 x < 2π (i) deduce the value of n
- June 2025, AS Pure, Q8 (5 marks): In this question you must show all stages of your working. Solutions relying entirely on calculator technology are not acceptable. Solve, for 0 x 90°, the e
- June 2024, Pure 2, Q8 (7 marks): In this question you must show all stages of your working. Solutions relying entirely on calculator technology are not acceptable. (a) Prove that o 1 1 2tan sec
- June 2024, AS Pure, Q13 (9 marks): In this question you must show all stages of your working. Solutions relying entirely on calculator technology are not acceptable. (a) Show that the equation si
- June 2023, Pure 2, Q14 (7 marks): In this question you must show all stages of your working. Solutions relying entirely on calculator technology are not acceptable. (a) Show that the equation 2
- June 2023, AS Pure, Q12 (9 marks): In this question you must show detailed reasoning. Solutions relying entirely on calculator technology are not acceptable. (a) Show that the equation 4 5 tan co
- June 2022, Pure 1, Q14 (8 marks): In this question you must show all stages of your working. Solutions relying entirely on calculator technology are not acceptable. (a) Given that 2 sin (x − 60°
- June 2022, Pure 2, Q15 (10 marks): In this question you must show all stages of your working. Solutions relying on calculator technology are not acceptable. Given that the first three terms of a
- June 2022, AS Pure, Q13 (8 marks): In this question you must show all stages of your working. Solutions relying entirely on calculator technology are not acceptable. (a) Show that 1 cosθ + tan θ
- November 2021, Pure 1, Q10 (8 marks): In this question you should show all stages of your working. Solutions relying entirely on calculator technology are not acceptable. (a) Given that 1 + cos 2θ +
- November 2021, AS Pure, Q12 (9 marks): In this question you should show all stages of your working. Solutions relying entirely on calculator technology are not acceptable. (i) Solve, for 0 < θ 450°
- November 2020, Pure 1, Q12 (8 marks): In this question you must show all stages of your working. Solutions relying entirely on calculator technology are not acceptable. (a) Show that cosec θ − sin θ
- November 2020, Pure 2, Q10 (8 marks): In this question you must show all stages of your working. Solutions relying entirely on calculator technology are not acceptable. (a) Show that cos 3 A ≡ 4 cos
- November 2020, AS Pure, Q9 (8 marks): P(c, d) y O x Figure 3 Figure 3 shows part of the curve with equation y = 3 cos x°. The point P(c, d) is a minimum point on the curve with c being the smallest
- June 2019, Pure 1, Q6 (8 marks): (a) Solve, for –180° - ș - 180°, the equation 5 sin 2ș= 9 tan ș giving your answers, where necessary, to one decimal place. [6ROXWLRQVEDVHGHQWLUHO\RQJUDSKL
- June 2019, Pure 2, Q12 (7 marks): (a) Prove cos3 sin θ θ + sin3 cos θ θ {FRWș ș z (90n)°, n ] (4) (b) Hence solve, for 90° ș 180°, the equation cos3 sin θ θ + sin3 cos θ θ = 4 giving any
- June 2019, AS Pure, Q12 (7 marks): (a) Show that 2 10sin 7cos 2 3 2cos θ θ θ − + + Ł±FRVș (4) (b) Hence, or otherwise, solve, for 0 - x 360q, the equation 10 7 2 3 2 2 sin cos cos x x x −
- June 2018, Pure 1, Q8 (5 marks): The depth of water, D metres, in a harbour on a particular day is modelled by the formula D = 5 + 2 sin (30t)° 0 t < 24 where t is the number of hours after m
- June 2018, Pure 2, Q7 (9 marks): (i) Solve, for 0 x < 2 π , the equation 4 sin x = sec x (4) (ii) Solve, for 0 θ < 360°, the equation 5 sin θ − 5 cos θ = 2 giving your answers to one decima
- June 2018, Pure 2, Q12 (9 marks): (a) Prove that 1 − cos 2θ ≡ tan θ sin 2θ, θ ≠ (2 1) 2 n π + , n ∈ (3) (b) Hence solve, for −2 π < x < 2 π , the equation (sec2 x − 5)(1 − cos 2x) = 3 tan2 x s
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