plumiTrig identities: WJEC A‑Level Maths questions
WJEC A-Level Maths past-paper questions on 5.6 Trig identities, 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 16 questions on Trig identities, as a list
- Summer 2025, Unit 3, Q2 (12 marks): 2. (a) Find all values of x in the range 0XxX2π satisfying the equation cos2 sin 0 x x . Give your answers in terms of π. [6] Find all values of θ in the ra
- Summer 2025, Unit 3, Q4 (6 marks): 2 sec x x d 4. (a) Using the trapezium rule with 5 ordinates, find an approximate value for . 0 Show your working and give your answer correct to three decima
- Summer 2025, AS Unit 1, Q10 (6 marks): 10. Solve the following equation for values of θ between 0° and 360°. [6] 15sin 2 2cos 14
- Summer 2025, AS Unit 1, Q13 (4 marks): 13. Given that 3 sin2x – cos2x = 2, prove that sin2x = 3 cos2x. Hence, or otherwise, find the possible values of tanx. [4]
- Summer 2024, Unit 3, Q2 (11 marks): Find all values of θ in the range 0° ! θ ! 360° satisfying 2. (a) 2 3cot 4cosec 5 [5] . , where R and α are constants with By writing 24cos x 7sin
- Summer 2024, AS Unit 1, Q15 (7 marks): y 2sin x 3cos 2 x 3 . 15. The diagram shows a sketch of part of the curve with equation The curve crosses the x-axis at the points O, A, B and C. y C O x
- Summer 2023, Unit 3, Q6 (15 marks): cos cos cos sin sin 0 6 A B A B A B a) Using the trigonometric identity , show that 6 − 2 the exact value of cos75° is . [3] 4 Solve the equation 2cot
- Summer 2023, AS Unit 1, Q2 (7 marks): Solve the following equation for values of θ between 0° and 360°. 0 2 2 2 3sin 5cos 2cos [7]
- Summer 2022, Unit 3, Q1 (6 marks): 1 Solve the equation 6sec2x – 8 = tanx for 0° X x X 360°. [6]
- Summer 2022, Unit 4, Q10 (9 marks): A golfer hits a ball towards a flag F, from a point O, with initial velocity of 35 ms−1, at 1 0 an angle θ above the horizontal. During its flight, the position
- Summer 2019, Unit 3, Q9 (8 marks): 9 a) Given that α and β are two angles such that tanα= 2cotβ, show that tan(α + β ) = – (tanα + tanβ ). [2] Find all values of θ in the range 0° X θX 360° satis
- Summer 2019, AS Unit 1, Q1 (6 marks): 1 Solve the following equation for values of θ between 0° and 360°. 3tanθ + 2cosθ = 0 [6]
- Summer 2018, Unit 3, Q4 (5 marks): 4 Solve the equation 2tan2θ + 2tanθ– sec2θ = 2, for values of θbetween 0° and 360°. [5]
- Summer 2018, Unit 3, Q11 (4 marks): π 1 1 Prove by contradiction that, for every real number x such that 0 X x X , 2 sinx + cosx x 1. [4]
- Summer 2018, AS Unit 1, Q3 (6 marks): 3 Solve the following equation for values of θ between 0° and 360°. 2 – 3cos2θ = 2sinθ. [6]
- Summer 2018, AS Unit 1, Q7 (3 marks): Prove that 0 7 sin3θ + sinθ cos2θ ≡ tanθ [3] . cosθ
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