plumiSolving trig equations: OCR MEI A‑Level Maths questions
OCR MEI A-Level Maths past-paper questions on 5.9 Solving trig equations, 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 22 questions on Solving trig equations, as a list
- June 2025, Paper 2, Q12 (6 marks): In this question you must show detailed reasoning 2i Solve the equation sec 3 2 tan 4 0 for 180 ° 180 ° . [6] + - = - 1 1 i i
- June 2025, AS Paper 1, Q6 (4 marks): In this question you must show detailed reasoning. 2 = Solve the equation cos 6 x 5 sin x giving all the roots in the interval ° 0 x 360 ° . [4] - 1 1
- June 2025, AS Paper 2, Q3 (2 marks): You are given that sin 5 9 cos and ° 0 360 ° . = 1 1 i i i Determine the possible values of i correct to 3 significant figures. [2]
- June 2024, Paper 2, Q4 (5 marks): (a) On the axes in the Printed Answer Booklet, sketch the graph of y sin 2i for 0 2 r. = i G G [2] 1 (b) Solve the equation sin2 i =- for 0 2 . [3] i r G G 2
- June 2024, Paper 3, Q6 (5 marks): In this question you must show detailed reasoning. Solve the equation tan x 3 cot x 2 for values of x in the interval 0 ° G x 360 ° . [5] - = G
- June 2024, AS Paper 2, Q14 (6 marks): In this question you must show detailed reasoning. 2 Solve the equation 5 cos 6 sin 0 for ° 0 1 1 360 ° . [6] i i i - - = for question 15
- June 2023, Paper 1, Q6 (5 marks): a k a k can be written in the form 1 1 6 (a) Show that the equation sin x cos x + = - r r 6 4 2 1 - tan x . [4] = 3 2 - a k a k for 1 1 (b) Hence solve the equa
- June 2023, Paper 1, Q10 (6 marks): 10 The diagram shows the graph of y 1 5 . sin x for 0 x 2 r. = + G G y x O 2r (a) Show that the equation of the graph can be written in the form y a b cos 2 x w
- June 2023, Paper 1, Q15 (8 marks): A projectile is launched from a point on level ground with an initial velocity u at an angle i above the horizontal. 2 2 u sin cos i i . (a) Show that the range
- June 2023, Paper 2, Q17 (6 marks): In this question you must show detailed reasoning. Solve the equation sin 2 x sec x 4 cos x , where x . [6] + = - 1 1 r r
- June 2023, AS Paper 1, Q4 (5 marks): In this question you must show detailed reasoning. 2 + Solve the equation cos 6 x sin x = , giving all the roots in the interval 5 180 ° x 180 ° . [5] - G G
- June 2022, Paper 1, Q3 (8 marks): (a) Sketch the graph of y arctan x where x is in radians. [2] = (b) In this question you must show detailed reasoning. 2 Find all points of intersection of the
- June 2022, Paper 3, Q4 (5 marks): In this question you must show detailed reasoning. 2 = Determine the exact solutions of the equation cos 2 x 3 sin x for 0 x 2 r [5] . G G
- June 2022, AS Paper 1, Q5 (6 marks): Part of the graph of y f ( ) x is shown below. The graph is the image of y tan x ° after a stretch in = = the x-direction. y 15 10 5 x -60 0 60 -5 -10 -15 (a) F
- November 2021, Paper 3, Q2 (2 marks): Solve the equation sin x 2 0 3 . for ° 0 x 180 ° . Give your answer(s) correct to 1 decimal place. = G G [2]
- November 2020, Paper 1, Q14 (10 marks): Douglas wants to construct a model for the height of the tide in Liverpool during the day, using a cosine graph to represent the way the height changes. He know
- November 2020, Paper 2, Q3 (4 marks): You are given that y 4 x sin 8 x . = + d . y (a) Find x [2] d d = y (b) Find the smallest positive value of x for which x 0 , giving your answer in an exact for
- November 2020, AS Paper 2, Q8 (6 marks): In this question you must show detailed reasoning. Solve the equation 3 cos 8 tan 0 for ° 0 1 1 360 ° , giving your answers correct to the + = i i i nearest deg
- June 2019, Paper 1, Q6 (7 marks): sin 1 i 6 (a) Prove that cot . [4] - = i 1 cos sin - i i sin 1 i (b) Hence find the exact roots of the equation 3 tan in the interval 0 G r. - = G i i 1 cos sin
- June 2019, AS Paper 1, Q2 (3 marks): In this question you must show detailed reasoning. Fig. 2 shows the graphs of y 4 sin x ° and y 3 cos x ° for 0 x 360 . = = G G y 4 2 x 0 0 90 180 270 360 -2 -4
- June 2018, Paper 1, Q3 (4 marks): In this question you must show detailed reasoning. 2i [4] Solve the equation sec 2 tan 4 for ° 0 1 360 ° . + i = G i
- June 2018, AS Paper 1, Q5 (7 marks): (i) Sketch the graphs of y 4 cos x and y 2 sin x for ° 0 x 180 ° on the same axes. [2] = = G G (ii) Find the exact coordinates of the point of intersection of t
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