plumiSolving trig equations: OCR A‑Level Maths questions
OCR A-Level Maths past-paper questions on 1.05.9 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 24 questions on Solving trig equations, as a list
- June 2025, Paper 1, Q9 (10 marks): (a) Express cos 3 2 x 4 sin 2 x in the form R cos ( 2 x ) , where R 2 0 and ° 0 1 1 90 ° . [3] + - a a (b) In this question you must show detailed reasoning. 3
- June 2025, AS Paper 1, Q4 (7 marks): cos 1 i 4 (a) Show that tan (where 90 n ° for any odd integer n). [3] - i i ! / 1 sin cos - i i cos 3 x 1 (b) Hence solve the equation = for 1 0 x 90 ° . [4] -
- June 2024, Paper 1, Q9 (9 marks): The depth of the water, d metres, in a tidal river during a given day is modelled by the equation d 1 9 . 1 1 . cos ( 30 t 60 )° = + - where t is the number of
- June 2024, Paper 2, Q6 (10 marks): In this question you must show detailed reasoning. (a) (i) Use the formula for cos A ( B ) , and the double angle formulae, to show that + 3i cos 3 4 cos 3 cos
- June 2024, Paper 3, Q4 (9 marks): - 4 (a) Show that the equation cot 2 x 9 cosec x 3 0 can be expressed in the form - = 2 + 5 sin x 9 sin x 2 0 . [3] - = (b) (i) In this question you must show d
- June 2024, AS Paper 2, Q7 (9 marks): y x O 12 The diagram shows the curve with equation y 5 3 cos ( 30 x 60 )° , for 0 x 12 . = + + G G (a) (i) State the greatest value of y for points on the curve
- June 2023, Paper 2, Q5 (12 marks): In this question you must show detailed reasoning. The function f is defined by f( ) x cos x 3 sin x with domain 0 x 2 r. = + G G (a) Solve the following equati
- June 2023, Paper 3, Q6 (6 marks): The first, third and fourth terms of an arithmetic progression are u1, u3 and u4 respectively, where 7 u 2 sin , u 3 cos , u sin , = i =- i = i 1 3 4 2 1 and 2
- June 2023, AS Paper 1, Q1 (5 marks): 1 1 (a) Prove that cos x sin x tan x (where x n r for any odd integer n). [3] + / ! cos x 2 2 2 (b) Solve the equation sin 2 x cos x for 0 x 180 c. [2] = c G G
- June 2023, AS Paper 2, Q3 (8 marks): A Ferris wheel at a fairground rotates in a vertical plane. The height above the ground of a seat on the wheel is h metres at time t seconds after the seat is a
- June 2022, Paper 1, Q4 (8 marks): + 2 4 (a) Write x x p x q + , where p, q and r are constants. r [3] 2 6 + in the form 7 ( ) + 2 (b) State the coordinates of the minimum point on the graph of y
- June 2022, Paper 3, Q7 (8 marks): In this question you must show detailed reasoning. (a) Show that the equation m sec 3 cos 4 sin can be expressed in the form i + i = i 2i m tan 4 tan ( m 3 ) 0
- June 2022, AS Paper 1, Q4 (8 marks): In this question you must show detailed reasoning. Solve the following equations, for ° 0 x 360 ° . G G (a) 2 tan x 1 4 [3] + = 2 (b) 5 sin x 1 2 cos x [5] - =
- November 2021, Paper 1, Q8 (10 marks): Functions f and g are defined for 0 x 2 by ( ) f x 2 tan x and ( ) g x sec x . G G = = r (a) (i) State the range of f. [1] (ii) State the range of g. [1] (b) (i
- November 2021, Paper 2, Q4 (10 marks): The size, P, of a population of a certain species of insect at time t months is modelled by the following formula. P = 5000 - 1000cos (30t)° (a) Write down the
- November 2021, Paper 3, Q5 (6 marks): - , A particle P moves along a straight line in such a way that at time t seconds P has velocity v m s 1 5 where v 12 cos t 5 sin t . = + 1 (a) Express v in the
- November 2021, AS Paper 2, Q5 (9 marks): = 5 (a) Show that the equation 2 cos tan x x 3 1 ( cos x ) can be expressed in the form + 2 + 5 cos x 3 cos x 2 0 . [3] - = (b) In this question you must show d
- November 2020, Paper 2, Q4 (5 marks): In this question you must show detailed reasoning. 4 2 Solve the equation 3 sin sin 4 , for 0 1 2 r, where z is measured in radians. [5] + z = G z z
- November 2020, AS Paper 1, Q3 (8 marks): In this question you must show detailed reasoning. 4sin2 2 (a) Solve the equation tan for 0 ° 180 ° . [5] i = i G i G sin2 1 cos - + i i (b) Prove that cos ( co
- June 2019, Paper 3, Q5 (9 marks): In this question you must show detailed reasoning. 1 cos + i 2 (a) Prove that ( cot cosec ) . [4] + = i i 1 cos - i 2 (b) Hence solve, for 0 1 1 2 , r ( 3 cot c
- June 2019, AS Paper 1, Q3 (10 marks): In this question you must show detailed reasoning. 3 2 (a) The polynomial ( )x f is defined by ( )x f 2 x 3 x 8 x + . 3 = + - (i) Show that ( ) f 1 0 . [1] = (i
- June 2019, AS Paper 2, Q6 (7 marks): In this question you must show detailed reasoning. 2i (a) Show that the equation cos 6 tan cos + 4 = i i 2i can be expressed in the form 6 sin sin 2 0 . [2] + -
- June 2018, AS Paper 1, Q3 (6 marks): 3 (i) Solve the equation sin 0 25 . for º 0 360 º . [3] 1 i = G i (ii) In this question you must show detailed reasoning. Solve the equation tan 3 3 for º 0 90
- June 2018, AS Paper 2, Q7 (8 marks): (i) Show that the equation x x x 2 sin tan cos 5 = + can be expressed in the form 2 + x x [3] 3 cos 5 cos 2 0 . - = (ii) Hence solve the equation 2 sin 2 tan 2
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