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1CIE P1 November 2013 Q4
(i) Solve the equation 4sin^2(x) + 8cos x - 7 = 0 for 0 <= x <= 360deg. (4) (ii) Hence find the solution of the equation 4sin^2((1/2)theta) + 8cos((1/2)theta) - 7 = 0 for 0 <= theta <= 360deg. (2)
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2OCR C2 June 2013 Q2
Solve each of the following equations, for 0 <= x <= 360deg. (i) sin((1/2)x) = 0.8. (3) (ii) sin x = 3cos x. (3)
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3EDEXCEL C2 January 2013 Q4
Solve, for 0 <= x < 180deg, cos(3x - 10deg) = -0.4, giving your answers to 1 decimal place. You should show each step in your working. (7)
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4OCR C2 January 2013 Q5
(i) Show that the equation 2sin x = (4cos x - 1)/tan x can be expressed in the form 6cos^2(x) - cos x - 2 = 0. (3) (ii) Hence solve the equation 2sin x = (4cos x - 1)/tan x, giving all values of x between 0 and 360deg. (4)
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5EDEXCEL C2 June 2012 Q6
(a) Show that the equation tan 2x = 5sin 2x can be written in the form (1 - 5cos 2x)sin 2x = 0. (2) (b) Hence solve, for 0 <= x <= 180deg, tan 2x = 5sin 2x, giving your answers to 1 decimal place where appropriate. You must show clearly how you obtained your answers. (5)
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6OCR C2 June 2012 Q4
Solve the equation 4cos^2(x) + 7sin x - 7 = 0, giving all values of x between 0deg and 360deg. (6)
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7EDEXCEL C2 June 2011 Q7
(a) Solve for 0 <= x < 360deg, giving your answers in degrees to 1 decimal place, 3sin(x + 45deg) = 2. (4) (b) Find, for 0 <= x < 2pi, all the solutions of 2sin^2(x) + 2 = 7cos x, giving your answers in radians. You must show clearly how you obtained your answers. (6)
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8EDEXCEL C2 January 2011 Q7
(a) Show that the equation 3sin^2(x) + 7sin x = cos^2(x) - 4 can be written in the form 4sin^2(x) + 7sin x + 3 = 0. (2) (b) Hence solve, for 0 <= x < 360deg, 3sin^2(x) + 7sin x = cos^2(x) - 4, giving your answers to 1 decimal place where appropriate. (5)
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9EDEXCEL C2 January 2010 Q2
(a) Show that the equation 5sin x = 1 + 2cos^2(x) can be written in the form 2sin^2(x) + 5sin x - 3 = 0. (2) (b) Solve, for 0 <= x < 360deg, 2sin^2(x) + 5sin x - 3 = 0. (4)
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10EDEXCEL C2 June 2009 Q7
(i) Solve, for -180deg <= theta < 180deg, (1 + tan(theta))(5sin(theta) - 2) = 0. (4) (ii) Solve, for 0 <= x < 360deg, 4sin x = 3tan x. (6)
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11EDEXCEL C2 January 2009 Q8
Question image is broken on examsolutions.net (dead upload, reported). The video solution below walks through the question.
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12EDEXCEL C2 June 2008 Q9
Solve, for 0 <= x < 360deg, (a) sin(x - 20deg) = 1/sqrt(2). (4) (b) cos 3x = -1/2. (6)
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13EDEXCEL C2 January 2008 Q4
(a) Show that the equation 3sin^2(theta) - 2cos^2(theta) = 1 can be written as 5sin^2(theta) = 3. (2) (b) Hence solve, for 0 <= theta < 360deg, the equation 3sin^2(theta) - 2cos^2(theta) = 1, giving your answers to 1 decimal place. (7)
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14EDEXCEL C2 January 2007 Q6
Question image is broken on examsolutions.net (dead upload, reported). The video solution below walks through the question.
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15Edexcel A Level June 2022 Paper 1 Q14
In this question you must show all stages of your working. Solutions relying entirely on calculator technology are not acceptable. (a) Given that 2sin(x - 60deg) = cos(x - 30deg), show that tan x = 3sqrt(3). (4) (b) Hence or otherwise solve, for 0 <= theta < 180deg, 2sin(2theta) = cos(2theta + 30deg), giving your answers to one decimal place. (4)
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16Edexcel A Level June 2019 Paper 2 Q12
(a) Prove cos(3theta)/sin(theta) + sin(3theta)/cos(theta) = 2cot(2theta), theta != (90n)deg, n integer. (4) (b) Hence solve, for 90deg < theta < 180deg, the equation cos(3theta)/sin(theta) + sin(3theta)/cos(theta) = 4, giving any solutions to one decimal place. (3)
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17Edexcel A Level June 2023 Paper 2 Q14
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 2tan(theta)(8cos(theta) + 23sin^2(theta)) = 8sin(2theta)(1 + tan^2(theta)) may be written as sin(2theta)(Acos^2(theta) + Bcos(theta) + C) = 0, where A, B and C are constants to be found. (3) (b) Hence, solve for 360deg <= x <= 540deg, 2tan x(8cos x + 23sin^2(x)) = 8sin(2x)(1 + tan^2(x)), x real, x != 450deg. (4)
18Edexcel AS June 2023 Paper 1 Q12
In this question you must show detailed reasoning. Solutions relying entirely on calculator technology are not acceptable. (a) Show that the equation 4tan x = 5cos x can be written as 5sin^2(x) + 4sin x - 5 = 0. (3) (b) Hence solve, for 0 < x <= 360deg, 4tan x = 5cos x, giving your answers to one decimal place. (4) (c) Hence find the number of solutions of the equation 4tan 3x = 5cos 3x in the interval 0 < x <= 1800deg, explaining briefly the reason for your answer. (2)
19Edexcel A Level June 2024 Paper 2 Q8
In this question you must show all stages of your working. Solutions relying entirely on calculator technology are not acceptable. (a) Prove that 1/(cosec(theta) - 1) + 1/(cosec(theta) + 1) = 2tan(theta)sec(theta), theta != (90n)deg, n integer. (3) (b) Hence solve, for 0 < x < 90deg, the equation 1/(cosec(2x) - 1) + 1/(cosec(2x) + 1) = cot(2x)sec(2x). Give each answer, in degrees, to one decimal place. (4)
