Pure Mathematics Year 1 Trigonometry
Edexcel
Pure Mathematics Year 1
Trigonometry
Past paper questions from Core Maths 2 and IAL C12
Edited by: K V Kumaran
kumarmaths. 1
Past paper questions from Edexcel Core Maths 2 and IAL C12.
From Jan 2005 to Oct 2019.
This Section 1 has 44 Questions on Solving Trigonometry Equations Identities
Please check the Edexcel website for the solutions.
kumarmaths. 2
1. (a) Show that the equation 5 cos2 x = 3(1 + sin x)
can be written as 5 sin2 x + 3 sin x ? 2 = 0.
(b) Hence solve, for 0 x < 360, the equation 5 cos2 x = 3(1 + sin x),
giving your answers to 1 decimal place where appropriate.
(2)
(5) Jan 2005, Q4
2. Solve, for 0 x 180, the equation
(a) sin (x + 10) = 3 , 2
(b) cos 2x = ?0.9, giving your answers to 1 decimal place.
(4)
(4) June 2005, Q5
3. (a) Find all the values of , to 1 decimal place, in the interval 0 < 360 for which
5 sin ( + 30) = 3. (4)
(b) Find all the values of , to 1 decimal place, in the interval 0 < 360 for which
tan2 = 4. (5)
Jan 2006, Q8
4. (a) Given that sin = 5 cos , find the value of tan . (1)
(b) Hence, or otherwise, find the values of in the interval 0 < 360 for which
sin = 5 cos ,
giving your answers to 1 decimal place.
(3) May 2006, Q6
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5. Find all the solutions, in the interval 0 x < 360?, of the equation
2 cos2 x + 1 = 5 sin x,
giving each solution in exact form.
(6) Jan 2007, Q6
6. (a) Sketch, for 0 x 360?, the graph of y = sin( + 30). (2)
(b) Write down the exact coordinates of the points where the graph meets the coordinate axes. (3)
(c) Solve, for 0 x 360?, the equation sin ( + 30) = 0.65,
giving your answers in degrees to 2 decimal places.
(5) May 2007, Q9
7. (a) Show that the equation
3 sin2 ? 2 cos2 = 1
can be written as
5 sin2 = 3. (2)
(b) Hence solve, for 0 < 360, the equation
3 sin2 ? 2 cos2 = 1,
giving your answer to 1 decimal place.
(7) Jan 2008, Q4
8. Solve, for 0 x < 360?, (a) sin(x ? 20) = 1 , 2 (b) cos 3x = ? 1 . 2
(4)
(6) June 2008, Q9
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9. (a) Show that the equation can be written as
4 sin2 x + 9 cos x ? 6 = 0 4 cos2 x ? 9 cos x + 2 = 0.
(b) Hence solve, for 0 x < 720?, 4 sin2 x + 9 cos x ? 6 = 0,
giving your answers to 1 decimal place.
10. (i) Solve, for ?180? < 180?, (1 + tan )(5 sin - 2) = 0.
(ii) Solve, for 0 x < 360?,
4 sin x = 3 tan x.
11. (a) Show that the equation
5 sin x = 1 + 2 cos2 x
can be written in the form 2 sin2 x + 5 sin x ? 3 = 0.
(b) Solve, for 0 x < 360, 2 sin2 x + 5 sin x ? 3 = 0.
12. (a) Given that 5 sin = 2 cos , find the value of tan .
(b) Solve, for 0 x ................
................
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