Pure Mathematics Year 1 Trigonometry - KUMAR'S MATHS REVISION

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

kumarmaths. 3

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

kumarmaths. 4

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 ................
................

In order to avoid copyright disputes, this page is only a partial summary.

Google Online Preview   Download