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C2 Trigonometry: Trigonometric Equations

1.

(a)

Given that 5sin�� = 2cos��, find the value of tan �� .

(1)

(b)

Solve, for 0 �� x < 360��,

5sin 2x = 2cos 2x,

giving your answers to 1 decimal place.

(5)

(Total 6 marks)

2.

(a)

Show that the equation

5 sin x = 1 + 2 cos2 x

can be written in the form

2 sin2 x + 5 sin x �C 3 = 0

(2)

(b)

Solve, for 0 �� x < 360��,

2 sin2 x + 5 sin x �C 3 = 0

(4)

(Total 6 marks)

3.

(i)

Solve, for �C180�� �� �� < 180��,

(1 + tan ��)(5 sin �� �C 2) = 0.

(4)

(ii)

Solve, for 0 �� x < 360��,

4sin x = 3tan x.

(6)

(Total 10 marks)

Edexcel Internal Review

1

C2 Trigonometry: Trigonometric Equations

4.

(a)

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Show that the equation

4 sin2 x + 9 cos x �C 6 = 0

can be written as

4 cos2 x �C 9 cos x + 2 = 0.

(2)

(b)

Hence solve, for 0 �� x < 720��,

4 sin2 x + 9 cos x �C 6 = 0,

giving your answers to 1 decimal place.

(6)

(Total 8 marks)

5.

Solve, for 0 �� x < 360��,

(a)

sin( x ? 20o ) =

1

2

(4)

(b)

cos 3 x = ?

1

2

(6)

(Total 10 marks)

6.

(a)

Show that the equation

3 sin2�� �C 2 cos2�� = 1

can be written as

5 sin2�� = 3.

(2)

Edexcel Internal Review

2

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C2 Trigonometry: Trigonometric Equations

(b)

Hence solve, for 0�� �� �� < 360��, the equation

3 sin2�� �C 2 cos2�� = 1,

giving your answers to 1 decimal place.

(7)

(Total 9 marks)

7.

Find all the solutions, in the interval 0 �� x < 2��, of the equation

2 cos2 x + 1 = 5 sin x,

giving each solution in terms of ��.

(Total 6 marks)

8.

(a)

Given that sin �� = 5cos ��, find the value of tan ��.

(1)

(b)

Hence, or otherwise, find the values of �� in the interval 0 �� �� < 360�� for which

sin �� = 5cos ��,

giving your answers to 1 decimal place.

(3)

(Total 4 marks)

9.

Solve, for 0 < �� < 360��, giving your answers to 1 decimal place where appropriate,

(a)

2 sin �� = 3 cos ��,

(3)

(b)

2 �C cos �� = 2 sin2 ��.

(6)

(Total 9 marks)

Edexcel Internal Review

3

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C2 Trigonometry: Trigonometric Equations

10.

(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)

(Total 9 marks)

11.

Solve, for �C90�� < x < 90��, giving answers to 1 decimal place,

(a)

tan (3x + 20��) =

3

,

2

(6)

(b)

2 sin2 x + cos2 x =

10

.

9

(4)

(Total 10 marks)

12.

Solve, for 0 �� x �� 180��, the equation

(a)

sin(x + 10��) =

��3

,

2

(4)

(b)

cos2x = �C0.9, giving your answers to 1 decimal place.

(4)

(Total 8 marks)

Edexcel Internal Review

4

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C2 Trigonometry: Trigonometric Equations

13.

Solve, for 0 �� �� < 2��, the equation

sin2 �� = 1 + cos �� ,

giving your answers in terms of ��.

(Total 5 marks)

14.

y

��3

O

p

q

360

x

The diagram above shows the curve with equation y = k sin (x + 60)��, 0 �� x �� 360, where k is a

constant.

The curve meets the y-axis at (0, ��3) and passes through the points (p, 0) and (q, 0).

(a)

Show that k = 2.

(1)

(b)

Write down the value of p and the value of q.

(2)

The line y = �C1.6 meets the curve at the points A and B.

(c)

Find the x-coordinates of A and B, giving your answers to 1 decimal place.

(5)

(Total 8 marks)

Edexcel Internal Review

5

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