C2 Trigonometr y: Trigonometric Equations www.aectutors.co
C2 Trigonometry: Trigonometric Equations
1. (a) Given that 5sin = 2cos, find the value of tan .
(b) Solve, for 0 x < 360?, 5sin 2x = 2cos 2x,
giving your answers to 1 decimal place.
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(1)
(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 ? 3 = 0
(b) Solve, for 0 x < 360?,
2 sin2 x + 5 sin x ? 3 = 0
(2)
(4) (Total 6 marks)
3. (i) Solve, for ?180? < 180?, (1 + tan )(5 sin ? 2) = 0.
(ii) Solve, for 0 x < 360?,
4sin x = 3tan x.
(4)
(6) (Total 10 marks)
Edexcel Internal Review
1
C2 Trigonometry: Trigonometric Equations
aectutors.co.uk
4. (a) Show that the equation 4 sin2 x + 9 cos x ? 6 = 0
can be written as 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.
(2)
(6) (Total 8 marks)
5. Solve, for 0 x < 360?, (a) sin(x - 20o ) = 1 2
(b) cos3x = - 1 2
(4)
(6) (Total 10 marks)
6. (a) Show that the equation 3 sin2 ? 2 cos2 = 1
can be written as
5 sin2 = 3.
(2)
Edexcel Internal Review
2
C2 Trigonometry: Trigonometric Equations
(b) Hence solve, for 0? < 360?, the equation 3 sin2 ? 2 cos2 = 1,
giving your answers to 1 decimal place.
aectutors.co.uk
(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 ? cos = 2 sin2 .
(6) (Total 9 marks)
Edexcel Internal Review
3
C2 Trigonometry: Trigonometric Equations
aectutors.co.uk
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 ?90? < x < 90?, giving answers to 1 decimal place, (a) tan (3x + 20?) = 3 , 2
(b) 2 sin2 x + cos2 x = 10 . 9
(6)
(4) (Total 10 marks)
12. Solve, for 0 x 180?, the equation (a) sin(x + 10?) = 3 , 2
(b) cos2x = ?0.9, giving your answers to 1 decimal place.
(4)
(4) (Total 8 marks)
Edexcel Internal Review
4
C2 Trigonometry: Trigonometric Equations
aectutors.co.uk
13. Solve, for 0 < 2, the equation giving your answers in terms of .
sin2 = 1 + cos ,
(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 = ?1.6 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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