Download TRIGONOMETRIC FUNCTIONS Paper 1 1. Solve the equation 15

TRIGONOMETRIC FUNCTIONS
Paper 1
1. Solve the equation 15 sin 2 x = sin x + 4 sin 30 for 0  x  360
[4 marks]
Answer: ..........................
2.
Solve the equation cos x + sin 55 = 0 for 0  x  360 .
[3 marks]
Answer: ..........................
3.
Given tan x =
12
dan 90  x  360 . Find the value of sin x.
5
[3 marks]
Answer: ..........................
1
4.
Given sin x = 2 cos x, find the values of x for 0  x  360 .
[3 marks]
Answer: ..........................
5.
Given 5 cot x = 2, find the values of x for 0  x  360
[3 marks]
Answer: ..........................
6.
Given tan x = t, 0  x  90 , express, in terms of t:
(a) cot x
(b) sin ( 90 – x)
[3 marks]
Answer: (a)..........................
(b)..........................
2
7.
Solve the equation 6 sek 2 x – 13 tan x = 0, for 0  x  360
[3 marks]
Answer: ..........................
8.
Solve the equation 3 cos 2x = 8 sin x – 5 for 0  x  360
9.
Solve the equation cos x – sin x = sin x for 0  x  360
2
2

[4 marks]

Answer: ..........................
[4 marks]
Answer: ..........................
3
PAPER 2
10. Sketch the graph of y = cos 2x for 0  x  2 .
[3 marks]
11. Sketch the graph of y = – 2sin x for 0  x  180 .
[3 marks]
12. Sketch the graph of y = 1 + sin x for 0  x  360
[3 marks]
13. Sketch the graph of y = sin 2 x for 0  x  360 .
[3 marks]
3
x for 0  x  2 .
[3 marks]
2
(b) Find the equation of a suitable straight line for solving the equation
3
3
x –1.
cos x =
2
4
Hence, using the same axes, sketch the straight line and state the number of
3
3
x –1 for 0  x  2
solutions to the equation cos x =
[3 marks]
2
4
14. (a) Sketch the graph of y = 2 cos
15. (a) Sketch the graph of y = –2 cos x for 0  x  2 .
[4 marks]
(b) Hence, using the same axes, sketch a suitable graph to find the number of solutions

to the equation + 2 cos x = 0 for 0  x  2 . State the number of solutions.
x
[3 marks]
4
TRIGONOMETRIC FUNCTIONS
ANSWERS
1.
23  35 ' , 156  25 ' ,199  268, 340  32 '
2.
145  , 215 
3.
–
4.
63.4  , 243.4  or 63  26 ' , 243  26 '
5.
68.2  , 248.2 
6.
(a)
7.
33.69  , 56.31  , 213.69  , 236.31  or 33  41 ' , 56  19 ' , 213  41 ' , 236  19 '
8.
41.81  , 138.19 
9.
30  , 150  , 270 
12
13
1
t
(b)
1
t 1
2
10.
y
1

2
x
-1
11.
y
2
o
90 
180
x
-2
5
12.
y
2
1
o
180
90 
270
360
x
13.
y
1
o
90 
270
180
360
x
-1
14.
y
2

0
2
x
-2
3
x –2
2
Number of solutions = 3
y=
15
y
2
0
/2

3/2
2
x
-2
Number of solutions = 2
6