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Trigonometry Test REVISION
Name: ___________________________
Section A Multiple Choice
1
Given sin  = 0.4, then cos  =
A 0.7
B 0.9
C 0.6
D 0.4
E 0.5
B
2
cos 1322′53″ correct to four decimal
places is:
A 0.2311
B 0.2312
C 0.9734
D 0.9735
E 0.9729
E
tan 13cos 82 =
A 0.37
B 0.44
C 1.4
D 0.032
E 0.97
D
3
4
The size of the angle, a, in the figure
below is:
5
A
B
C
D
E
6
C
4244′25″
4215′13″
4744′47″
3355′3″
4755′33″
MathsQUEST Chapter 4 (A,B,C,D,E,F,G) - Trigonometry Test REVISION
C
50.3
25.4
28.5
50.1
113
The size of the angle, d, in the figure
below is:
A
B
C
D
E
A
98.3
63.4
181.5
63.5
89.3
The length of the side, c, in the figure
below is:
A
B
C
D
E
7
A
B
C
D
E
The length of the side, b, in the figure
below is:
2618′42″
6341′18″
4152′23″
487′37″
6814′15″
B
8
The size of the angle, e, in the figure
below is:
A
B
C
D
E
B
12
A hiker travels for 9.8 km on a bearing
082T. The distance the hiker is north
of the starting point is:
A 7.9 km
B 9.7 km
C 1.4 km
D 4.9 km
E 9.4 km
432'
4658'
5541'
3418'
469'
9
A tree 34 m high casts a shadow 12 m
A
long. The angle of inclination of the sun
is closest to:
A 70
B 21
C 69
D 19
E 79
10
A chord of a circle subtends an angle of E
15 at the centre. If the chord is 13 cm
long, then the radius of the circle is
closest to:
A 100 cm
B 104 cm
C 39 cm
D 52 cm
E 50 cm
11
The true bearing of N75W is:
A 075T
B 255T
C 105T
D 285T
E 345T
D
MathsQUEST Chapter 4 (A,B,C,D,E,F,G) - Trigonometry Test REVISION
C
Trigonometry Test REVISION
Name: ___________________________
Section B Short/Extended answer
1
Find the angle for each of the following in
degrees, minutes and seconds.
(a) cos  = 0.8
(b)
2
tan  = 10.6732
Find the length of the side, f, in the figure
below.
4
(a)
cos = 0.8
  cos 1 0.8
  365212
(b)
tan  = 10.6732
  tan 1 10.6732
  843851
A
H
f
cos 30 
17.2
f  17.2  cos 30
cos  
3
f  14.9
3
Find the length of the side, g, in the figure
below.
O
H
2.14
sin 166' 
g
2.14
g
sin 166'
sin  
3
g  7.72
4
Find the size of the angle, h, in the figure
below, correct to the nearest minute.
O
A
15.1
tan h 
14.7
tan  
15.1
14.7
h  4546'
h  tan 1
MathsQUEST Chapter 4 (A,B,C,D,E,F,G) - Trigonometry Test REVISION
3
5
Find the length of the side, i, in the figure
below.
sin  
3
O
H
i
27.12
i  27.12  sin 2712'
sin 2712' 
i  12.40
6
Find the length of the side, j, in the figure
below.
A
H
1046
cos 2417' 
j
1046
j
cos 2417'
cos  
3
j  1148
7
Find the length of the side, k, in the figure
below.
O
A
k
tan 571' 
2.36
k  2.36  tan 571'
tan  
3
k  3.64
8
From the top of a building, 202 m high, the
angle of depression to another building, 120 m
away, is 25. How high is this second building?
4
O
A
x
tan 25 
120
x  120  tan 25
tan  
x  55.96
Height of 2nd building  h
h  202  55.96
h  146.04
h  146 m
MathsQUEST Chapter 4 (A,B,C,D,E,F,G) - Trigonometry Test REVISION
9
The diameter of a vertical cone is 7.5 cm and
its semi-vertical angle is 27. Calculate the
length of the slant edge of the cone.
4
Right-angled triangle constructed by halving
diameter.
O
sin  
H
3.75
sin 27 
l
3.75
l
sin 27
l  8.26 cm
10
Change the following true bearings to compass
bearings:
(a) 193T
(a)
(b)
272T
(b)
4
180 + 13 = 193
193T = S13W
360 – 272 = 88
272T = N88W
MathsQUEST Chapter 4 (A,B,C,D,E,F,G) - Trigonometry Test REVISION
11
A plane flies for 195 km on a bearing of
10211'T and then for 104 km on a bearing
21322'T How far south of the starting point is
the plane?
5
First leg of journey.
opposite
sin  
hypotenuse
s
sin 1211'  1
195
s1  195  sin 1211'
s1  41.15
Second leg of journey.
adjacent
cos 
hypotenuse
s
cos 3322'  2
104
s 2  104  cos 3322'
s 2  86.86
Distance south of starting point
 s1  s 2
 41.15  86.86
 128 .01
 128 km
MathsQUEST Chapter 4 (A,B,C,D,E,F,G) - Trigonometry Test REVISION
12
13
14
If sin  = 0.0305:
(a) What is the angle  (to the nearest
minute)?
(a)
sin  = 0.0305
  sin 1 0.0305
  145'
(b)
What is the value of cos  ?
(b)
cos  cos145'
cos145'  0.9995
(c)
Calculate tan  .
(c)
tan   tan 145'
tan 145'  0.0306
(d)
Show this information on a well labelled
diagram.
(d)
State in which quadrant each of the following
angles lies.
(a) 192
(a)
192 is in 3rd quadrant
as 180  192  270
(b)
(b)
172 is in 2nd quadrant
as 90  172  180
172
6
2
Calculate sin 65 and compare this answer with sin 65 = 0.9063
each of the following. What can you conclude?
(a) sin 115
(a) sin 115= 0.9063
Therefore sin 115 = sin 65
(b)
sin 245
(b)
sin 245 = 0.9063
Therefore sin 245 = –sin 65
(c)
sin 295
(c)
sin 295 =  0.9063
Therefore sin 295 = sin 65
MathsQUEST Chapter 4 (A,B,C,D,E,F,G) - Trigonometry Test REVISION
4
15
Complete the table of values for the rule
y = sin x
and use the range of x values given to sketch
the graph.
x
0°
30°
60°
90° 120° 150° 180°
y
x
210° 240° 270° 300° 330° 360° 390°
y
16
(a)
Convert 120º to radian measure,
expressing the answer in terms of π.
5
Convert the radian measurement
to
6
degrees.
4
x
0°
30°
60°
y
0
0.5
0.9
1
0.9
0.5
0
x
210° 240° 270° 300° 330° 360° 390°
y
–0.5 –0.9
(a)
120º =
(b)
5
6
c
(b)
90° 120° 150° 180°
MathsQUEST Chapter 4 (A,B,C,D,E,F,G) - Trigonometry Test REVISION
c
–1

–0.9 –0.5
 120
180
c
2
=
3
180 5

=

6
= 150º
0
0.5
4