Trigonometry Review Package
Multiple Choice
1
The angle  in standard position,  180 o    0 o , as
represented by the terminal arm in the diagram to the right,
must be;
A
–53.1o
B
–36.9o
C
–126.9o
D
–143.1o
2
The approximate location of an ordered pair on the unit circle
is given by (-0.98, 0.22). The angle created by a terminal
arm passing through this point could be;
A
20o
B
160o
C
40o
D
140o
3
If sin  
A
B
C
D
-5
5
-2
-4
A: (-3, -4)
-6
3
, then the value of tan  could be;
5
4
4
or
3
3
3
3
or
4
4
3
only
4
3
only
4
4
If the value of tan   0 , and sin   0 , then the angle  must lie in;
A
quadrant I
B
quadrant II
C
quadrant III
D
quadrant IV
5
If the terminal arm of  passes through the point (-3k, k) where k  0 , then the exact value of sin 
must be;
5
A
1
B
5
10
C
1
D
10
6
If tan( ) 
A
B
C
D
5
, and cos( )  0 , then the value of sin(  ) must be;
12
–5
5
13
–12
 12
13
10
7
1
If sin    , then the total number of angles,  in the domain 0    720 making this expression
2
true are
A
2
B
4
C
6
D
8
8
6
4
8
If angle x is less than 90 as shown in the diagram, which of the
following is also equal to the sin x ?
A
cos x
tan x
B
sin(180  x)
C
cos(180  x)
D
-10
9
12
2
10
x
-5
5
8
-2
The positive standard position angle,  , shown in the diagram to the right
must be
68
A
B
24
66
C
D
22
6
(2, 5)
-4
4
2

-5
5
10
Which of the following conditions must be given in order to use the Law of Cosines to find a missing
side?
A
Any two sides and the included angle.
B
Any two sides and any angle.
C
Any two angles and the side opposite one of the given angles
B
D
All three angles and no sides
11
Correct to the nearest degree, the value of ABC in the diagram on the
right is
61
A
65
B
67
C
71
D
-2
6.2 cm
A
6.0 cm
69
C
12
The standard position angle of 141 has a reference angle of
A
41
29
B
51
C
39
D
13
If cos A 
A
B
C
D
3
, then sin A could be
5
4
5
5
4
2
3
3
2
14
Which of the following statements is true?
A
cos(20 )  cos(160 )
B
sin(20 )  sin(160 )
C
tan(20 )  tan(160 )
D
sin(20 )  cos(160 )
15
A triangle has A  30 , B  80 and a  12.0 cm . The measure of c must be
A
22.5 cm
B
6.4 cm
C
23.6 cm
D
7.1 cm
16
The ordered pair (-5,12) sits on the terminal arm of  in standard position. The value of  must be
122.5
A
117.3
B
114.7
C
112.6
D
J
17
A hockey player is located at point C on the diagram shown to the
right. The width of the hockey net, JK, according to this diagram,
must be
A
188.2 cm
B
182.9 cm
C
180.1 cm
D
178.5 cm
537 cm
C
mJCK = 9.4
690.3 cm
K
18
The ordered pair ( x, y ) is on the terminal arm of angle  in
standard position. Which of the following is true?
sin   0, cos   0, tan   0
A
sin   0, cos   0, tan   0
B
sin   0, cos   0, tan   0
C
sin   0, cos   0, tan   0
D
19
Given the triangle ABC with A  30, b  42 and
A
61 only
B
119 only
C
Both 61 or 119
D
Neither 61 or 119
(x,y)
a  24 , the measure of B is;
Numerical Response
1.
5
If sin(  )  0 , and tan( )  , 0    360 o , then  , correct to the nearest whole angle, must be _____.
3
2.
Given cos( k ) 
 3
, and 450o<k<630o, the smallest possible value for k must be _____ degrees.
2
10
8
6
3.
The reference angle of the standard position angle 635o is _____.
4.
The reference angle of the terminal arm shown in the diagram to the
right is 32 . The smallest positive standard position angle must be
_____o.
4
2
-5
5
-2
5.
If cos  0.8660 , then the smallest value of  correct to the nearest whole angle, in standard
position must be _____.
-4
B
6.
The measure of side AB in the diagram on the right, correct
to the nearest tenth is _____ cm.
-6
A
mBAC = 71
13 m
C
mBCA = 52
7.
A standard position angle measures 125 . The measure of the reference angle is _____ .
8.
In the diagram shown to the right, the measure of
side BC, correct to the nearest tenth is _____.
B
A
26
118
7.6 cm
9.
C
William is working on three problems involving trigonometric ratios. The answers to his three problems
are shown in the chart below.
Answer
1 Must be in quadrant I.
2 Must be in quadrant II.
3 Could be in either quadrant I or II.
Which of the answer numbers complete the following statements.
If sin A  0.3216 , A _____.
If tan B  1.2853 , B _____.
If cos C  0.8513 , C _____.
10.
The triangle PQR has Q  43,
to the nearest tenth is _____.
p  20cm and
q  15cm . The smallest value of P + R + r, correct
6
Written Response
4
1.
A positive angle rotation, in standard position, yields the
terminal arm OP, shown in the diagram to the right.
a.
Determine the distance OP.-10
2
O
-5
5
F
2.
b.
Determine the values of sin  , cos and tan  , if  is
the smallest possible positive standard position angle.
c.
Determine the angle  , to the nearest tenth of a radian.
d.
If the distance OF  1, determine the exact values of x and y on the ordered pair for point F.
-2
P
-4
-6
-8
The questions below are based on the diagram shown to
the right.
a.
According to the diagram, if  is a standard
position angle represented by the terminal arm,
determine the values of sin  , cos and tan  .
3
3
2
1
y
b.
A point has been placed on the terminal arm,
represented by (a, b). This point is on the unit
circle. Determine the value of a and b, and
represent your answers correct to the nearest
tenth.
4
b
2
1
0
1
2
3
4
1
2
3
3
4
3.
3
x, a
A terminal arm passes through the point (-2, 3).
a.
Determine the values of sin, cos, and tan for an angle passing through that point.
b.
Determine the smallest possible positive angle, in standard position, that passes through this
point. Express your answer to the nearest whole degree.
4
20
18
16
4.
Use the diagram shown on the right to answer each of the
following questions.
14
P (-5, 12)
12
10
a.
Point P is on the terminal arm of angle  , in
standard position. If O is located at the origin, find
the length of side OP.
8
6
4
2
b.
State the value of tan  .
-10
-5
5
-2
-4
c.
5.
6.
Find the value of both the standard position angle and the reference angle. State your answers
to the nearest tenth of a degree.
Using its navigation system, the Airplane
shown in the diagram determines it is
flying a distance of 1018 m from the base
of the control tower, and 2313 m from the
end of the runway.
Airplane
a.
If the angle between the two given
Control Towe r
End of Runway
sides is 35 , use the law of cosines,
and find the distance from the control tower to the end of the runway to the nearest metre.
b.
Correct to the nearest tenth of a degree, find the measure of the angle of elevation of the end
of the runway to the airplane.
Use the diagram on the right to answer each of the
following.
A
C
D
mADB = 122
a.
Using the law of cosines, find the measure of
side AC, and state your answer to the nearest
tenth.
DB = 3.7 cm
CB = 5.2 cm
AB = 7.8 cm
B
mABC = 119
b.
Find the measure of angle A.