Pre-Calculus 6.0
FINAL EXAM Review Packet
Name: __________________
Date: ___________ Pd: ___
Graph the given angle and then find a positive and negative coterminal
angle.
=
θ 173°
1.)
2.)
pos: _____
neg: _____
θ= −
7π
6
pos: _____
neg: _____
θ=
3.)
19π
3
pos: _____
neg: _____
Convert to Decimal Degree. Round to 4 decimal places.
4.) −145°54'37 " = _________
5.) 23°41'46" = ___________
Convert to DMS. Round to the nearest second.
6.) 241.7614° = __________
7.) 1.36 = ___________
Convert from degrees to radian measure without a calculator.
8.) 105° = _______
9.) 135° = ________
10.) 50° = ________
Convert from radians to degrees without using a calculator.
11.)
7π
= _______
4
12.) −
17π
13π
= _________ 13.)
= ________
3
6
Find the length of the arc (s) intercepted by a central angle ( θ ) of a
circle with given dimension. Round to 2 decimal places and include units
of measure.
14.) θ =
π
7
and diameter = 16”
15.)
=
θ 122.6° and radius = 2.1 m.
Pre-Calculus 6.0
FINAL EXAM Review Packet
Find the central angle of a circle, in DMS rounded to the nearest
second, for the following situations:
16.) The arc length intercepted by
a central angle is 3”. The
diameter of the circle is 1.7”
17.) The arc length intercepted by
a central angle is equal to
the radius of the circle.
Solve for linear speed and/or angular speed as requested.
18) A car is moving at 35 mph. What is the linear speed of a pebble that is
stuck in the tread of the 20” diameter tires on the car in feet per
second? What is the rotational speed of the tires, in rpm? What is the
angular speed of the tires under these conditions?
19.) The rotational speed of a pulley on a drill press is 2500 rpm. If the
pulley is 4” in diameter, find the angular speed of the pulley and the
linear speed of a drive belt which rides on the edge of the pulley.
Find the values of the six trig functions:
20.) sin θ = _____
cscθ = _____
cosθ = _____
secθ = _____
tan θ = _____
cotθ = _____
θ
8
3 2
Pre-Calculus 6.0
FINAL EXAM Review Packet
Set up a trig equation, then solve for the indicated values. Round to 2
decimal places as necessary.
21.)
22.)
13
x
7
4
x
θ
41°
y
θ = _________ (DMS)
x = _________
X = ________
y = ________
23.)
24.)
θ
11
7
2π
5
8
x
X = ________
θ = __________ (Dec Radian)
Use your calculator to find the indicated values. Round to 4 decimal
places.
25.) sin 123° = ______
26.) cos 54°12’ = _______
27.) cot 54°34” = ______
28.) csc 85.51° = _______
29.) sec 25.73° = _______
30.) tan 54.22° = _______
31.) sec q = -2.1503; q = _______
32.) cot q = 0.1766; q = ________
33.) cos q = 1.0449; q = _______
34.) tan q = 2.1266; q = ________
35.) csc q = 0.4819; q = _______
36.) csc q = 1.4819; q = _______
Pre-Calculus 6.0
FINAL EXAM Review Packet
2
and sec θ < 0 , find the value of the other 5
5
trigonometric functions, expressed in simplest radical form.
Given sin = −
37.) sin θ = _____
cscθ = _____
cosθ = _____
secθ = _____
tan θ = _____
cotθ = _____
Find all angles over [0, 2) that meet the given criteria. Express answer
in radian measure. If answer is not a common angle, round to 4 decimal
places.
38.) sin θ =
3
11
40.) csc θ = −
7
3
39.) cos θ = −
2
7
41.) cot θ = −
4
9
42.)
A six foot Eskimo is standing 20 ft from the base of a heptangonal
prism ice castle. His eyes are about 6” below the top of his head.
He can see the top of the castle if he looks up at an angle
of 63
. Find the height of the ice castle.
43.)
A shepherd is cautiously watching over his flock of sheep from the
top of a 75 foot cliff. Assuming that the shepherd is lying on the
ground at the top of the cliff to avoid being spotted by predators,
at what angle of depression does the shepherd need to look in order
to keep an eye on a rare orange spotted sheep that is located 92
feet from the base of the cliff? Express answer in DMS format.
Pre-Calculus 6.0
FINAL EXAM Review Packet
44.)
The top of a 200 foot lighthouse is spotted at an angle of elevation
of 27from a ship that is headed straight towards the lighthouse.
About 15 minutes later, lighthouse keeper who lives at the top of
the lighthouse, observes the ship at an angle of depression of 33
.
How far did the ship move and what was its speed over the last 15
minutes? Express answer in feet and feet per min respectively.
45.)
From a certain location on a street leading straight to a tall
building, the angle of elevation to the top of the building is 24
.
From another location on the same street that is 500 feet away
from the first location, the angle of elevation is measured to be
30
. Find the height of the building.
Building
A
B
Ground
Find the reference angle for the following:
46.) 210°
47.) 300°
48.) -97°
49.) 384°
50.) -205°
51.)
53.) 3.3571
54.) 4.1950
52.) −
7π
11
5π
3
In which quadrant(s) do the following conditions hold true?
55.) sin q > 0 and sec q < 0 ______ 56.) sec q > 0 and cot q < 0 ______
Pre-Calculus 6.0
FINAL EXAM Review Packet
Find the complement and supplement of the following angles. Answer in
the same units of measure as given in the problem.
3π
5π
57.)
58.)
59.) 123
7
9
Identify the amplitude, period, phase shift and vertical shift for each of
the following.
60.) y = 5 cos (2q - p)
61.) y = 5 −
Amp: __________
Period: __________
Phase Shift: ________
Vertical Shift: _________
1
sin q
2
Amp: __________
Period: __________
Phase Shift: ________
Vertical Shift: _________
π
1
62.) y = 1 - sin  θ + 
2
2
Amp: __________
Period: __________
Phase Shift: ________
Vertical Shift: _________
3π 

63.) y = -3 cos  3x +

2 

Amp: __________
Period: __________
Phase Shift: ________
Vertical Shift: _________
Graph the following:
4
3
64.) y = cos (q + p)
2
1
- 2π
- 3π
2
-π
-π
2
-1
-2
-3
-4
π
2
π
3π
2
2π
5π
2
3π
7π
2
4π
Pre-Calculus 6.0
FINAL EXAM Review Packet
π
1
65.) y = 2 sin  x − 
2
2
4
3
2
1
-π
2
-π
- 3π
2
- 2π
π
2
-1
π
3π
2
5π
2
2π
4π
7π
2
3π
-2
4
66.) y = sec (x - p)
-3
3
-4
2
1
- 2π
Asymptotes: x =
- 3π
2
-π
-π
2
π
2
-1
π
3π
2
5π
2
2π
4π
7π
2
3π
-2
-3
-4
4
67.) y = 2 csc x
3
2
1
- 2π
Asymptotes: x =
- 3π
2
-π
2
-π
π
2
-1
π
3π
2
2π
5π
2
3π
7π
2
-2
-3
-4
4
68.) y = tan x
3
2
1
- 2π
Asymptotes: x =
- 3π
2
-π
-π
2
π
2
-1
π
3π
2
5π
2
2π
4π
7π
2
3π
-2
-3
-4
4
69.) y = cot x
3
2
1
- 2π
Asymptotes: x =
- 3π
2
-π
-π
2
-1
-2
-3
-4
π
2
π
3π
2
2π
5π
2
3π
7π
2
4π
4π
Pre-Calculus 6.0
FINAL EXAM Review Packet
Evaluate the following. Answers must be in simplest rational, radical form.

3
70.) arcsin  −
71.) sin −1 ( −1 ) = ___________
 = ________
 2 
 2
72.) arccos 
73.) tan −1 3 = ___________
 = _________
 2 
3

74.) sin  arcsin  = ________
75.) tan ( arctan ( −549 ) ) = _____
8


 1 
76.) cos ( arccos π ) = ________
77.) tan  arcsin  −   = ______
 2 

( )
(
78.) cos arc cot


3 
79.) cos  arctan  −
  = _____

3




 2 
81.) tan  arcsin  −   = _____
 5 


 4π  
83.) arcsin  sin 
  = _____
 3 

( 3 )) = _____

 3 
80.) sin  arc cos    = _____
 7 


 5π  
82.) arc cos  cos 
  = _____
 4 

Complete the chart with the domain and range of the following functions
using interval notation where possible:
Function
84)
85)
86)
87)
88)
89)
90)
91)
92)
sin x
cos x
tan x
csc x
sec x
cot x
arcsin x
arccos x
arctan x
Domain
Range
Graph the following:
93) y=arcsinx
94) y=arccosx
95) y=arctanx
Pre-Calculus 6.0
FINAL EXAM Review Packet
Simplify using the trig identities:
96.)
− tan( −θ )
= ________
π


cos  − θ 
2

97.)
sin2 x − 1
= _________
csc2 x − 1
Find the general solutions to the given equations as well as the specific
solutions over [0, 2Π).
98.) 2 cos x + 1 = 0
99.) 2 sin2 x = 1
100.) 3tan3 x = tan x
101.) 2 sin x −
102.) sin(2x ) − 4 cos x =
0
103.)
1
cos x =
0
3
1
x
−1
sin   − 4 cos(x ) =
2
2
State the case (SSS, SAS, AAS or SSA), whether or not it is ambiguous,
and then use Law of Sines or the Law of Cosines to solve if possible.
DRAWINGS ARE NOT TO SCALE.
A
104.)
80°
9.5
70°
B
C
Pre-Calculus 6.0
FINAL EXAM Review Packet
105.)
A
15
14
60°
B
C
A
106.)
7
63°
B
C
23
A
107.)
14
8
B
C
10
Find the area of the following triangles:
A
108.)
A
109.)
7
34°
B
B
C
5
Area = _________
14
6
8
Area = __________
C
A
111.)
5
B
17
Area = ___________
A
110.)
12
7
C
B
35°
8
Area = ____________
C