Download (Ch. 4) Test Review - Kenton County Schools

Name: ______________________ Class: _________________ Date: _________
ID: A
Trigonometry (Ch. 4) Test Review - CALCULATOR ALLOWED
____
1. A guy wire runs from the ground to a cell tower. The wire is attached to the cell tower a = 190 feet
above the ground. The angle formed between the wire and the ground is q = 75∞(see figure).
How long is the guy wire? Round your answer to one decimal place.
The guy wire is about 393.4 feet long.
The guy wire is about 65.6 feet long.
The guy wire is about 590.1 feet long.
The guy wire is about 98.4 feet long.
The guy wire is about 196.7 feet long.
2. A passenger in an airplane at an altitude of a = 40 kilometers sees two towns directly to the east of
the plane. The angles of depression to the towns are 28∞and 55∞(see figure). How far apart are the
towns? How far apart are the ships? Round your answer to one decimal place.
a.
b.
c.
d.
e.
____
a.
b.
c.
d.
e.
49.2 km
47.2 km
48.2 km
50.2 km
51.2 km
1
____
3. A television camera at ground level is filming the lift-off of a space shuttle at a point a = 700 meters
from the launch pad (see figure). Let q be the angle of elevation to the shuttle and let s be the height
of the shuttle. Write q as a function of s.
a.
q = arccot
b.
q = arcsin
c.
q = arccsc
d.
q = arctan
e.
q = arctan
s
700
s
700
s
700
700
s
s
700
2
____
4. A boat is pulled in by means of a winch located on a dock a = 5 feet above the deck of the boat (see
figure). Let q be the angle of elevation from the boat to the winch and let s be the length of the rope
from the winch to the boat. Write q as a function of s.
a.
q = arcsec
b.
q = arccos
c.
q = arcsin
d.
q = arctan
e.
q = arccsc
5
s
5
s
5
s
5
s
5
s
3
____
5. A television camera is on a reviewing platform a meters from the street on which a parade will be
passing from left to right (see figure). Write the distance d from the camera to a particular unit in the
parade as a function of the angle x.
a = 28
d = 28 cos x
d = 28 sec x
d = 28 cot x
d = 28 sin x
d = 28 tan x
6. Solve the right triangle shown in the figure for all unknown sides and angles. Round your answers to
two decimal places.
a.
b.
c.
d.
e.
____
A = 30∞, b = 15
a.
b.
c.
d.
e.
a
a
a
a
a
ª
ª
ª
ª
ª
17.32, c ª 8.66, B = 60∞
0.59, c ª 1.16, B = 60∞
8.66, c ª 17.32, B = 60∞
8.66, c ª 17.32, B = 30∞
8.66, c ª 17.32, B = 45∞
4
____
7. State the quadrant in which q lies if tanq < 0 and cscq > 0.
____
Quadrant I
Quadrant III
Quadrant II
Quadrant IV
8. Evaluate the expression. Round your result to two decimal places.
a.
b.
c.
d.
-1
sin 0.75
1.85
–1.15
–0.15
2.85
0.85
9. Find the exact values of the three trignometric functions of the angle q ÊÁË cot q, sec q, csc q ˆ˜¯ shown in
the figure. (Use the Pythagorean Theorem to find the third side of the triangle.)
a.
b.
c.
d.
e.
____
a = 9, b = 41
a.
cot q =
b.
cot q =
c.
cot q =
d.
cot q =
e.
cot q =
9
40
40
9
40
9
9
40
9
40
, secq =
, secq =
, secq =
, secq =
, secq =
1
, cscq =
9
41
9
41
40
41
9
1
40
, cscq =
, cscq =
, cscq =
, cscq =
1
41
41
40
41
9
41
40
1
9
5
____ 10. The point ÊÁË -5,- 12 ˆ˜¯ is on the terminal side of an angle in standard position. Determine the exact
value of tanq.
13
12
12
b. tanq = 13
17
c. tanq =
12
1
d. tanq = 12
12
e. tanq =
5
____ 11. Use the Pythagorean Theorem to determine the third side and then find the three trignometric
functions of q: sin q, cos q , and cot q
a.
tanq = -
tan q =
5
12
a.
sin q =
b.
sin q =
c.
sin q =
d.
sin q =
e.
sin q =
13
5
13
5
5
13
5
13
12
13
, cos q =
, cos q =
, cos q =
, cos q =
, cos q =
13
12
13
12
12
13
12
13
5
13
, cot q =
, cot q =
, cot q =
, cot q =
, cot q =
12
5
5
12
12
5
5
12
12
5
6
____ 12. Find the radian measure of the central angle of a circle of radius r that intercepts an arc of length s.
Radius r
ArcLengths
8inches
24 inches
q = 3 radians
1
b. q = radians
4
c. q = 192 radians
d. q = 32 radians
1
e. q = radians
3
____ 13. Evaluate the expression. Round your result to two decimal places.
a.
arccos 0.32
1.25
0.25
–0.75
2.25
3.25
____ 14. An airplane, flying at an altitude of a = 6 miles, is on a flight path that passes directly over an
observer (see figure). If q is the angle of elevation from the observer to the plane, find the distance d
from the observer to the plane when q = 30∞.
a.
b.
c.
d.
e.
a.
b.
c.
d.
e.
d
d
d
d
d
=
ª
=
=
=
12 miles
6.9 miles
13 miles
6 miles
7 miles
7
____ 15. Determine the period and amplitude of the following function.
ÊÁ 2x p ˆ˜˜
y = 2 cos ÁÁÁÁ
+ ˜˜˜˜
ÁË 5
2¯
a.
b.
c.
d.
e.
period: 3p ; amplitude: 3
2p
period:
; amplitude: 3
3
period: 3p ; amplitude: 4
period: 10p ; amplitude: 2
period: 5p ; amplitude: 2
____ 16. A plane is 57 miles west and 42 miles north of an airport. The pilot wants to fly directly to the
airport. What bearing should the pilot take? Answer should be given in degrees and minutes.
a. 127∞25'
b. 129∞22'
c. 124∞20'
d. 53∞ 37'
e. 126∞23'
____ 17. A ladder 20 feet long leans against the side of a house. Find the height from the top of the ladder to
the ground if the angle of elevation of the ladder is 80∞. Approximate the answer to one decimal
place.
a.
b.
c.
d.
e.
22.7 ft
23.7 ft
19.7 ft
20.7 ft
21.7 ft
8
____ 18. Find the area of the sector of the circle with radius r and central angle q. Round to two decimal
places.
Radius r
CentralAngle q
8inches
p
5
A ª 20.11 square inches
A ª 22.11 square inches
A ª 18.11 square inches
A ª 160.85 square inches
A ª 40.21 square inches
____ 19. Find the exact values of the three trignometric functions of the angle q ÊÁË sin q, cos q, tan q ˆ˜¯ shown in
the figure. (Use the Pythagorean Theorem to find the third side of the triangle.)
a.
b.
c.
d.
e.
a=5
2
a.
sin q =
b.
sin q = 1, tanq =
c.
sin q = 1, tanq =
d.
sin q =
e.
sin q =
2
, tanq =
2 , secq = 1
2 , secq =
2
2
2
2
, secq =
2 , tanq = 1, secq =
2
2
, tanq = 1, secq =
2
2
2
2
9
____ 20. Find the value of given trigonometric function. Round your answer to four decimal places..
csc
2p
9
a.
csc
b.
csc
c.
csc
d.
csc
2p
9
2p
9
2p
9
2p
9
2p
ª 1.7557
ª 1.5557
ª – 1.5557
ª 1.6557
ª 1.4557
9
____ 21. A granular substance such as sand naturally settles into a cone-shaped pile when poured from a small
aperture. Its height depends on the humidity and adhesion between granules. The angle of elevation
of a pile, q, is called the angle of repose. If the height of a pile of sand is 13 feet and its diameter is
approximately 45 feet, determine the angle of repose. Round answer to nearest degree.
e.
csc
a.
b.
c.
d.
e.
27∞
28∞
29∞
30∞
26∞
10
____ 22. The point ÊÁË 7,24 ˆ˜¯ is on the terminal side of an angle in standard position. Determine the exact value
of tanq.
25
24
7
b. tanq = 24
24
c. tanq =
25
25
d. tanq =
24
24
e. tanq =
7
____ 23. Find the length of the arc on a circle of radius r intercepted by a central angle q. Round to two
decimal places.
a.
tanq = -
Radius r
CentralAngle q
29centimeters
52 ∞
a.
b.
c.
d.
e.
s
s
s
s
s
ª
ª
ª
ª
ª
24.32 centimeters
28.32 centimeters
29.29 centimeters
26.32 centimeters
8.38 centimeters
11
____ 24. A land developer wants to find the distance across a small lake in the middle of his proposed
development. The bearing from A to B is N 20∞W. The developer leaves point A and travels 59 yards
perpendicular to AB to point C. The bearing from C to point B is N 70∞W. Determine the
distance,AB, across the small lake. Round distance to nearest yard.
a.
b.
c.
d.
e.
80 yards
50 yards
65 yards
32 yards
25 yards
12
ID: A
Trigonometry (Ch. 4) Test Review - CALCULATOR ALLOWED
Answer Section
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OBJ:
E
PTS: 1
REF: 4.3.71a
B
PTS: 1
REF: 4.8.25
E
PTS: 1
REF: 4.7.106a
C
PTS: 1
REF: 4.7.105a
A
PTS: 1
REF: 4.6.92
C
PTS: 1
REF: 4.8.5
C
PTS: 1
REF: 4.4.19
Determine quadrant given constraints
E
PTS: 1
REF: 4.7.29
C
PTS: 1
REF: 4.3.6
E
PTS: 1
REF: 4.4.15
Determine value of trig function given point on terminal side
C
PTS: 1
REF: 4.3.13
A
PTS: 1
REF: 4.1.93
A
PTS: 1
REF: 4.7.23
A
PTS: 1
REF: 4.4.97a
E
PTS: 1
REF: 4.5.6
Determine period and amplitude of trig graph
E
PTS: 1
REF: 4.8.36b
OBJ: Find bearings
C
PTS: 1
REF: 4.8.21
A
PTS: 1
REF: 4.1.101
E
PTS: 1
REF: 4.3.8
B
PTS: 1
REF: 4.2.52
D
PTS: 1
REF: 4.7.108a
Use inverse functions to solve for theta
E
PTS: 1
REF: 4.4.13
Determine value of trig function given point on terminal side
D
PTS: 1
REF: 4.1.92
B
PTS: 1
REF: 4.8.41
Find distance using surveying bearings
1