Download Trigonometry Test #2 Review

Name: ______________________
Class: _________________
Date: _________
ID: A
Trigonometry Test #2 Review
1. Solve ΔABC using the diagram and the given measurements. (The triangle is not drawn to scale.)
B = 42°, a = 17
2. Solve triangle ABC given that A = 47°, B = 52°, and b = 78.
____
3. Solve triangle ABC given that A = 45°, B = 54°, and b = 70.
a. C = 81°, a = 80.09, c = 97.78
c. C = 81°, a = 61.18, c = 85.46
b. C = 261°, a = 61.18, c = 85.46
d. C = 261°, a = 80.09, c = 97.78
4. Find the area of ΔABC. The figure is not drawn to scale.
5. Solve ΔABC with A = 110°, a = 5, and b = 7.3.
____
6. Solve ΔABC with A = 69°, b = 34, and c = 46.
a. a = 46.38, B = 43.19°, C = 67.81°
c.
b. a = 46.38, B = 41.74°, C = 69.26°
d.
a = 45.15, B = 43.19°, C = 67.81°
a = 45.15, B = 41.74°, C = 69.26°
7. Solve triangle ABC given that a = 19, b = 10, and c = 14.
1
Name: ______________________
ID: A
8. Find the area of ΔABC .
____
9. Determine the graph of: y = cos x
a.
b.
c.
d.
2
Name: ______________________
____ 10. Determine the graph of : y = 2 sin x
a.
b.
ID: A
c.
d.
Find the amplitude and period of the graph.
11. y = 3 sin 2 πx
12. y = −3 cos πx
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Name: ______________________
ID: A
13. Graph y = tan x. Include vertical asymptotes in your sketch. Be sure to pay attention to the horizontal
axis to determine whether you should graph in degrees or radians!
1
x. Include vertical asymptotes in your sketch. Be sure to pay attention to the horizontal
2
axis to determine whether you should graph in degrees or radians!
14. Graph y = tan
15. a. Graph y = sin x and y = sin (–x) on a graphing calculator.
b. Graph y = –sin x and y = sin (–x) on a graphing calculator.
c. Graph y = cos x and y = cos (–x) on a graphing calculator.
d. Graph y = –cos x and y = cos (–x) on a graphing calculator.
e. Describe any patterns that you observed in your graphs. Be sure to include comments about which
graphs are the same and which are reflections of each other.
16. Compare the graphs of y = cos x, y = 4 cos x, and y = cos 4x. Specifically compare the amplitude and
period of the graphs.
17. Consider the related equations y = sin x, y = 2 sin x, and y = sin 2x. Explain the effect that the coefficient
2 has on the graphs of y = 2 sin x and y = sin 2x when compared to the graph of y = sin x.
4
Name: ______________________
ID: A
ÁÊ
π ˜ˆ
____ 18. Graph y = 4 cos ÁÁÁÁ x − ˜˜˜˜ on the interval −π ≤ x ≤ π.
ÁË
4 ˜¯
a.
c.
b.
d.
5
Name: ______________________
ID: A
Graph:
ÊÁ
π ˆ˜
____ 19. y = −tan ÁÁÁÁ x + ˜˜˜˜
ÁË
2 ˜¯
a.
b.
c.
d.
6
none of these
ID: A
Trigonometry Test #2 Review
Answer Section
1. ANS:
A = 48°, b = 15.31, c = 22.88
PTS: 1
DIF: Level B
REF: MAL21702
TOP: Lesson 13.1 Use Trigonometry with Right Triangles
KEY: solve | trigonometry | right triangle
BLM: Comprehension
NOT: 978-0-618-65615-8
2. ANS:
C = 81°, a = 72.39, c = 97.76
PTS: 1
DIF: Level B
REF:
TOP: Lesson 13.5 Apply the Law of Sines
BLM: Comprehension
NOT:
3. ANS: C
PTS: 1
DIF:
TOP: Lesson 13.5 Apply the Law of Sines
BLM: Comprehension
NOT:
4. ANS:
2
14.67 cm
MAL21756
KEY: solve | triangle | Law of Sines
978-0-618-65615-8
Level B
REF: MAL21757
KEY: solve | triangle | Law of Sines
978-0-618-65615-8
PTS: 1
DIF: Level B
REF: MAL21768
TOP: Lesson 13.5 Apply the Law of Sines
KEY: area | acute | triangle | trigonometry | sine | SAS
BLM: Comprehension
NOT: 978-0-618-65615-8
5. ANS:
No solution. It is not possible to draw the indicated triangle.
PTS: 1
DIF: Level B
REF:
TOP: Lesson 13.5 Apply the Law of Sines
BLM: Comprehension
NOT:
6. ANS: A
PTS: 1
DIF:
TOP: Lesson 13.6 Apply the Law of Cosines
BLM: Comprehension
NOT:
7. ANS:
A = 103.4°, B = 30.8°, C = 45.8°
PTS:
TOP:
KEY:
NOT:
A2.13.05.FR.11
KEY: Free response | law of sines | SSA
978-0-618-65615-8
Level B
REF: MAL21778
KEY: Law of Cosines | solve
978-0-618-65615-8
1
DIF: Level B
REF: MAL21779
Lesson 13.6 Apply the Law of Cosines
triangle | Law of Sines | Law of Cosines
BLM: Comprehension
978-0-618-65615-8
1
ID: A
8. ANS:
276.96
PTS: 1
DIF: Level B
REF: MAL21785
TOP: Lesson 13.6 Apply the Law of Cosines
KEY:
BLM: Comprehension
NOT: 978-0-618-65615-8
9. ANS: B
PTS: 1
DIF: Level B
REF:
TOP: Lesson 14.1 Graph Sine, Cosine, and Tangent Functions
KEY: graph | trigonometry | cosine
BLM: Knowledge NOT:
10. ANS: A
PTS: 1
DIF: Level B
REF:
TOP: Lesson 14.1 Graph Sine, Cosine, and Tangent Functions
KEY: graph | trigonometry | sine
BLM: Knowledge NOT:
11. ANS:
Amplitude: 3
Period: 1
area | heron | triangle
MAL21793
978-0-618-65615-8
MAL21791
978-0-618-65615-8
PTS: 1
DIF: Level A
REF: MAL21800
TOP: Lesson 14.1 Graph Sine, Cosine, and Tangent Functions
KEY: period | amplitude | sin
BLM: Knowledge NOT: 978-0-618-65615-8
12. ANS:
Amplitude: 3
Period: 2
PTS: 1
DIF: Level A
REF: MAL21801
TOP: Lesson 14.1 Graph Sine, Cosine, and Tangent Functions
KEY: period | amplitude | cos
BLM: Knowledge NOT: 978-0-618-65615-8
13. ANS:
PTS: 1
DIF: Level B
REF: MAL21809
TOP: Lesson 14.1 Graph Sine, Cosine, and Tangent Functions
KEY: tangent | graph
BLM: Knowledge NOT: 978-0-618-65615-8
2
ID: A
14. ANS:
PTS: 1
DIF: Level B
REF: MAL21810
TOP: Lesson 14.1 Graph Sine, Cosine, and Tangent Functions
KEY: graph | tangent
BLM: Knowledge NOT: 978-0-618-65615-8
15. ANS:
e. The graphs of y = –sin x and y = sin (–x) are the same. The graphs of y = –sin x and y = sin (–x) are
reflections over the x-axis of the graph of y = sin x. The graphs of y = cos x and y = cos (–x) are the
same. The graphs of y = cos x and y = cos(–x) are reflections over the x-axis of the graph of y = –cos x.
PTS:
NAT:
TOP:
KEY:
NOT:
1
DIF: Level C
REF: MAL21798
NCTM 9-12.NOP.3.a | NCTM 9-12.GEO.4.e
Lesson 14.1 Graph Sine, Cosine, and Tangent Functions
characteristics | graph | cosine | sine | amplitude
BLM: Analysis
978-0-618-65615-8
3
ID: A
16. ANS:
The graphs of y = cos x and y = cos 4x have an amplitude of 1, while the graph of y = 4 cos x has an
amplitude of 4. The graphs of y = cos x and y = 4 cos x both have a period of 360°, while the graph of
y = cos 4x has a period of 90°.
PTS: 1
DIF: Level B
REF: MAL21796
NAT: NCTM 9-12.CON.2 | NCTM 9-12.PRS.1 | NCTM 9-12.GEO.4.e
TOP: Lesson 14.1 Graph Sine, Cosine, and Tangent Functions
KEY: cosine | frequency | period | amplitude | compare | graph
BLM: Comprehension
NOT: 978-0-618-65615-8
17. ANS:
In the equation y = 2 sin x, the 2 is the amplitude of the function. So the graph of y = 2 sin x is bounded
by the lines y = 2 and y = –2, rather than y = 1 and y = –1 as in the graph of y = sin x. In the equation y =
sin 2x, the 2 represents the frequency and therefore determines the period (in this case, π ). So the graph
of y = sin 2x completes one cycle in π units, which is twice the frequency of the graph of y = sin x which
has a period of 2π.
PTS:
NAT:
TOP:
KEY:
NOT:
18. ANS:
TOP:
KEY:
19. ANS:
TOP:
KEY:
1
DIF: Level B
REF: MAL21797
NCTM 9-12.CON.2 | NCTM 9-12.PRS.4 | NCTM 9-12.PRS.1 | NCTM 9-12.GEO.4.e
Lesson 14.1 Graph Sine, Cosine, and Tangent Functions
amplitude | characteristics | period | sine
BLM: Comprehension
978-0-618-65615-8
A
PTS: 1
DIF: Level B
REF: MAL21816
Lesson 14.2 Translate and Reflect Trigonometric Graphs
graph | sine | cosine
BLM: Knowledge NOT: 978-0-618-65615-8
C
PTS: 1
DIF: Level B
REF: MAL21819
Lesson 14.2 Translate and Reflect Trigonometric Graphs
tangent | graph
BLM: Knowledge NOT: 978-0-618-65615-8
4