Alg II Honors Trig Test
Multiple Choice
Identify the choice that best completes the statement or answers the question.
1. Identify the expression that completes the equation so that it is an identity.
=
a.
b.
c.
d.
Simplify the trigonometric expression.
2.
a.
b.
c.
d.
3.
tan
1
cot
sin
a.
b.
c.
d.
Find the remaining sides and angles in the triangle. Round your answers to the nearest tenth.
4. a = 11, b = 12, and c = 17
a.
= 84.8°,
= 49.9°,
b.
= 44.7°,
= 40.1°,
c.
= 84.8°,
= 45.3°,
d.
= 40.1°,
= 44.7°,
= 45.3°
= 95.2°
= 49.9°
= 95.2°
5. Use the Law of Cosines. Find b to the nearest tenth.
C
60
b
48°
B
a. 102.2
A
85
b. 62.4
6. Use the Law of Cosines. Find
c. 132.9
to the nearest tenth of a degree.
d. 63.2
C
17
22
B
A
30
a. 33.9
b. 57.7
7. In
, j = 9 in., k = 5 in., and
.
a. 28°
b. 59°
c. 32°
d. 75°
c. 46.3
d. 85.7
= 43°. Find
8. In
, b = 7, c = 10, and
= 146°. Find a.
Round your answer to the nearest tenth.
a. 16.3
b. 14.4
c. 5.7
d. 6.2
Use the graph of y = sin  to find the value of sin  for each value of .
9. 270º
y
1





–1
a. –0.4
1
10.
radians
4
b. –0.8
c. –0.6
d. –1
c.
y
y
4
1
2
O

_

2
3_
2
2 
O
–1

2

3

2

3
–2
a.
b.
c.
d.
–0.7
0.7
–0.9
0.9
–4
d.
y
4
11. Sketch one cycle of y = 4 sin 4.
y
a.
2
4
2
O
–2

O
2

3
–4
–2
–4
b.
y
4
2
O

2

3
–2
–4
Short Answer
12.
Sketch the angle in standard position.
355º
13. –350º
14. Find the exact value of cos 300º and sin 300º.
Write the measure in radians. Express the answer in terms of .
15. –310º
Write the measure in degrees.
16.
radians
17. Find the exact values of
and
20. The line of sight from a small boat to the light at the
top of a 50-foot lighthouse built on a cliff 25 feet
above the water makes a 60° angle with the water.
To the nearest foot, how far is the boat from the
cliff?
.
18. Find the exact value of sin
.
50
ft
19. Use the circle below. Find the length s to the nearest
tenth.
s
60 o
4_
5
Drawing is not to scale.
4 in.
Find the length x. Round to the nearest tenth.
21.
x
19
66 °
25 ft
22.
10
x
20 °
23. In
,
is a right angle. Find
nearest tenth of a degree.
to the
25. In XYZ, Y is a right angle and
. Find
sin Z in fraction and in decimal form. Round to the
nearest hundredth, if necessary.
B
x
Z
54.4
47.4
5
A
26.6
4
C
X
Y
24. Find the measure of x in the right triangle.
8
x
21
In
,
is a right angle. Find the remaining sides and angles. Round your answers to the nearest tenth.
26. a = 3.4, c = 5.8
Find the remaining sides and angles in the triangle. Round your answers to the nearest tenth.
27.
= 55°,
= 44°, and b = 68
28. Find the period of the graph shown below.
2 y
1
O

3 
2
–1
–2
29. Find the amplitude of the sine curve shown below.
y
4
2
O

2
3

–2
–4
30. Write the equation for the sine function shown below.
y
4
2
O
–2
–4

2

Alg II Honors Trig Test
Answer Section
MULTIPLE CHOICE
1.
2.
3.
4.
5.
6.
7.
8.
9.
10.
11.
A
B
B
D
D
A
D
A
D
B
C
SHORT ANSWER
12.
y

355
x
13.
y

–350
x
14.
15.
16. 210º
17.
18.
19.
20.
21.
22.
23.
24.
10.1 in.
43 feet
17.4
3.4
29.3
67.6°
25.
26.
27.
2

3
29. 4
30.
28.
= 35.9°,
= 54.1°, b = 4.7
= 81°, a = 80.2, c = 96.7