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Review of Trigonometry
Math
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1. Which of the following values has a different sign from the others?
Sine in Quadrant III
Cosine in Quadrant II
Cotangent in Quadrant IV
Secant in Quadrant IV
2. Which of the following values is unequal to the others?
sin(60
^{o}
)
cos(150
^{o}
)
cos(330
^{o}
)
sin(120
^{o}
)
3. Which of the following angles has a reference angle of
60
^{o}
?
150
^{o}
120
^{o}
210
^{o}
30
^{o}
4. An arc along the unit circle begins at (1,0) and is
units long. What are the coordinates of its endpoint?
(
,
)
(
,
)
(
, 
)
(
,
)
5. Which of the following graphs is not the same as the others?
y
= sin(
x

Π
)
y
= sin(
x
)
y
= cos(
x

)
y
= cos(
x
+
)
6. Which of the following graphs has a different period from the others?
y
= cos(2
x
)
y
= tan(
x
)
y
= sin(2
x
)
y
= csc(
x
)
7. Which of the following graphs has a different amplitude from the others?
y
= sin(2
x
)
y
= 2 cos(
x

Π
)
y
= cos(
x
+
)
y
= sin(3
x
) + 2
8. What fraction of angles has a tangent less than 1?
Impossible to tellthere are an infinite number of angles in existence.
9. Which of the following is unequal to the others?
sin(
x
)csc(
x
)
sec
^{2}
(
x
)  tan
^{2}
(
x
)
csc
^{2}
(
x
)  cot
^{2}
(
x
)
sin
^{2}
(
x
)  cos
^{2}
(
x
)
10. Which of the following is unequal to the others?
cos(
x
)tan(
x
)
11. Which of the following functions is even?
sine
tangent
cosecant
secant
12. Which of the following is unequal to the others?
sin(
x
)cos(
x
)csc(
x
)
sin(
x
)cot(
x
)
13. If
sin(
x
) =
, what is
sin(
x
)
?

Impossible to tell
14. Solve for
x
.
2 sin(
x
)cos(
x
) = 1
.
x
=
,
x
=
,
x
=
Impossible to calculate
15. Solve for
x
.
sin(
x
) 
= cos(
x
)
.
x
=
,
x
=
,
x
=
,
x
=
,
16. Solve for
x
.
cos(
x
)tan(
x
) + 1 = sec
^{2}
(
x
)  tan
^{2}
(
x
)  1
.
x
=
x
=
,
No solution
x
=
17. Solve for
x
.
2 cos(
x
) = sin(
x
)csc(
x
)
.
x
= 30
^{o}
, 150
^{o}
x
= 60
^{o}
, 300
^{o}
x
= 90
^{o}
x
= 45
^{o}
, 225
^{o}
18. Solve for
x
.
sin(
x
)tan(
x
)sec(
x
) =
.
x
=
x
=
,
x
=
,
x
=
,
19. Solve for
x
.
= sin
^{2}
(
x
) + cos
^{2}
(
x
)  sin(
x
)csc(
x
)
.
x
= 0,
Π
x
=
x
=
,
No solution
20. Solve for
x
.
tan(
x
)sin(
x
)cos(
x
) = sin(
x
)sec(
x
)
.
x
=
,
x
= 0,
x
=
,
,
,
x
= 0,
,
Π
,
21. Solve for
x
.
2 cos(
x
) = 
(csc
^{2}
(
x
) 
)
x
=
,
x
=
,
x
=
,
x
=
,
22. Which of the following numbers is part of the domain of Arcsecant?
23. Which of the following is uneequal to the others?
arcsin
arccos
arctan(1)
They're all equal to each other
24. Which of the following is undefined?
arcsin(
)
arccos(1)
arcsec(
)
arccsc(1)
25. Solve the right triangle ABC with right angle
C
given
c
= 5
,
b
= 3
.
a
= 4
,
A
36.9
^{o}
,
B
53.1
^{o}
.
a
= 4
,
A
53.1
^{o}
,
B
36.9
^{o}
.
a
= 4
,
A
=
B
= 45
^{o}
.
a
=
,
A
53.1
^{o}
,
B
36.9
^{o}
.
26. Right triangle ABC has right angle
C
,
A
= 30
^{o}
, and
b
=
. Find
a
.
a
= 2
.
a
=
c
cos(30)
a
= 1
The previous two answers are both right
27. A boat sails
40
^{o}
south of east for 30 miles. How far south and east does it travel?
23.0
miles south and 19.3 miles east
19.3
miles east and south
19.3
miles south and 23.0 miles east
25.2
miles south and east
28. An airplane flies
5
^{o}
west of north for 240 miles. How far west and north does it travel?
20
miles west and 220 miles north
200
miles west and 40 miles north
20.9
miles west and 239.1 miles north
239.1
miles west and 20.9 miles north
29. A 20 foot ladder leans against a wall and forms a
45
^{o}
angles with the ground. How high up on the wall does the ladder reach?
20 feet
10 feet
20
feet
feet
30. Which of the following right triangles ABC with
C
= 90
^{o}
is not congruent to the others?
a
= 6
,
B
36.9
^{o}
b
= 6
,
c
= 10
A
53.1
^{o}
,
B
36.9
^{o}
c
= 10
,
A
53.1
^{o}
31. Which of the following right triangles ABC with
C
= 90
^{o}
is not congruent to the others?
c
= 2
,
B
= 30
^{o}
a
=
,
B
= 30
^{o}
b
= 1
,
A
= 60
^{o}
A
= 60
^{o}
,
c
=
32. One boat sails 30 miles west and 22 miles north. Another boat sails 55 miles west and 42 miles north. Which boat traveled in the direction closest to due north?
They both traveled in the same direction
The first boat
The second boat
Impossible to calculate
33. The sun's rays hit the earth's surface at a 45 degree angle. How long a shadow does a 50 foot tree cast?
25 feet
50 feet
100 feet
50
feet
34. A ship's final destination is 310 miles east and 48 miles north. It sails for 260 miles in a direction
22
^{o}
south of east to an intermediate destination. What is the required distance and direction for the ship to reach its final destination?
69.3
miles,
64.6
^{o}
north of east
98
miles,
44
^{o}
north of east
160.9
miles,
44
^{o}
north of east
160.9
miles,
64.6
^{o}
north of east
35. Which of the following triangles ABC is not congruent to the others?
A
23.5
^{o}
,
B
= 130
^{o}
,
c
= 7
B
= 130
^{o}
,
b
= 12
,
a
6.25
A
23.5
^{o}
,
c
6.25
,
C
26.5
^{o}
b
= 12
,
A
23.5
^{o}
,
C
26.5
^{o}
36. Calculate
A
given the following information about triangle ABC:
a
= 12
,
b
= 14
,
B
= 40
^{o}
.
A
56.6
^{o}
A
.551
^{o}
A
33.4
^{o}
Impossible to calculate
37. Given
b
,
c
, and
C
of an oblique trianlge, in which
C
is acute and
c
<
b
, how many triangles are determined?
0
1 OR 2
0 OR 2
0, 1, OR 2
38. Solve for
C
, in the following triangle ABC, given that
a
= 5
,
b
= 5
, and
B
= 110
^{o}
.
C
= 40
^{o}
C
32.3
^{o}
The triangle does not exist
Impossible to calculate
39. Find angle
B
of triangle ABC given
a
= 5
,
b
= 6
, and
c
= 7
A
57.1
^{o}
A
32.9
^{o}
A
47.1
^{o}
Impossible to calculate
40. Find angle
B
of triangle ABC given that
c
= 17
and
A
= 55
^{o}
B
= 45
^{o}
B
24.7
^{o}
The triangle does not exist
Impossible to calculate
41. Find side
b
in triangle ABC given that
a
= 18
,
c
= 21
, and
C
= 43
^{o}
.
b
= 20
b
20.6
b
30.2
Impossible to calculate
42. Find the area of triangle ABC given
a
= 5
,
b
= 17
, and
c
= 19
Area = 20.5
Area
40.8
Area
13.8
Impossible to calculate
43. Find the area of triangle ABC given
a
= 5.6
,
b
= 4.2
, and
C
= 110
^{o}
Area = 9.8
Area
11.0
Area = 11.76
Area = 23.52
44. Find the area of triangle ABC given that
A
= 25
^{o}
,
B
= 135
^{o}
, and
c
= 14
.
Area
42.8
Area = 14
Area
85.6
Area
112.4
45. Find the area of triangle ABC given that
a
= 3
,
c
= 5
, and
C
= 90
^{o}
.
Area = 12
Area =
3
Area = 7.5
Area = 6
46. Which of the following expressions is unequal to the others?
cos(2
x
)
2 sin(
x
)cos(
x
)
2 cos
^{2}
(
x
)  1
1  2 sin
^{2}
(
x
)
47. Which of the following expressions is unequal to the others?
sin(60
^{o}
)cos(20
^{o}
) + cos(60
^{o}
)sin(20
^{o}
)
cos(40
^{o}
)
cos(60
^{o}
)cos(20
^{o}
) + sin(60
^{o}
)sin(20
^{o}
)
cos(60
^{o}
)cos( 20
^{o}
)  sin(60
^{o}
)sin( 20
^{o}
)
48. Which of the following expressions is unequal to the others?
cos(
β
)sin(
α
)
(sin(
α
+
β
) + sin(
α

β
))
sin(
α
)cos(
β
)
(sin(
α
+
β
)  sin(
α

β
))
49. Which of the following expressions is unequal to the others?
sin(
x
)cos(
x
)
sin(2
x
)
sin
^{2}
(
x
)cot
^{2}
(
x
)
tan(
x
)cos
^{2}
(
x
)
50. Which of the following expressions is unequal to the others?
sin
^{2}
(
x
)(1 + cot
^{2}
(
x
)
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