309
Trigonometric Ratio Practice Questions
DO NOT USE A CALCULATOR ON ANY OF THE FOLLOWING QUESTIONS UNLESS INDICATED.
1. In Triangle
ABC
above, what is the value of
Bsin
?
(A)
29
2
(B)
5
2
(C)
29
5
(D)
2
5
2. In Triangle
ABC
above, what is the value of
Bcos
?
(A)
13
2
(B)
13
3
(C)
3
2
(D)
2
3
310
3. In Triangle
ABC
above, what is the value of
Ctan
?
(A)
9
5
(B)
106
5
(C)
106
9
(D)
5
9
4. FREE RESPONSE: In Triangle
FGH
, the
measure of
G
is
90
and
3FG
. If
3
4
tan F
, what is the length of
FH
?
5. (CALCULATOR) FREE RESPONSE: In
Triangle
ABC
, the measure of
C
is
90
and
26AB
. If
13
5
sin B
, what is the
length of
BC
?
6. FREE RESPONSE: Triangle
LMN
has right
angle M. If
5
3
cos L
, what is the value of
Nsin
?
Note: Figure not drawn to scale.
7. FREE RESPONSE: In Triangle
ABC
above,
the sine of
y
is
8.0
. What is the cosine of
x
?
311
Note: Figure not drawn to scale.
8. In the figure above, triangle
ABC
is similar
to triangle
DEF
and
EB
. What is the
value of
)tan(F
?
(A)
12
5
(B)
13
5
(C)
13
12
(D)
5
12
Note: Figure not drawn to scale.
9. (CALCULATOR) FREE RESPONSE: In the
figure above,
5
4
)cos( D
. If
16CD
and
10DE
, what is the length of
BC
?
10. (CALCULATOR) FREE RESPONSE: In
triangle
DEF
, the measure of
E
is
90
,
12DE
and
16EF
. Triangle
LMN
is
similar to triangle
DEF
, where vertices
L
,
M
, and
N
correspond to vertices
D
,
E
,
and
F
, respectively, and each side of triangle
LMN
is
7
2
the length of the corresponding
side of triangle
DEF
. What is the value of
Ncos
?
329
Additional Trigonometry Topics Practice Questions
DO NOT USE A CALCULATOR ON ANY OF THE FOLLOWING QUESTIONS UNLESS INDICATED.
1. If
90yx
and
13
7
cos y
, what is the
value of
xsin
?
(A)
7
13
(B)
13
6
(C)
13
7
(D)
7
6
2. If
x
n
3
sin
and
0x
, what is
n
in terms
of
x
?
(A)
)
3
(sin
1
x
(B)
)3sin( x
(C)
)
3
(sin
1
x
(D)
)
3
sin(
x
3. In a right triangle, one angle measures
w
,
where
13
5
sin w
. What is
)90cos( w
?
(A)
13
5
(B)
13
12
(C)
13
8
(D)
5
13
4. If
m
n
b
4
3
tan2
, what is
b
in terms of
m
and
n
?
(A)
)
3
8
(tan
1
n
m
(B)
)
4
6
(tan
1
m
n
(C)
)
6
4
(tan
1
n
m
(D)
)
8
3
(tan
1
m
n
330
Note: Figure not drawn to scale.
5. FREE RESPONSE: In the triangle above, the cosine of
t
is
35.0
. What is the sine of
n
?
6. If
nx )90sin(
, which of the following
must be true for all values of
x
?
(A)
nx )cos(
(B)
nx )90cos(
(C)
nx 90)sin(
(D)
xn )90sin(
7. If
t
nx
84
cos
, what is
x
in terms of
n
and
t
?
(A)
)
2
cos(
t
n
(B)
)
2
(cos
1
t
n
(C)
)
2
cos(
n
t
(D)
)
2
(cos
1
n
t
331
Note: Figures not drawn to scale.
8. (CALCULATOR) The angles shown above are acute and
yx cossin
. If
53 zx
and
102 zy
, what is the value of
z
?
(A) 15
(B) 17
(C) 19
(D) 37
9. FREE RESPONSE: If
)
2
1
(cos
1
n
, what is
the value of
n
?
10. (CALCULATOR) FREE RESPONSE : In
Triangle
NOP
above, point
K
(not shown)
lies on
NP
. What is the value of
)sin()cos( NOKKOP
?
