MTH 113 - Practice Test 1
Sections 4.1-4.6
No Calculator problems 1-18
13) csc
Find the value of the trigonometric function.
π
1) csc
3
2) tan
3) sin
4) sec
14) tan 570°
2π
3
15) cot 750°
Convert the angle in degrees to radians. Express answer as
a multiple of π.
16) -30°
9π
4
Convert the angle in radians to degrees.
9
17)
π
10
π
6
5) tan -
Convert the angle in radians to degrees. Round to two
decimal places.
10
18)
π radians
9
5π
4
Find the radian measure of the central angle of a circle of
radius r that intercepts an arc of length s.
2
19) r = feet, s = 16 feet
3
6) cos π
7) sec
π
2
Find the length of the arc on a circle of radius r intercepted
by a central angle θ. Round answer to two decimal places.
20) r = 7 centimeters, θ = 55°
8) cos (-150°)
The point P(x, y) on the unit circle that corresponds to a
real number t is given. Find the value of the indicated
trigonometric function at t.
2
21
21) ,
Find tan t.
5 5
9) sin (-120°)
10) sin
22π
3
22)
11) cos
12) sin
4π
3
8π
3
3
2 10
,7
7
Find csc t.
Solve the problem.
23) What is the domain of the cosine function?
-2π
3
24) What is the range of the sine function?
1
Sin t and cos t are given. Use identities to find the
indicated value. Where necessary, rationalize
denominators.
7
3
25) sin t = , cos t = - . Find cot t.
4
4
0≤t<
31) Find sin θ.
2
π
and cos t is given. Use the Pythagorean identity
2
3
sin2 t + cos2 t = 1 to find sin t.
33
26) cos t =
7
4
33
A)
C)
B)
7
4
D)
Find a cofunction with the same value as the given
expression.
π
32) sin
14
4
33
4
7
Use a calculator to find the value of the trigonometric
function to four decimal places.
27) sec 8
28) cot
A) cos
π
14
B) cos
3π
7
C) sin
π
14
D) sin
3π
7
33) tan 33°
A) sec 33°
C) cot 33°
π
10
B) cot 57°
D) cot 123°
Solve the problem.
34) A building 250 feet tall casts a 60 foot long
shadow. If a person looks down from the top
of the building, what is the measure of the
angle between the person's line of sight and
the vertical side of the building (to the nearest
degree)? (Assume the person's eyes are level
with the top of the building.)
Use the Pythagorean Theorem to find the length of the
missing side.Then find the indicated trigonometric
function of the given angle. Give an exact answer with a
rational denominator.
29) Find tan θ.
9
35) A radio transmission tower is 250 feet tall.
How long should a guy wire be if it is to be
attached 8 feet from the top and is to make an
angle of 28° with the ground? Give your
answer to the nearest tenth of a foot.
8
Find the measure of the side of the right triangle whose
length is designated by a lowercase letter. Round your
answer to the nearest whole number.
36)
30) Find sec θ.
2
a
3
39°
b = 15
2
37)
c
36°
b = 19
47) sec θ =
3
, θ in quadrant IV
2
Find tan θ.
48) tan θ =
21
, 180°< θ < 270°
20
Find cos θ.
49) cot θ = -
Use a calculator to find the value of the acute angle θ in
radians, rounded to three decimal places.
38) tan θ = 13.2894
7
, cos θ < 0
2
Find csc θ.
Find the reference angle for the given angle.
50) 98°
Use a calculator to find the value of the acute angle θ to
the nearest degree.
39) sin θ = 0.8659
51) -268°
52) Sin t and cos t are given. Find the indicated value. Where
necessary, rationalize denominators.
11
5
40) sin t = , cos t = - . Find cot t.
6
6
53)
4π
3
11π
12
54) Which of the following trigonometric functions
is an even function?
A) Cosine
B) Sine
C) Tangent
D) Cosecant
Sin t and cos t are given. Use identities to find the
indicated value. Where necessary, rationalize
denominators.
2
3 5
41) sin t = , cos t =
. Find csc t.
7
7
A point on the terminal side of angle θ is given. Find the
exact value of the indicated trigonometric function of θ.
42) (-15, 36) Find sin θ.
43) (-4, -3) Find sec θ.
44) (3, -2) Find sin θ.
Let θ be an angle in standard position. Name the quadrant
in which the angle θ lies.
45) cos θ < 0, csc θ < 0
A) quadrant I
B) quadrant II
C) quadrant III
D) quadrant IV
Find the exact value of the indicated trigonometric
function of θ.
4
46) cos θ = , tan θ < 0
Find sin θ.
9
3
Answer Key
Testname: PRACTICE TEST 1
1)
2 3
3
2) - 3
2
3)
2
4)
5) -1
6) -1
7) undefined
3
8) 2
3
2
3
10) 2
1
11) 2
3
12) 2
13) 14)
2 3
3
31)
2 13
13
41)
7
2
42)
12
13
43) -
5
4
44) -
2 13
13
45) C
3
3
15)
3
π
16) radians
6
17) 162°
18) 200°
19) 24 radians
20) 6.72 centimeters
21
21)
2
22) -
13
2
32) B
33) B
34) 13°
35) 515.5 feet
36) a = 12 cm
37) c = 23cm
38) 1.496 radians
39) 60°
5 11
40)
11
2 3
3
9) -
30)
46) -
65
9
47) -
5
2
48) -
20
29
49)
53
2
50) 82°
51) 88°
π
52)
3
7 10
20
53)
23) all real numbers
24) all real numbers from -1 to 1, inclusive
3 7
25)
7
π
12
54) A
26) D
27) -6.8729
28) 3.0777
9
29)
8
4