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MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question.
Use the appropriate identity to find the indicated function value. Rationalize the denominator, if applicable. If the given
value is a decimal, round your answer to three decimal places.
1) csc , given that sin = -0.4271
1)
A) -2.341
B) 2.341
C) 1.171
D) -1.171
The triangles are similar. Find the missing side, angle or value of the variable.
2)
a=6
b=8
c=5
d=3
e=4
A) x = 5
B) x = 11
C) x = 10
2)
D) x = 15
Use the fundamental identities to find the value of the trigonometric function.
2
3) Find cos , given that tan = - and is in quadrant II.
7
A)
7 53
53
B) -
7 53
53
C) -
Convert the angle to degrees, minutes, and seconds.
4) 140.54°
A) 140°30 54
B) 140°32 54
53
7
C) 140°33 24
3)
D)
53
2
D) 140°32 24
4)
Determine the signs of the given trigonometric functions of an angle in standard position with the given measure.
5) csc (608°) and cot (608°)
5)
A) positive and positive
B) negative and negative
C) negative and positive
D) positive and negative
If r is a positive number and the point (x, y) is in the indicated quadrant, decide whether the given ratio is positive or
negative.
x
6) III,
6)
y
A) Positive
Identify the quadrant for the angle
7) sin > 0 and cos < 0
A) Quadrant II
B) Negative
satisfying the following conditions.
B) Quadrant III
C) Quadrant IV
1
D) Quadrant I
7)
Draw the given angle in standard position. Draw an arrow representing the correct amount of rotation. Find the measure
of two other angles, one positive and one negative, coterminal with the given angle.
8) 50°
8)
230° and -130°
A)
B) 230° and -130°
C)
Sketch an angle
side of .
9) (3, 6)
D)
410° and -310°
in standard position such that
410° and -310°
has the least positive measure and the given point is on the terminal
9)
A)
B)
C)
D)
2
The triangles are similar. Find the missing side, angle or value of the variable.
10) x and y
A) x = 17; y =
17
4
B) x = 12; y = 3
C) x = 8; y = 2
10)
D) x = 10; y =
5
2
If n is an integer, n · 180° represents an integer multiple of 180°, and (2n + 1) · 90° represents an odd integer multiple of
90°. Decide whether the expression is equal to 0, 1, -1, or is undefined.
11) tan(n · 180°)
11)
A) -1
B) Undefined
C) 1
D) 0
Provide an appropriate response.
12) Find the complement of an angle whose measure is 73°.
A) 107°
B) 73°
C) 17°
D) 163°
Convert the angle to degrees, minutes, and seconds.
13) 40.78°
A) 40°46 36
B) 40°46 78
D) 40°46 54
C) 40°46 48
Use the fundamental identities to find the value of the trigonometric function.
2
14) Find cos , given that tan = - and sin > 0.
5
A)
5 29
29
B) -
29
5
C)
29
2
Decide whether the statement is possible or impossible for an angle .
15) sin = 5.46
A) Possible
B) Impossible
3
12)
13)
14)
D) -
5 29
29
15)
Draw the given angle in standard position. Draw an arrow representing the correct amount of rotation. Find the measure
of two other angles, one positive and one negative, coterminal with the given angle.
16) -85°
16)
A) 175° and -5°
B) 275° and -445°
C) 85° and -105°
D) 185° and -355°
Classify the triangle as acute, right, or obtuse and classify it as equilateral, isosceles, or scalene.
17)
A) Acute, scalene
C) Acute, isosceles
17)
B) Obtuse, scalene
D) Obtuse, equilateral
Determine the signs of the given trigonometric functions of an angle in standard position with the given measure.
18) cos (459°) and tan (459°)
18)
A) positive and negative
B) negative and negative
C) negative and positive
D) positive and positive
4
Sketch an angle
side of .
19) (-5, 3)
in standard position such that
has the least positive measure and the given point is on the terminal
19)
A)
B)
C)
D)
Use the fundamental identities to find the value of the trigonometric function.
20) Find csc , given that cot = - 15 and is in quadrant II.
1
1
A)
B) 4
C) 4
4
20)
D) -4
Use the appropriate identity to find the indicated function value. Rationalize the denominator, if applicable. If the given
value is a decimal, round your answer to three decimal places.
6
21) tan , given that cot = 21)
7
A) -
7
6
B) -
6
7
C)
5
7
6
D)
13
7
Convert the angle to decimal degrees and round to the nearest hundredth of a degree.
22) 131°57 32
A) 132.02°
B) 131.92°
C) 131.97°
D) 131.96°
Identify the quadrant for the angle
23) cos < 0 and csc < 0
A) Quadrant I
D) Quadrant III
satisfying the following conditions.
B) Quadrant II
C) Quadrant IV
22)
23)
Use the appropriate identity to find the indicated function value. Rationalize the denominator, if applicable. If the given
value is a decimal, round your answer to three decimal places.
24) cot , given that tan = 0.2407
24)
A) 4.148
B) 4.155
C) 4.169
D) 4.162
Use the fundamental identities to find the value of the trigonometric function.
4
25) Find sin , given that cos = and tan < 0.
7
A) -
33
7
Perform the calculation.
26) 90° - 54°52
A) 35°52
33
4
B) - 33
C) -
B) 36°8
C) 35°8
25)
D) -
7
4
D) 36°52
Without using a calculator, give the exact trigonometric function value with rational denominator.
27) sin 60°
3
2
1
A)
B)
C) 3
D)
2
2
2
Solve the problem.
28) In one area, the lowest angle of elevation of the sun in winter is 21° 34 . A fence is to be built 13.3 ft
away from a plant in the direction of the sun. (See drawing) Find the maximum height, x , for the
fence so that the plant will get full sun. Round your answer to the tenths place when necessary.
13.3 ft
A) 4.6 ft
21° 34
B) 6.8 ft
C) 5.6 ft
6
D) 5.3 ft
26)
27)
28)
29) Find a formula for the area of the figure in terms of s.
A)
6 2
s
4
B)
3 2
s
2
29)
C)
6 s2
D)
3 2
s
6
30) Any offset between a stationary radar gun and a moving target creates a "cosine effect" that reduces
the radar mileage reading by the cosine of the angle between the gun and the vehicle. That is, the
radar speed reading is the product of the actual reading and the cosine of the angle. Find the radar
reading to the nearest hundredth for the auto shown in the figure.
30)
31° angle
Actual speed: 83 mph
A) 83.86 mph
B) 71.14 mph
C) 82.14 mph
D) 42.75 mph
Use a calculator to decide whether the statement is true or false.
31) sin (45° + 120°) = sin 45° + sin 120°
A) True
B) False
Find all values of , if is in the interval [0, 360°) and has the given function value.
32) tan = 1
A) 45° and 315°
B) 225° and 315°
C) 135° and 225°
31)
D) 45° and 225°
32)
Write the function in terms of its cofunction. Assume that any angle in which an unknown appears is an acute angle.
33) cos 48°
33)
A) sec 42°
B) cos 138°
C) sin 42°
D) sin 48°
Find the exact value of the expression.
34) cos 30°
2
2 3
A)
B)
2
3
34)
C)
3
3
D)
2
Solve the problem.
35) The angle of elevation from a point on the ground to the top of a tower is 35° 16 . The angle of
elevation from a point 130 feet farther back from the tower is 24° 18 . Find the height of the tower.
Round to the nearest foot.
A) 1624 ft
B) 173 ft
C) 162 ft
D) 158 ft
7
35)
Suppose ABC is a right triangle with sides of lengths a, b, and c and right angle at C. Find the unknown side length using
the Pythagorean theorem and then find the value of the indicated trigonometric function of the given angle. Rationalize
the denominator if applicable.
36) Find sin A when a = 7 and b = 6.
36)
85
6 85
85
7 85
A)
B)
C)
D)
6
85
7
85
Find all values of , if
3
37) cos =
2
is in the interval [0, 360°) and has the given function value.
A) 225° and 315°
37)
B) 30° and 330°
C) 135° and 225°
D) 45° and 225°
Use a calculator to find the function value. Give your answer rounded to seven decimal places, if necessary.
38) sec 57°31
A) 3.7250186
B) 1.8620093
C) 1.8610093
D) 3.7240186
Solve the problem for the given information.
39) Find the equation of a line passing through the origin and making a 45° angle with the positive
x-axis.
2
3
x
x
A) y =
B) y =
C) y = x
D) y = -x
2
3
Find a solution for the equation. Assume that all angles are acute angles.
40) tan(3 + 32°) = cot( + 36°)
A) 5.5°
B) 2°
C) 6°
Find the exact value of the expression.
41) sin 2115°
2
1
A) B) 2
2
D) 9.5°
38)
39)
40)
41)
C) 2 3
D) -
3
2
Without using a calculator, give the exact trigonometric function value with rational denominator.
42) tan 45°
2 3
1
A) 1
B)
C) 2
D)
3
2
Solve the problem.
43) The grade resistance F of a car traveling up or down a hill is modeled by the equation F = W sin ,
where W is the weight of the car and is the angle of the hill's grade ( > 0 for uphill travel, < 0
for downhill travel). What is the grade resistance (to the nearest pound) of a 2050-lb car on a level
road ( = 0°)?
A) -2050 lb
B) 0 lb
C) undefined
D) 2050 lb
8
42)
43)
44) A 5.2-ft fence is 11.463 ft away from a plant in the direction of the sun. It is observed that the
shadow of the fence extends exactly to the bottom of the plant. (See drawing) Find , the angle of
elevation of the sun at that time. Round the measure of the angle to the nearest tenth of a degree
when necessary.
44)
5.2 ft
11.463 ft
A)
= 25.8°
B)
= 24.6°
C)
= 24.4°
D)
= 24.2°
45) A center-pivot irrigation system waters a sector-shaped field. Find the area of the field if the
central angle, = 35° and the radius, r = 150 meters. Round to the nearest whole number.
A) 46 m 2
B) 92 m 2
C) 13,744 m 2
D) 6872 m 2
45)
Find the area of a sector of a circle having radius r and central angle . If necessary, express the answer to the nearest
tenth.
46) r = 16.0 m, = 20°
46)
2
2
2
2
A) 89.4 m
B) 44.7 m
C) 2.8 m
D) 0.5 m
Solve the problem.
47) Find for a spoke on a bike tire revolving 85 times per minute.
A) 170 radians per min
C)
85
B) 85 radians per min
radians per min
D)
9
170
radians per min
47)
The figure shows an angle in standard position with its terminal side intersecting the unit circle. Evaluate the indicated
circular function value of .
48) Find sin .
48)
7
24
,25
25
A) -
7
24
B) -
24
25
C)
24
25
D)
7
25
Solve the problem.
49) A circular sector has an area of 16 in2 and an arc length of 6 inches. What is the measure of the
central angle in degrees? Round to the nearest degree.
A) 32°
B) 129°
C) 64°
D) 11°
Find the value of s in the interval [0, /2] that makes the statement true. Round to four decimal places.
50) sin s = 0.8065
A) -0.7966
B) 0.9382
C) 0.3450
D) 2.2034
49)
50)
Use the formula s = r t to find the value of the missing variable. Give an exact answer.
51) r = 4 cm,
A)
16
9
=
cm
9
radian per sec, t = 4 sec
B)
51)
16 cm
9
C)
9
cm
16
D)
9
16
cm
For the given value of s, decide in which quadrant an angle of s radians lies by evaluating sin s and cos s.
52) s = 52
A) I
B) II
C) IV
D) III
10
52)
Find the corresponding angle measure in radians.
53) 120°
A)
6
B)
53)
C)
2
3
D)
6
Use the formula v = r to find the value of the missing variable. Give an exact answer unless otherwise indicated.
54) v = 19 ft per sec, r = 9.7 ft (Round to four decimal places when necessary.)
54)
A) 1.9588 radians per sec
B) 0.3239 radian per sec
C) 0.5105 radian per sec
D) 6.0479 radians per sec
Find the value of s in the interval [0, /2] that makes the statement true. Round to four decimal places.
55) tan s = 2.8438
A) 1.0505
B) 4.3743
C) 1.2327
D) 0.8035
Solve the problem.
56) Find the measure (in radians) of a central angle of a sector of area 46 square inches in a circle of
radius 5 inches. Round to the nearest hundredth.
A) 1.84 radians
B) 5.52 radians
C) 7.36 radians
D) 3.68 radians
Decide whether the statement is possible or impossible for an angle .
57) sec = -0.41
A) Impossible
B) Possible
55)
56)
57)
The triangles are similar. Find the angle or side that corresponds to the given angle or side in the other triangle.
58) AC
58)
(AB is parallel to DE.)
A) Cannot be determined
C) EC
B) DE
D) CD
11
The triangles are similar. Find the missing side, angle or value of the variable.
59) x
a = 25
b = 75
c = 52
A) x = 39
B) x = 52
C) x = 13
59)
D) x = 26
Use the fundamental identities to find the value of the trigonometric function.
9
60) Find csc , given that cot = - and cos < 0.
8
A) -
145
9
B)
9 145
145
C)
145
8
60)
D) -
9 145
145
The triangles are similar. Find the angle or side that corresponds to the given angle or side in the other triangle.
61) AC
61)
A) RT
C) ST
Evaluate the expression.
62) cos 0° - 8 sin 90°
A) 0
63) tan(-540)°
A) -1
B) Cannot be determined
D) RS
B) -8
C) 1
D) -7
B) Undefined
C) 1
D) 0
12
62)
63)
Sketch an angle
side of .
64) (3, -6)
in standard position such that
has the least positive measure and the given point is on the terminal
64)
A)
B)
C)
D)
Solve the problem for the given information.
65) Find the equation of a line passing through the origin so that the cosine of the angle between the
3
line in quadrant I and the positive x-axis is
.
2
A) y = x
B) y =
3
x
2
C) y =
3
x
3
Decide whether the statement is true or false.
66) cos 72° cos 59°
A) True
B) False
Determine whether the statement is true or false.
67) cos 60° = cos 180° - cos 120°
A) True
B) False
13
D) y =
65)
3x
66)
67)
Solve the problem.
68) Find the exact value of x in the figure.
68)
14
x
A) 7 3
Find the sign of the following.
69) cot ( + 180°), given that
A) negative
B) 7 6
C)
is in the interval (90°, 180°).
14 6
3
D)
14 3
3
69)
B) positive
Convert the radian measure to degrees. Give answer using decimal degrees to the nearest hundredth. Use 3.1416 for .
70) 1.6816
70)
A) 96.85°
B) 96.35°
C) 95.65°
D) 97.35°
Solve the problem.
71) A pulley rotates through 51° in one minute. How many rotations (to the nearest tenth of a rotation)
does the pulley make in an hour?
A) 306.0 rotations
B) 8.5 rotations
C) 17.0 rotations
D) 153.0 rotations
Find the exact circular function value.
-2
72) cos
3
A) -
3
2
71)
72)
B) -
1
2
C)
3
2
D) undefined
The triangles are similar. Find the angle or side that corresponds to the given angle or side in the other triangle.
73) B
73)
A) S
B) T
C) R
Provide an appropriate response.
74) Find the complement of an angle whose measure is 38°18 .
A) 52°42
B) 52°41
C) 51°18
14
D) C
D) 51°42
74)
Solve the problem.
75) A tunnel is to be dug from point A to point B. Both A and B are visible from point C. If AC is 220
miles and BC is 547 miles, and if angle C is 90°, find the measure of angle B. Round your answer to
the tenths place.
A) 34.1°
B) 21.9°
C) 18.7°
D) 31.4°
Determine whether the statement is true or false.
76) cos 540° = 1 - 2 sin2 270°
A) True
76)
B) False
Convert the degree measure to radians. Leave answer as a multiple of .
77) -30°
A) -
7
Evaluate the expression.
78) tan(-180°)
A) -1
B) -
C) -
5
B) 0
Find the exact value of the expression.
79) csc (-240°)
2 3
A)
B)
3
6
C) 1
75)
77)
D) -
8
D) Undefined
78)
79)
2
C) -2
D) -
3
3
Solve the problem.
80) Electrical wire is being wound around a drum with radius of 0.95 meters. How much line (to the
nearest hundredth of a meter) would be wound around the drum if it is rotated through an angle of
340.8°?
A) 5.55 m
B) 5.75 m
C) 5.45 m
D) 5.65 m
15
80)
Answer Key
Testname: PRACTICE1TRIG
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A
C
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D
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D
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B
B
B
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D
D
B
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B
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B
D
C
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C
D
B
B
C
A
A
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C
D
B
A
B
C
B
16
Answer Key
Testname: PRACTICE1TRIG
51)
52)
53)
54)
55)
56)
57)
58)
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60)
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80)
A
B
C
A
C
D
A
C
A
C
D
D
D
B
C
A
B
C
A
B
B
B
B
D
B
A
C
B
A
D
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