Download Review Trigonometry Test 1.tst

MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question.
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.
1)
1) 115°
B)
475° and -245°
A)
295° and -65°
C)
475° and -245°
D)
295° and -65°
Suppose that is in standard position and the given point is on the terminal side of
indicated trig function for .
2) (0, -9); Find csc .
A) -9
B) -1
C) 9
. Give the exact value of the
2)
D) 1
Use the properties of angle measures to find the measure of each marked angle.
3)
a = (2x + 5)°
b = (4x - 33)°
A) -21°, -21°
B) 43°, 43°
C) 19°, 19°
3)
D) 71°, 71°
Classify the triangle as acute, right, or obtuse and classify it as equilateral, isosceles, or scalene.
4)
A) Acute, equilateral
C) Right, scalene
B) Obtuse, scalene
D) Obtuse, equilateral
1
4)
Use the properties of angle measures to find the measure of each marked angle.
5) Lines m and n are parallel.
a = (3x + 9)°
b = (2x + 76)°
A) 18°, 161°
B) 19°, 161°
Convert the angle to degrees, minutes, and seconds.
6) 342.49°
A) 342°23 49
B) 342°29 49
5)
C) 66°, 114°
D) 71°, 109°
C) 342°30 23
D) 342°29 24
6)
The triangles are similar. Find the missing side, angle or value of the variable.
7) R
7)
a = 18 cm
b = 118 °
A) 52°
B) 118°
C) 18 cm
Provide an appropriate response.
8) Find the complement of an angle whose measure is 39°16 50 .
A) 50°43 9
B) 51°44 10
C) 50°44 10
D) 10°
8)
D) 50°43 10
Decide whether the statement is possible or impossible for an angle .
5
7
9) cos = and sec =
7
5
A) Possible
Identify the quadrant for the angle
10) sec < 0 and tan < 0
A) Quadrant IV
9)
B) Impossible
satisfying the following conditions.
10)
B) Quadrant III
C) Quadrant II
D) Quadrant I
An equation of the terminal side of an angle in standard position is given along with a restriction on x. Find the
indicated trigonometric function value of . Do not use a calculator.
11) -6x - 5y = 0, x 0; Find sec .
11)
5
5 61
6
61
A) B) C) D) 6
61
5
5
2
Suppose that is in standard position and the given point is on the terminal side of
indicated trig function for .
12) (21, 28); Find sin .
4
4
3
A)
B)
C)
3
5
4
Sketch an angle
side of .
13) (-2, 5)
in standard position such that
. Give the exact value of the
12)
3
D)
5
has the least positive measure and the given point is on the terminal
13)
y
x
A)
B)
C)
D)
3
The triangles are similar. Find the missing side, angle or value of the variable.
14)
a=6
b=8
c=5
d=3
e=4
A) x = 15
B) x = 11
14)
C) x = 10
D) x = 5
C) 0
D) -5
Evaluate the expression.
15) 9 tan2 180° - 5 sin2 0° + 5 csc2 270°
A) 5
15)
B) 14
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.
y
16) II,
16)
x
A) Positive
B) Negative
Find the measure of the third angle of a triangle if the measures of the other two angles are given.
17) 10° and 90°
A) 100°
B) -10°
C) 260°
D) 80°
Use the fundamental identities to find the value of the trigonometric function.
4
18) Find sin , given that cos = and tan < 0.
7
A) -
33
4
B) -
7
4
C) -
33
7
18)
D) - 33
Classify the triangle as acute, right, or obtuse and classify it as equilateral, isosceles, or scalene.
19)
A) Acute, scalene
C) Obtuse, equilateral
17)
19)
B) Obtuse, scalene
D) Acute, isosceles
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
20) IV,
20)
y
A) Positive
B) Negative
4
The triangles are similar. Find the missing side, angle or value of the variable.
21) C .
m A = 63°
m E = 35°
A) 63°
Perform the calculation.
22) 90° - 35°16 46
A) 54°43 13
21)
B) 35°
C) 92°
D) 82°
B) 55°44 14
C) 54°43 14
D) 54°44 14
C) -1
1
D)
2
22)
Evaluate the expression.
23) sin 270°
A) 0
Identify the quadrant for the angle
24) csc > 0 and sec > 0
A) Quadrant I
23)
B) Undefined
satisfying the following conditions.
24)
B) Quadrant II
C) Quadrant IV
D) Quadrant III
The triangles are similar. Find the missing side, angle or value of the variable.
25)
a = 14
b = 21
c = 10
d = 15
e = 20
A) x = 26
B) x = 20
C) x = 28
25)
D) x = 35
Solve the problem. Round answers to the nearest tenth if necessary.
26) A tree casts a shadow 16 m long. At the same time, the shadow cast by a 62-centimeter-tall statue
is 93 cm long. Find the height of the tree.
A) 22.5 m
B) 9.2 m
C) 10.7 m
D) 24.0 m
5
26)
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
27) III,
27)
y
A) Negative
28) II,
B) Positive
x
y
28)
A) Negative
B) Positive
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.
29)
29) 170°
B)
530° and -190°
A) 350° and -10°
C)
350° and -10°
D) 530° and -190°
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.
30) cot(n · 180°)
30)
A) -1
B) Undefined
C) 1
D) 0
Find the angle of least positive measure coterminal with the given angle.
31) 500°
A) 250°
B) 130°
C) 320°
31)
D) 140°
Use the fundamental identities to find the value of the trigonometric function.
2
32) Find sin , given that cos = and is in quadrant IV.
3
A) -
3
2
B) -
5
3
C)
5
4
32)
D)
3 7
7
Determine the signs of the given trigonometric functions of an angle in standard position with the given measure.
33) sec (-35°) and sin (-35°)
33)
A) negative and negative
B) positive and positive
C) positive and negative
D) negative and positive
Give an expression that generates all angles coterminal with the given angle. Let n represent any integer.
34) 179°
A) 179° + n · 90°
B) 179° + n · 180°
C) 179° + n · 720°
D) 179° + n · 360°
34)
Convert the angle to decimal degrees and round to the nearest hundredth of a degree.
35) 68°40 8
A) 68.67°
B) 68.73°
C) 68.63°
35)
6
D) 68.68°
Suppose that is in standard position and the given point is on the terminal side of
indicated trig function for .
36) (18, 24); Find csc .
5
5
4
A)
B)
C)
4
3
3
. Give the exact value of the
36)
3
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
37)
37) tan , given that cot = 7
A)
13
7
B) -
7
6
C) -
6
7
D)
7
6
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.
r
38) IV,
38)
y
A) Negative
B) Positive
7
Exam
N ame___________________________________
MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question.
Convert the degree measure to radians. Leave answer as a multiple of .
1) 36°
A)
B)
5
C)
6
1)
D)
4
7
Convert the radian measure to degrees. Round to the nearest hundredth if necessary.
12
2)
7
A) 308.07°
B) 309.57°
C) 309.07°
2)
D) 308.57°
Find the exact value without using a calculator.
2
3) cos
3
A)
3
2
B) -
3)
3
2
1
2
C) -
D) undefined
4) cos 2
4)
1
B)
2
A) - 1
Find the length of an arc intercepted by a central angle
7
radians
5) r = 26.13 cm.; =
6
A) 191.5 cm
C) 1
D) 0
in a circle of radius r. Round your answer to 1 decimal place.
5)
B) 95.8 cm
C) 47.9 cm
D) 30.5 cm
Assume that the cities lie on the same north-south line and that the radius of the earth is 6400 km.
6) Find the distance betw een City A, 62° N and City B, 29° N . (Round to the nearest kilometer.)
A) 3624 km
B) 3715 km
C) 3686 km
D) 3777 km
6)
Find the area of a sector of a circle having radius r and central angle . If necessary, express the answer to the nearest
tenth.
7) r = 11.3 cm,
=
10
radians
A) 20.1 cm 2
7)
B) 40.2 cm 2
C) 6.4 cm 2
D) 1.8 cm 2
Find the exact circular function value.
-3
8) tan
4
A) 1
8)
B) - 1
C)
1
3
3
D)
3
Use a table or a calculator to evaluate the function. Round to four decimal places.
9) tan 0.2377
A) 1.0289
B) 0.2355
C) 0.2423
9)
D) 0.9719
Find the value of s in the interval [0, /2] that makes the statement true. Round to four decimal places.
10) sec s = 3.9448
A) 0.2563
B) 4.9687
C) 1.8271
D) 1.3145
Find the exact value of s in the given interval that has the given circular function value.
3
1
, 2 ; cos s =
11)
2
2
A) s =
7
4
B) s =
C) s =
3
5
3
Solve the problem.
12) Let angle POQ be designated . Angles PQR and VRQ are right angles. If
length of OQ.
A) 0
Use the formula
13)
B)
=
t
2
2
11)
D) s =
11
6
= 45°, find the exact
C) 1
D)
to find the value of the missing variable. Give an exact answer unless otherwise indicated.
Solve the problem.
14) Find for a spoke on a bike tire revolving 85 times per minute.
C)
170
85
12)
2
= 7.4962 radians per min, = 12.25 radians (Round to four decimal places w hen necessary.)
A) 1.6342 min
B) 0.6119 min
C) 19.7462 min
D) 91.8285 min
A)
10)
radians per min
B) 85 radians per min
radians per min
D) 170 radians per min
2
13)
14)
Answer Key
Testname: REVIEW TRIGONOMETRY TEST 1
1) C
2) B
3) B
4) B
5) C
6) D
7) B
8) D
9) A
10) C
11) D
12) B
13) B
14) C
15) A
16) B
17) D
18) C
19) D
20) B
21) D
22) C
23) C
24) A
25) C
26) C
27) B
28) A
29) B
30) B
31) D
32) B
33) C
34) D
35) A
36) A
37) B
38) A
8
Answer'Key'second'part'of'review'test'1:'
1)A'
2)D'
3)C'
4)C'
5)B'
6)C'
7)A'
8)A'
9)C'
10)D'
11)C'
12)B'
13)A'
14)D'
'